^{1,a)}and Yoshihiro Okuno

^{1}

### Abstract

We describe experiments and numerical simulations on high-density energy conversion using a compact closed-cycle magnetohydrodynamic electrical power generator, where shock-tube-based experiments and quasi-three-dimensional numerical simulations are fully coupled. The temporal plasma-fluid behavior, the one- and two-dimensional plasma-fluid structures, the enthalpy-entropy diagram, the Hall voltage-Hall current characteristics, and the quality of the energy conversion efficiency are investigated. The slightly divergent channel configuration, the application of high- and uniform-density magnetic flux to the entire generator, the high electrical conductivity, the symmetric plasma structure and stable plasma behavior, and the sufficient pressure gradient used to drive the fluid overcome the disadvantages of the generator due to its compactness, and markedly improve its energy conversion performance, namely, a power density of , an isentropic efficiency of 51%, and an enthalpy extraction ratio of 17.0%.

This work was partly supported by a Grant-in-Aid for Scientific Research (B) No. 19360127 from the Japan Society for the Promotion of Science (JSPS) from 2007 to 2009.

I. INTRODUCTION

II. EXPERIMENTAL SETUP

A. Shock-tube facility

B. Disk MHD generator

C. Diagnostics

D. Time trace of power generation experiment

III. NUMERICAL MODELING AND PROCEDURES

A. Basic equations

B. Numerical procedures

C. Calculating conditions and boundary conditions

IV. RESULTS AND DISCUSSION

A. Quality of MHD power-generating plasma

B. Power-generating performance

V. CONCLUSIONS

### Key Topics

- Magnetohydrodynamics
- 73.0
- Magnetic flux
- 46.0
- Plasma temperature
- 17.0
- Photon density
- 16.0
- Electrical conductivity
- 15.0

## Figures

Schematic of shock-tube facility.

Schematic of shock-tube facility.

Schematic illustration of the MHD generator.

Schematic illustration of the MHD generator.

Schematics of the MHD generator. Front view (upper) and cross-sectional view (lower).

Schematics of the MHD generator. Front view (upper) and cross-sectional view (lower).

Typical image of MHD power generation plasma.

Typical image of MHD power generation plasma.

Typical time variations of (a) total inflow temperature , (b) total pressure at the inlet and exit obtained with and without magnetic flux (indicated by and , respectively), (c) exit Mach number , (d) Hall current , and (e) electron temperature measured at the radius of .

Typical time variations of (a) total inflow temperature , (b) total pressure at the inlet and exit obtained with and without magnetic flux (indicated by and , respectively), (c) exit Mach number , (d) Hall current , and (e) electron temperature measured at the radius of .

Calculation region of quasi-three-dimensional numerical simulation.

Calculation region of quasi-three-dimensional numerical simulation.

Effect of the inlet boundary conditions on the power generation performance. (a) IE and EER as a function of electron temperature under the fixed gas temperature condition. (b) IE and EER as a function of under the fixed condition.

Effect of the inlet boundary conditions on the power generation performance. (a) IE and EER as a function of electron temperature under the fixed gas temperature condition. (b) IE and EER as a function of under the fixed condition.

(a) Cross-sectional view of the generator, the radial profiles of (b) static pressure , (c) Hall potential , (d) electron temperature and static temperature , (e) Mach number (M), (f) Hall parameter and modified electrical conductivity , (g) electrical efficiency and loading parameter , and (h) normalized fraction of the enthalpy extraction factor (power output PW) and the entropy production factors (Joule heating JH and wall friction loss WL). Experimental results are indicated by closed [(●) ] and open circles [(○) ]. Numerical results are indicated by solid [(–) ] and dashed curves [(---) ]. The total inflow pressure is . The seed fraction is . The loading condition is . The magnetic flux density is .

(a) Cross-sectional view of the generator, the radial profiles of (b) static pressure , (c) Hall potential , (d) electron temperature and static temperature , (e) Mach number (M), (f) Hall parameter and modified electrical conductivity , (g) electrical efficiency and loading parameter , and (h) normalized fraction of the enthalpy extraction factor (power output PW) and the entropy production factors (Joule heating JH and wall friction loss WL). Experimental results are indicated by closed [(●) ] and open circles [(○) ]. Numerical results are indicated by solid [(–) ] and dashed curves [(---) ]. The total inflow pressure is . The seed fraction is . The loading condition is . The magnetic flux density is .

Image of the discharge structure of the MHD power generation plasma and the two-dimensional distributions of the electron number density and the RD velocity under (a) weak MHD interaction and (b) strong MHD interaction. The seed fractions are (a) and (b) . The total inflow pressure is . The loading condition is . The magnetic flux density is .

Image of the discharge structure of the MHD power generation plasma and the two-dimensional distributions of the electron number density and the RD velocity under (a) weak MHD interaction and (b) strong MHD interaction. The seed fractions are (a) and (b) . The total inflow pressure is . The loading condition is . The magnetic flux density is .

Numerical result of enthalpy -entropy diagram calculated in the MHD channel for the cases of (a) weak MHD interaction and (b) strong MHD interaction. Calculating condition is the same as that in Fig. 9.

Numerical result of enthalpy -entropy diagram calculated in the MHD channel for the cases of (a) weak MHD interaction and (b) strong MHD interaction. Calculating condition is the same as that in Fig. 9.

(a)IE as a function of seed fraction (SF). (b) Hall voltage -Hall current characteristics. The experimental conditions are the load resistance of , the seed fraction of , and the magnetic flux density of . The numerical conditions are the load resistance of , the seed fraction of , and the magnetic flux density of .

(a)IE as a function of seed fraction (SF). (b) Hall voltage -Hall current characteristics. The experimental conditions are the load resistance of , the seed fraction of , and the magnetic flux density of . The numerical conditions are the load resistance of , the seed fraction of , and the magnetic flux density of .

Numerical prediction of the relationship between the plasma-fluid properties and the generator performance. IE as functions of (a) Hall parameter , (b) modified electrical conductivity , (c) Mach number , and (d) electrical efficiency . The calculating conditions are the total inflow pressure of , and the magnetic flux density of . For a fixed magnetic flux density, the loading condition is optimized to achieve the best performance by varying the seed fraction and load resistance.

Numerical prediction of the relationship between the plasma-fluid properties and the generator performance. IE as functions of (a) Hall parameter , (b) modified electrical conductivity , (c) Mach number , and (d) electrical efficiency . The calculating conditions are the total inflow pressure of , and the magnetic flux density of . For a fixed magnetic flux density, the loading condition is optimized to achieve the best performance by varying the seed fraction and load resistance.

Experimental and numerical results of IE and EER. The experimental and numerical results are indicated by closed circles and solid curves, respectively. Experimental conditions are the total inflow pressure of and the magnetic flux density of . Numerical conditions are the total inflow pressure of and the magnetic flux density of . For a fixed combination of the total inflow pressure and magnetic flux density, the loading condition is optimized to achieve the best performance by varying the seed fraction and load resistance.

Experimental and numerical results of IE and EER. The experimental and numerical results are indicated by closed circles and solid curves, respectively. Experimental conditions are the total inflow pressure of and the magnetic flux density of . Numerical conditions are the total inflow pressure of and the magnetic flux density of . For a fixed combination of the total inflow pressure and magnetic flux density, the loading condition is optimized to achieve the best performance by varying the seed fraction and load resistance.

Comparison of the power-generating performance between the present and previous experiments. (a) IE and EER as a function of , which we refer to as the modified magnetic flux density, defined as the square of the applied magnetic flux density at the MHD channel center divided by the total inflow pressure. (b) The ratio of IE to EER (IE/EER) as a function of the MHD channel divergence (cross-sectional-area ratio, AR). (c) The power output density (PD) as a function of . The present data and previous data for larger-scale RD and SW generators using Ar–Cs are shown.

Comparison of the power-generating performance between the present and previous experiments. (a) IE and EER as a function of , which we refer to as the modified magnetic flux density, defined as the square of the applied magnetic flux density at the MHD channel center divided by the total inflow pressure. (b) The ratio of IE to EER (IE/EER) as a function of the MHD channel divergence (cross-sectional-area ratio, AR). (c) The power output density (PD) as a function of . The present data and previous data for larger-scale RD and SW generators using Ar–Cs are shown.

## Tables

Geometry of generator and operating conditions.

Geometry of generator and operating conditions.

Conditions used in calculations.

Conditions used in calculations.

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