Study on numerical design method of frozen inert gas plasma MHD generators
Translated from Volume 140, Number 3, pages 229–237, DOI: 10.1541/ieejpes.140.229 ofIEEJ Transactions on Power and Energy (Denki Gakkai Ronbunshi B).
Abstract
A numerical design method to determine basic specifications of high‐performance frozen inert gas plasma (FIP) MHD generators is proposed. To validate the proposed method, time‐dependent, two‐dimensional (r‐z)MHD numerical analyses are performed for several FIP MHD generators with different thermal inputs (30, 100, 300, or 1000 MW) designed by the proposed method. The numerical results indicate that the designed FIP MHD generators with the thermal input of 100 MW or more are able to be operated with the performance approximately same as the designed one. For the designed MHD generator with the thermal input of 30 MW; however, the performance shown by the MHD numerical analysis is considerably lower than the designed one. For such a case, the performance can be improved by operating the MHD generator under an applied magnetic flux density larger and an inlet ionization degree lower than those designed values.
1 INTRODUCTION
Closed‐cycle MHD (CCMHD) systems using nonequilibrium MHD generators are expected to be implemented as next‐generation high‐temperature, high‐efficiency power generation systems with total thermal efficiency exceeding 60% (HHV).1 Inert gases seeded with alkali metals (seed material), featuring a low ionization potential at a concentration about 10−5 and temperature about 2200 K, are normally employed as working gases in nonequilibrium MHD generators. Working gas injected into MHD generator accelerates to a certain Mach number in the supersonic nozzle, and changes to nonequilibrium plasma state due to Joule heating produced by self‐induced EMF. In so doing, heavy particle temperature is as low as about 1000 K, but electron temperature is about 5000 K, and thus generated plasma with fully ionized seed features high electrical conductivity. In nonequilibrium MHD generators, this thermal nonequilibrium seeded plasma is used as a power generation medium; as a result, power generation with high output density can be realized without applying excessive thermal load to the channel wall surface. Such MHD generation using thermal nonequilibrium seed plasma is called below “seed plasma MHD generation.”
For practical use of CCMHD generation systems, nonequilibrium MHD generators must have enthalpy extraction ratio (= generated electrical output/thermal input) about 30% and isentropic efficiency above 80%. Research in nonequilibrium MHD generators has been advanced toward this target performance. In the recent years, researchers at Tokyo Institute of Technology achieved high‐efficiency generation at enthalpy extraction ratio of 31% and isentropic efficiency above 63% by using an experimental shock‐tube driven nonequilibrium disk MHD generator.2 This isentropic efficiency lacks about 20% to the target value. However, isentropic efficiency of MHD generator has a scale advantage against thermal input (generator size) and applied magnetic flux density; considering that the experimental generator was very small (thermal input: 4 MW, applied magnetic flux density: 3 T), this result is noteworthy and encouraging for further research on large‐scale generators.
In addition to improving performance of seed plasma MHD generation, there is also recent research on nonequilibrium MHD generation not using any seed materials (seed‐free MHD generation). This is because handling of seed materials, including recovery and recycling, is difficult. One of such seed‐free nonequilibrium MHD generation schemes is FIP (frozen inert gas plasma) MHD generation proposed by Kobayashi and Okuno.3 With FIP MHD generation, the working gas is a pure inert gas preionized using an external power supply. Then Joule heating produced by self‐induced EMF and slow recombination of inert gas plasma are utilized to maintain thermal nonequilibrium plasma with electrical conductivity comparable to that of seed plasma, thus realizing MHD generation. Kobayashi et al confirmed feasibility of FIP MHD generation via MHD numerical analysis.3 In addition, researchers at Tokyo Institute of Technology conducted recently verification experiments on FIP MHD generation using a small experimental MHD generator (thermal input of several ten kW) provided with RF preionization technique.4
Further topics in experimental research on FIP MHD generation include accumulation of knowledge about high‐temperature plasma control in small experimental FIP MHD generators as well as about generator shapes and operating conditions to improve power generation efficiency. In addition, when designing a roadmap of future research, specifications must be determined for pilot‐scale generators (thermal input: 100 MW class) and commercial‐scale generators (thermal input: 1000 MW class); for this purpose, design methods applicable to large FIP MHD generators must be established.
In seed plasma MHD generators, numerical design methods based on inversely solving MHD equations are used to derive basic specifications (channel shape and operating conditions) of generators to obtain required performance.5, 6 On the other hand, there are still no numerical design methods for FIP MHD generators. Though there is past research on numerical analysis of large FIP MHD generators,7 that analysis could not be extended to generator shape and operating conditions for high generation efficiency required in CCMHD power generation systems.
In this context, the present paper proposes a numerical design method to derive basic specifications for large FIP MHD generators; adequacy of the proposed method is discussed based on results of time‐dependent MHD analysis of the designed FIP MHD generators.
2 NUMERICAL DESIGN METHODS FOR SEED PLASMA MHD GENERATORS AND FIP MHD GENERATORS
Numerical design method proposed in this study for FIP MHD generators is based on a proven numerical design method for seed plasma MHD generators.5, 6 The numerical design method for seed plasma MHD generators is first described below, and then application of the design method to FIP MHD generators is explained. This study deals with a Hall type disk MHD generator shown in Figure 1.
2.1 Numerical design process for seed plasma MHD generators
The numerical design method for seed plasma MHD generators adopted in this study involves two stages. First, channel shape and operating conditions to obtain high‐efficiency power generation are determined by a numerical design method (quasi‐one‐dimensional MHD analysis) based on quasi‐one‐dimensional MHD equations proposed by Okuno et al.5 However, these quasi‐one‐dimensional MHD equations assume that MHD quantities are spatially distributed only in the radial direction (r direction in Figure 1). That is, the influence of boundary layer near the side wall cannot be taken into account when designing channel shape. Therefore, one can say that channel shape determined by quasi‐one‐dimensional design is suited to MHD quantities of core flow. Thus, a numerical design method (two‐dimensional numerical analysis) based on two‐dimensional (r‐z) MHD equations proposed by Inui et al6 is applied at the next stage of numerical design. In so doing, under operating conditions for high‐efficiency MHD generators derived through quasi‐one‐dimensional numerical design, channel height is corrected with regard to nonuniformity of MHD quantities in the height direction (z direction in Figure 1) due to the boundary layer, and the channel shape is finalized. Because of space limitations, only the quasi‐one‐dimensional design method underlying numerical design of seed plasma MHD generators is outlined below. Please refer to Ref. (6) for details of the two‐dimensional numerical design method.
2.2 Quasi‐one‐dimensional numerical design method for seed plasma generators
First, design conditions for total temperature and total pressure at hot duct inlet and for thermal input are specified based on assumed CCMHD generation system. After that, throat cross section of the supersonic nozzle is calculated on the assumption that MHD interaction is weak and flow is isentropic from the hot duct to the generation channel inlet in Figure 1. Then Mach number in the hot duct and ratio of throat radius to hot duct radius are specified as design conditions to determine hot duct radius and throat radius/height. In this study, Mach number in the hot duct and ratio of throat radius to hot duct radius are set to 0.5 and 1.5, respectively. Next, Mach number at the generation channel inlet is specified as a design condition, and cross section area at the channel inlet is calculated. Channel height from the throat to the generation channel inlet is varied in the radial direction at a certain inclination angle, and radius/height at the generation channel inlet is determined so as to match the channel's cross section area. In this study, inclination angle is set to 5° in design.
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(7)These calculations are performed along the radial direction from the generation channel inlet (downstreamward); a radial position where enthalpy extraction ratio reaches its required value is adopted as the output of generation channel, and the numerical calculations are terminated. If enthalpy extraction ratio did not reach its required value, then the numerical calculations are redone with modified design conditions. This process is repeated to determine operating conditions of seed plasma MHD generators with required performance, generation channel shape, radial distributions of MHD quantities, current density and Hall field inside the channel, load current (Hall current) and load voltage (Hall voltage).
Electron temperature at the inlet and inside the generation channel is usually set to 5000 K in design of seed plasma MHD generators. This design condition is set in order to obtain plasma with fully ionized seed9 in the generation channel for high‐efficiency power generation. Besides, average inclination angle of the generation channel is sometimes excessively large in numerical design. A large inclination angle may result in flow detachment phenomena that cannot be handled with quasi‐one‐dimensional numerical design. Channel inclination angle determined via numerical design heavily depends on seed fraction; the higher is seed fraction, the larger is inclination angle. Thus, in this study, seed fraction is adjusted so that average inclination angle of the generation channel is about 5°.
2.3 Numerical design method for FIP MHD generators
In case of seed plasma MHD generators, plasma ionization degree under high‐efficiency power generation approximately corresponds to seed fraction (plasma with fully ionized seed).9 On the other hand, in case of FIP MHD generators, plasma ionization degree at the generation channel inlet is supposed to be maintained almost constant throughout the channel as long as recombination rate develops very slowly against fluid velocity according to the principle of power generation. Therefore, one can expect comparable level of plasma ionization degree in the generation channel for both power generation schemes provided that inlet ionization degree in a FIP MHD generator is set equivalently to seed fraction in a seed plasma MHD generator. That is, if MHD generators of both types have same shape and operating conditions, while seed fraction in a seed plasma MHD generator and inlet ionization degree in a FIP MHD generator are mutually adjusted, then one can assume that distribution of MHD quantities in the generation channel is same in both cases, and therefore, generation performance is comparable as well. Rough adequacy of the above assumptions can be confirmed by comparison in performance between seed plasma MHD generator and FIP MHD generator based on r‐θ two‐dimensional MHD numerical analysis (with boundary layer effect ignored) by Kobayashi et al10 applied to a small disk MHD generator with thermal input about 10 MW.
The numerical design method proposed in this study for FIP MHD generators is inspired by the above assumptions. First, a seed plasma MHD generator is numerically designed as explained above to meet required performance. Then generation channel shape and operating conditions of thus designed seed plasma MHD generator are adopted in a FIP MHD generator. Particularly, inlet ionization degree of the FIP MHD generator is set equal to seed fraction determined in design of the seed plasma MHD generator. Other inlet conditions for hydrodynamic values and electron temperature are set same as in the designed seed plasma MHD generator. It should be noted that in so doing, ionization equilibrium is not established at the inlet of generation channel in FIP MHD generator.
3 RESULTS OF NUMERICAL DESIGN AND PERFORMANCE EVALUATION BY TIME‐DEPENDENT TWO‐DIMENSIONAL MHD ANALYSIS
In order to validate the numerical design method for FIP MHD generators proposed in the previous section, here we design FIP and seed plasma MHD generators, and compare their performance via time‐dependent two‐dimensional (r‐z) MHD analysis. Such analysis makes it possible to examine recombination process in plasma, ionization instability, and other items that cannot be confirmed on the stage of numerical design; in addition, one can check whether a designed FIP MHD generator steadily works with expected generation performance, or whether generation performance corresponds to that of a seed plasma MHD generator (as assumed in the proposed design method).
3.1 Object, conditions, and results of design
The main design object of this study is a large FIP MHD generator with thermal input of 1000 MV (assuming a commercial‐scale CCMHD generation system). However, generators with thermal input of 30, 100, and 300 MW are also designed to check whether adequacy of the proposed numerical design method for FIP MHD generators depends on thermal input (generator size). Design performance is set to enthalpy extraction ratio of 30% (±0.05%), isentropic efficiency of 80% (±0.5%), regardless of thermal input. Other design conditions—total temperature, total pressure, and Mach number at the inlet—are also set same for any thermal input. Based on these design conditions, hydrodynamic quantities at the inlet of generation channel are determined from isentropic flow relation; therefore, inlet static temperature, static pressure, and radial velocity are also same at any thermal input. In this study, MHD interaction is assumed weak from the hot duct to the generation channel inlet, while generators to be designed are not provided with inlet swirl vanes; therefore, circumferential velocity at the channel inlet is set to 0. Electron temperature inside the generator is designed at 5000 K. This value is set so as to obtain plasma with fully ionized seed in the seed plasma MHD generators. Thus high‐efficiency seed plasma MHD generators can be designed; besides, FIP MHD generators are designed with same thermal input and power generation efficiency, as explained above.
Basic specifications of seed plasma generators and FIP MHD generators obtained by numerical design are listed in Table 1. In addition, shapes of the generation channel (see Figure 1) in the numerically designed generators are shown in Figure 2. It should be noted that the channel shapes in Figure 2 were first obtained via quasi‐one‐dimensional numerical design and then corrected via two‐dimensional numerical design. It should also be noted that in Table 1 and Figure 2, operating conditions and channel shapes are same for both generator types, except that seed fraction of the seed plasma MHD generators is treated as inlet ionization degree in the FIP MHD generators. Now, inlet ionization degree in the seed plasma MHD generators is determined assuming Saha equilibrium at inlet electron temperature of 5000 K; in so doing, inlet ionization degree becomes equivalent to seed fraction because the seed is fully ionized. That is, electron temperature and ionization degree at the generation channel inlet are same in the FIP and seed plasma MHD generators. As can be seen from Table 1, under common conditions (applied flux density, inlet MHD quantities, electron temperature, and required enthalpy extraction ratio), size, load current, and load voltage of designed generators increase with higher thermal input, while seed fraction (inlet ionization degree) decreases. These thermal input dependences qualitatively agree with the scaling law for seed plasma MHD generators shown by Inui et al.11
| Thermal input (MW) | 30 | 100 | 300 | 1000 |
|---|---|---|---|---|
| Working gas | He / Cs (Seed), He (FIP) | |||
| Enthalpy extraction ratio (%) | 30(±0.05) | |||
| Isentropic efficiency (%) | 80(±0.5) | |||
| Stagnation pressure (atm) | 3.5 | |||
| Stagnation temperature (K) | 2200 | |||
| Inlet Mach number (–) | 1.8 | |||
| Magnetic flux density (T) | 10 | |||
| Seed fraction (–) (inlet ionization degree) | 5.16 × 10−5 | 2.80 × 10−5 | 1.61 × 10−5 | 8.81 × 10−6 |
| Mach number in hot duct (–) | 0.5 | |||
| Electron temperature (K) | 5000 | |||
| Ratio of throat radius to hot duct radius (–) | 1.5 | |||
| Hot duct radius (mm) | 67.7 | 124 | 214 | 391 |
| Throat radius (mm) | 102 | 185 | 321 | 586 |
| Throat height (mm) | 34.1 | 62.4 | 108 | 197 |
| Inlet radius (mm) | 123 | 225 | 390 | 713 |
| Inlet channel height (mm) | 38.0 | 69.4 | 120 | 219 |
| Outlet radius (mm) | 213 | 386 | 664 | 1205 |
| Outlet channel height (mm) | 54.6 | 98.9 | 170 | 309 |
| Load voltage (kV) | 3.01 | 5.55 | 9.62 | 17.6 |
| Load current (kA) | 2.99 | 5.41 | 9.36 | 17.1 |
3.2 Outline of basic equations and calculation method used in time‐dependent two‐dimensional MHD analysis
A time‐dependent two‐dimensional (r‐z) MHD analysis program for seed plasma MHD generators12 developed and proven by our research group was used to evaluate performance of numerically designed MHD generators. In this program, time‐dependent conservation equations (mass, momentum, total energy) involving MHD interaction terms are employed as the governing equations for flow field of heavy‐particle system; influence of turbulence is taken into account by using Baldwin‐Lomax model.13 The governing equations for electron system are time‐dependent continuity equations for monovalent ions (inert gas, seed) with regard for electron‐impact ionization and three‐body recombination reactions and quasi‐stationary thermal energy equation for free electrons. The governing equations for electromagnetic field are Maxwell's equations with low‐Reynolds number MHD approximation and generalized Ohm's equations. These governing equations are discretized with two‐dimensional (r‐z) approximation, and then solved using appropriate numerical methods. Please refer to Ref. (12) for details of the governing equations and numerical methods. However, only seed plasma MHD generators are analyzed in Ref. (12). In the present paper, expressions and terms related to seed material were excluded from the governing equations when dealing with FIP MHD generators.
Analysis region was defined as the generation channel shown in Figure 2. Computational grid was set as a structured grid. The grid points were equally spaced in the radial direction; in the direction of channel height, the grid points were distributed so that grid density was higher in the boundary layer. Grid interval was varied with thermal input so that generators with higher input had greater grid interval. In case of the generator with thermal input of 1000 MW (main object of this study), grid interval was 4.0 mm in radial direction and about 2.7 mm in height direction, being reduced to about 17 μm near the side wall; the number of grid points was 124 in radial direction and 161 in height direction. In case of the generator with thermal input of 30 MW (the smallest one considered in this study), grid interval was 0.7 mm in radial direction and about 0.5 mm in height direction, being reduced to about 2.9 μm near the side wall; the number of grid points was 131 in radial direction and 161 in height direction.
3.3 Results of performance evaluation
Performance data (enthalpy extraction ratio and isentropic efficiency) estimated by time‐dependent two‐dimensional MHD analysis of the designed MHD generators are summarized in Table 2. Designed performance values are also shown in the table. It should be noted that designed performance is same for both seed plasma MHD generators and FIP MHD generators. Below, we first discuss power generation performance and MHD quantities of the main object of this study, namely, FIP MHD generator and seed plasma MHD generator with thermal input of 1000 MW.
| Enthalpy extraction ratio (%) | Isentropic efficiency (%) | |||||
|---|---|---|---|---|---|---|
| Thermal input (MW) | Des. | Seed | FIP | Des. | Seed | FIP |
| 1000 | 30.02 | 29.97 | 29.91 | 80.40 | 80.75 | 80.87 |
| 300 | 30.05 | 29.96 | 29.83 | 80.10 | 80.53 | 80.72 |
| 100 | 30.00 | 29.99 | 29.71 | 80.01 | 80.15 | 80.37 |
| 30 | 30.04 | 29.96 | 24.44 ± 1.06 | 79.51 | 79.42 | 63.92 ± 5.57 |
As indicated by Table 2, enthalpy extraction ratio and isentropic efficiency estimated by time‐dependent two‐dimensional MHD analysis for the FIP MHD generator with thermal input of 1000 MV almost coincide with respective design values (29.91% vs 20.02% and 80.87% vs 80.40%). In addition, analysis results confirm steady performance. Comparing generation performance estimated by time‐dependent two‐dimensional MHD analysis of the FIP and seed plasma MHD generators with thermal input of 1000 MW, the difference is 0.06% in terms of enthalpy extraction ratio and 0.12% in terms of isentropic efficiency; that is, both generators have almost same performance.
Figure 4 shows analyzed two‐dimensional distributions of radial fluid velocity, electron temperature, and electrical conductivity in the generation channels of FIP and seed plasma MHD generators with thermal input of 1000 MW. In addition, respective distributions obtained in numerical design are also shown in the diagrams. It should be noted that the distributions of MHD quantities in numerical design are almost same for the generators of both types, just as with power generation performance. As can be seen from Figure 3, there are no substantial difference in the distributions of radial fluid velocity, electron temperature, and electrical conductivity estimated by time‐dependent two‐dimensional MHD analysis; besides, the distributions are close to designed ones. Besides, the analysis results confirmed the same for other MHD quantities.
Figure 4 shows radial distributions of ionization degree estimated by time‐dependent two‐dimensional MHD analysis at the middle of generation channels (z = 0 m) in FIP and seed plasma MHD generators with thermal input of 1000 MW. Here ionization degree is defined as the ratio of total ion number density to total heavy particle number density. As can be seen from Figure 4, in the seed plasma MHD generator, ionization degree corresponding to seed fraction (8.81 × 10−6) is obtained in the entire generation channel; that is, plasma with fully ionized seed suitable for high‐efficiency power generation is realized. On the other hand, in the FIP MHD generator, ionization degree decreases downstreamward, even though very slowly. This is because inert gas ion recombination proceeds with flow. However, decrease rate of ionization degree is very low at about 0.4% even at the generation channel outlet (on inlet basis), and ionization degree in the generation channel is maintained almost the same as seed fraction n the seed plasma MHD generator. Thus, the difference in plasma's electrical conductivity in core flow between FIP and seed plasma MHD generators is just about 0.07 S/m at the most, while other MHD quantities and performance parameters are nearly same as well.
As explained above, time‐dependent two‐dimensional MHD analysis was applied to the FIP MHD generator with thermal input of 1000 MW designed by the method of numerical design proposed in this study, and the generator's operation was almost as designed. Below, we discuss adequacy of the proposed numerical design in terms of thermal input.
As can be seen from Table 2, time‐dependent two‐dimensional MHD analysis of the FIP MHD generators with thermal input of 100 MW and 300 MW showed that operation was almost as designed, same as in the FIP MHD generator with thermal input of 1000 MW. On the other hand, in case of the FIP MHD generator with thermal input of 30 MW, generation performance estimated by time‐dependent two‐dimensional MHD analysis was substantially lower than designed; in addition, performance showed periodical fluctuation. Time‐averaged enthalpy extraction ratio and isentropic efficiency were lower by 5.60% and 15.59%, respectively, than their design values. In so doing, distributions of MHD quantities in the generation channel estimated by time‐dependent two‐dimensional MHD analysis were substantially different from designed distributions, while fluctuating periodically (diagrams are omitted here). In case of the seed plasma MHD generators, generation performance parameters and distributions of MHD quantities were almost at designed at any thermal input.
Figure 5 presents analyzed two‐dimensional distribution of ionization degree in the FIP MHD generator with thermal input of 30 MW. It should be noted that this distribution pertains to some moment during periodical fluctuations. As indicated by Figure 5, ionization degree greatly decreases in middle and downstream areas of the generation channel. Time‐average decrease rate of outlet ionization degree with respect to that at the channel inlet was 16.7% (fluctuating in the range of 1.8%‐51.5%), which is substantially higher than in the FIP MHD generator with thermal input of 1000 MW. That is, the assumption made in the proposed numerical design method about maintaining inlet ionization degree does not hold true for the FIP MHD generator with thermal input of 30 MW. As a result, the generator's performance is not achieved as designed, and operation is not stable.
Let us again consider enthalpy extraction ratios of FIP and seed plasma MHD generators with thermal input of 100‐1000 MW in Table 2. In case of the FIP MHD generators, enthalpy extraction ratios estimated by time‐dependent two‐dimensional MHD analysis tend to monotonely decrease, even very slightly, with lower input ratio (the difference in enthalpy extraction ratio between 1000‐MW and 100‐MW FIP MHD generators is 0.20%). In contrast, such trends are not observed in numerical design and in results of time‐dependent two‐dimensional MHD analysis for the seed plasma MHD generators.
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(9)| Thermal input (MW) | 30 | 100 | 300 | 1000 |
| Rate of decrease in ionization degree (%) | 16.7 | 2.27 | 0.95 | 0.43 |
| Residence time (10−5 s) | 3.90 | 5.54 | 9.42 | 16.9 |
With thermal input from 100 to 1000 MW when FIP MHD generators work steadily, electron temperature of plasma in the generation channel was almost as designed at 4200‐5300 K. In this range of electron temperature, three‐body recombination reaction, rather than electron‐impact ionization reaction, dominates the process of plasma generation and extinction. In so doing, maintaining inlet ionization degree throughout the channel outlet becomes more difficult with higher speed of three‐body recombination and with longer residence time of plasma in the generation channel. Generator's channel length decreases with lower thermal input, and plasma residence time becomes shorter as shown in Table 3. Therefore, the higher decrease rate of ionization degree at the channel output with lower thermal input is due to increase in three‐body recombination speed. When considering only monovalent ionization and assuming electroneutrality, speed of plasma three‐body recombination is proportional to cubed ion number density. As shown in Table 1, the lower is thermal input, the higher is designed ionization degree (ion number density) at the inlet. For this reason, three‐body recombination speed grows nonlinearly with lower thermal input, and maintaining inlet ionization degree in the channel becomes more difficult.
Thus, time‐dependent two‐dimensional MHD analysis confirmed that numerically designed FIP MHD generators with thermal input of 100 MW or higher work steadily, almost as designed. On the other hand, accuracy of the numerical design method proposed in this study declined with lower thermal input. This decline in accuracy is due to increase in three‐body recombination speed with higher ionization degree at the inlet; in so doing, the time during which inlet ionization degree can be maintained becomes shorter than the time during which plasma resides in the generation channel. As a result, in case of the FIP MHD generator with thermal input of 30 MW (the lowest input considered in this study), performance estimated by time‐dependent two‐dimensional MHD analysis was considerably lower than designed, and moreover, fluctuated over time so that the generator did not work as designed. Below we briefly report on measures to improve power generation performance of FIP MHD generators designed by the proposed method when performance drops substantially below design values because inlet ionization degree cannot be maintained throughout the generation channel, as is the case with thermal input of 30 MW.
From the standpoint of maintaining inlet ionization degree inside the generation channel of FIP MHD generators, one should set the inlet ionization degree as low as possible, and suppress three‐body recombination. However, when a generator is operated at lower ionization degree than designed, electrical conductivity in the generation channel decreases, and one can expect that output (enthalpy extraction ratio) declines as well. In such cases, increase of applied magnetic flux density against its design value to compensate for decline in output density caused by decrease in electrical conductivity can be efficient to improve generation performance.
Figure 6 presents analysis of time‐dependent two‐dimensional MHD analysis obtained for distribution of ionization degree in the generation channel of FIP MHD generator designed with thermal input of 30 MW (Table 1, Figure 2) in case that inlet ionization degree is reduced from its design value of 5.16 × 10−5 to 3.00 × 10−5, while applied flux density is increased from its design value of 10‐12 T. It should be noted that in this analysis, load voltage is set not to its design value, but to voltage (5.30 kV) required for load matching with respect to modified magnetic flux density and inlet ionization degree. As can be seen from Figure 6, by contrast with operation at design conditions (Figure 5), ionization degree is maintained almost constant along the entire generation channel. Decrease of ionization degree at the outlet against the inlet is 0.03%. In so doing, enthalpy extraction ratio is 30.22% and isentropic efficiency is 79.94%; that is, the generator works steadily with performance corresponding to the design parameters in Table 2. In addition, inlet ionization degree was also maintained along the channel, same as in Figure 6, when applied flux density was as designed (10 T), and only inlet ionization degree was changed from 5.16 × 10−5 to 3.00 × 10−5. In so doing, enthalpy extraction ratio was 28.23% and isentropic efficiency was 73.27%; that is, performance was substantially improved as compared to operation under the conditions adopted in numerical design (Table 2).
Thus, in case that generation performance of a FIP MHD generator designed by the method proposed in this study drops substantially below design values because designed ionization degree cannot be maintained throughout the generation channel, performance can be improved by operating the generator at higher magnetic flux density and lower inlet ionization degree.
4 CONCLUSION
This paper proposed a method of numerical design for FIP MHD generators, particularly, for commercial‐scale (thermal input: 1000 MW) generators.
In order to validate the proposed method, four FIP MHD generators with different thermal input (30, 100, 300, 1000 MW) were designed and evaluated using time‐dependent two‐dimensional (r‐z) MHD analysis. The analysis results showed that FIP MHD generator with thermal input of 1000 MW (main object of this study) works almost as designed. The same was confirmed for FIP MHD generators with thermal input of 100 and 300 MW. Thus the method of numerical design proposed in this study was proven applicable to large (pilot or commercial scale) FIP MHD generators.
On the other hand, it was found that accuracy (adequacy) of the proposed numerical design for FIP MHD generators declines with lower thermal input (generator size). This is because with lower thermal input, the inlet ionization degree determined by numerical design increases so that three‐body recombination of plasma in the generation channel accelerates, and the assumption made in the proposed numerical design method about maintaining inlet ionization degree throughout the generation channel holds less true. Thus, in case of FIP MHD generator designed with thermal input of 30 MW, there was a significant difference in generation performance between numerical design and time‐dependent two‐dimensional (r‐z) MHD analysis. As regards such cases when designed ionization degree cannot be maintained in the generation channel of a small FIP MHD generator so that generation performance drops substantially lower than designed, it was confirmed via time‐dependent two‐dimensional (r‐z) MHD analysis that operating the generator at higher magnetic flux density and lower inlet ionization degree is useful to improve the performance.
ACKNOWLEDGMENT
In closing, we add that this study was supported by JSPS Grant‐in‐Aid for Scientific Research (15H02346, 17K07026).
Biographies
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Soshi Ito, student member. In 2018 graduated from University of Tsukuba (College of Eng. Systems) and started postgraduate studies at the University (Grad. School of Systems and Information Eng., Mech. and Energy). Now 1st term of doctorate, research in frozen inert gas plasma MHD generators.
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Takayasu Fujino, member. In 2002 completed doctorate at Tokyo Institute of Technology (Interdiscipl. Grad. School of Sci. and Eng., then JSPS PD Research Fellow, 2004 lecturer at University of Tsukuba (Grad. School of Systems and Information Eng.), 2010 adjunct professor, since 2011 adjunct professor at Fac. of Information, Engineering and Systems. D. Eng. Research in magnetohydrodynamics, plasma engineering.
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Toru Takahashi, member. In 2013 completed doctorate at University of Tsukuba (Grad. School of Systems and Information Eng., Mech. and Energy), then researcher at National Institute of Advanced Industrial Science and Technology, 2014 researcher at a private company, since 2016 assistant at University of Tsukuba (Fac. of Information, Engineering and Systems). D. Eng. Research in electromagnetic compatibility, rotary machines.
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Yasuhiro Okuno, member. In 1982 graduated from Kyushu Institute of Technology (Electrical Eng.), 1987 completed doctorate at Tokyo Institute of Technology (Energy Eng.), and was employed as assistant by Nagasaki University, 1988 lecturer at Saga University, 1989 assistant professor, 1994 assistant professor at Tokyo Institute of Technology (school of Eng.), since 2000 professor. D.Eng. Research in magnetohydrodynamics, plasma engineering.
