Steven J. Schneider

Glenn Research Center, Cleveland, Ohio

Annular MHD Physics for Turbojet Energy Bypass

NASA/TM—2011-217210

September 2011

AIAA–2011–2230
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Steven J. Schneider

Glenn Research Center, Cleveland, Ohio

Annular MHD Physics for Turbojet Energy Bypass

NASA/TM—2011-217210

September 2011

AIAA–2011–2230

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

17th International Space Planes and Hypersonic Systems and Technologies Conference

sponsored by the American Institute of Aeronautics and Astronautics

San Francisco, California April 11–14, 2011
Acknowledgments

The author wishes to acknowledge many fruitful discussions with Dr. Isaiah Blankson during this analysis.

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subject to revision as analysis proceeds.
NASA/TM—2011-217210 1 

Annular MHD Physics for Turbojet Energy Bypass 

Steven J. Schneider 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated 

assuming weakly ionized flows obtained from pulsed nanosecond discharges. The equations for a 1-D, 

axisymmetric MHD generator/accelerator are derived and numerically integrated to determine the 

generator/accelerator performance characteristics. The concept offers a shockless means of interacting 

with high speed inlet flows and potentially offers variable inlet geometry performance without the 

complexity of moving parts simply by varying the generator loading parameter. The cycle analysis 

conducted iteratively with a spike inlet and turbojet flying at M = 7 at 30 km altitude is estimated to have 

a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at 

an aggressive 2200 K. The annular MHD Hall generator/accelerator is L = 3 m in length with a 

Br = 5 Tesla magnetic field and a conductivity of = 5 mho/m for the generator and = 1.0 mho/m for 

the accelerator. The calculated isentropic efficiency for the generator is sg = 84 percent at an enthalpy 

extraction ratio, Ng = 0.63. The calculated isentropic efficiency for the accelerator is sa = 81 percent at 

an enthalpy addition ratio, Na = 0.62. An assessment of the ionization fraction necessary to achieve a 

conductivity of = 1.0 mho/m is ne/n = 1.90×10–6, and for = 5.0 mho/m is ne/n = 9.52×10–6. 

Nomenclature 

A flow area normal to z axis 

B vector magnetic field 

B tangential magnetic field 

Br radial magnetic field 

Bz axial magnetic field 

ce mean random thermal velocity of the electrons 

Cp specific heat at constant pressure of air 

E vector of applied electric field 

e magnitude of electron charge 

E tangential applied electric field 

Er radial applied electric field 

Ez axial applied electric field 

h enthalpy per unit mass of gas 

I current 

j vector current density 

j tangential current density 

jr radial current density 

jz axial current density 

k Boltzmann’s constant 

Kh MHD generator-accelerator Hall loading parameter 

m mass flow 

me mass of an electron 

MHD Magnetohydrodynamics 

n number density of atoms or molecules in the flow 
NASA/TM—2011-217210 2 

ne electron number density in the flow 

Pe Electrical power 

Po total pressure of flow 

Ps static pressure of flow 

Q electron-molecule momentum transfer cross section 

R gas constant of air 

r radial coordinate of flow 

S entropy 

Te electron temperature 

To total temperature of flow 

U internal energy of gas 

V Hall voltage across generator or accelerator, integral of Ezdz 

v vector velocity of flow 

v tangential velocity of flow 

vr radial velocity of flow 

vz axial velocity of flow 

 Hall parameter 

z axial coordinate, axis of symmetry of flow 

 fraction of discharge energy going into Joule heating of the flow 

Na enthalpy addition ratio of accelerator 

Ng enthalpy extraction ratio of generator 

sa isentropic efficiency of accelerator 

sg isentropic efficiency of generator 

 tangential coordinate of flow 

 density of gas 

 electrical conductivity 

Introduction 

The Russian AJAX hypersonic vehicle was the first to propose magnetohydrodynamic (MHD) energy 

bypass of a scramjet as a means of extending the scramjet’s performance to higher mach numbers 

(Ref. 1). Analyses of the concept lead to the conclusion that energy bypass of a scramjet can result in 

subsonic ramjet propulsion being maintained in the Mach No. 10 to 16 speed range (Ref. 2). A simplified 

thermodynamic cycle analysis of scramjet energy bypass demonstrated that the concept merits further 

investigation (Ref. 3). Based on these results, an examination of the feasibility of MHD energy bypass 

with turbojets was proposed (Ref. 4). As with the scramjet, the enthalpy into the combustor is to be 

reduced allowing more efficient addition of energy in the combustor without exceeding temperature 

limitations on the turbine materials. Preliminary 1-D analysis of the energy extraction process shows that 

significant enthalpy extraction is possible, but this extraction also results in significant total pressure 

losses (Ref. 5). The annular MHD Hall generator concept was proposed for geometric compatibility with 

the turbojet (Ref. 6). This geometry was successfully applied to in-space propulsion engine by the 

Russians with their Stationary Plasma Thruster using very low pressure xenon plasmas and is flying on 

the Russian Express satellite (Ref. 7). The geometry was also previously explored for stationary 

combustion driven MHD power generation in the 1950s (Ref. 8). A concept vehicle showing power 

generation and distribution is shown in Figure 1. These efforts are motivated by a need to develop a single 

flow path solution to a Mach 7 air breathing engine without the need for mode transitions. 

Besides NASA’s traditional use of plasmas in space thrusters (Refs. 9 and 10), there is a growing 

interest in plasma-based aerodynamics, including flow manipulation through MHD forces, power 

generation, drag reduction, and shock mitigation (Refs. 11 to 14). The goal of this paper is to examine the 
NASA/TM—2011-217210 3 

physics necessary to conduct a 1-D, axisymmetric analysis of an annular MHD generator/accelerator for 

extracting energy electrically by MHD forces from the flow upstream of a turbojet such that the turbojet 

can operate within its thermal limits up to a higher Mach number. This electrical energy can be used for 

vehicle drag reduction or can be reintroduced by MHD acceleration in the nozzle to provide positive 

thrust to the vehicle at the higher Mach number. An important goal is to determine whether 

nonequilibrium ionization efficiently generated in a supersonic flow using pulsed nanosecond discharges 

(Ref. 15) can be used to produce a Lorentz force of a magnitude sufficient to generate substantial amounts 

of electrical power, and to considerably reduce the kinetic energy of the flow. Nonequilibrium ionization 

is believed to be a key factor in this analysis, since the customarily introduced alkali metals are corrosive 

to super alloys. 

The term “plasma” is used to describe a fourth state of matter along with solids, liquids, and gases. 

One usually thinks of them as a high temperature “fully ionized” medium, but the definition of “plasmas” 

is extended to the “partially ionized” gases of interest in this analysis. The most important difference 

between “ionized” and “ordinary” gases is that they can be acted upon by electromagnetic forces. The 

chosen method of analytical treatment called “plasma dynamics” is to define the macroscopic properties 

of the plasma using the theory of the “continuum”. We postulate the macroscopic properties by 

considering the conservation laws of mass, momentum, energy, and charge. In general, however, the 

plasma should be considered as a mixture of ions, electrons, and neutral particles that is neutral overall 

and the “kinetic theory of plasmas” should be applied. The ions and electrons continually experience 

MHD forces which accelerate their motion. All of the particles suffer collisions and the forces acting on 

the ions and electrons are transmitted to the neutrals by collisions thus becoming forces acting on the gas 

as a whole. It is left to future work to investigate the relationship between these two approaches. 

Generalized 3-D MHD Equations 

The fundamental equations of “plasma dynamics” have been greatly simplified by the MHD 

approximation (Ref. 16) which uses the assumptions given below. The assumptions that went into these 

simplified equations (Ref. 17) have been tested experimentally and found to be valid in the Department of 

Energy’s MHD power generation program (Ref. 18) of the 1970s and 1980s. These assumptions are: 

1. The plasma is a single continuous medium of definite composition 

2. Electromagnetic forces are of the same order as gas dynamic forces 

3. The time scale of the problem is the characteristic length divided by a characteristic velocity. 

4. The applied electric field E is of the same order as the induced electromotive force. 

5. The flow velocity is much smaller than the speed of light. 
NASA/TM—2011-217210 4 

6. Maxwell’s equations are unaffected by the gasdynamic motion or, in other words, the magnetic 

field induced by the fluid motion is small compared to the applied magnetic field 

7. Invicid flow is assumed, but a friction term can be easily added to the momentum equation. 

8. No heat loss is assumed, but a heat loss term can be easily added to the energy equation. 

9. The equation of state of the gas is assumed to be the perfect gas law, but other equations of state 

can be implemented. 

10. Body forces due to gravity are neglected 

11. Steady state is assumed 

These simplified 3-D equations (Ref. 17) are as follows: 

Momentum: 

ρሺv∙׏ሻv ൌ j ൈ B ‐ ׏p (1) 

Mass: 

׏ ∙ ሺρܞሻ ൌ 0 (2)

Energy: 

ρv∙׏ ቀ

|୴|

మ

ଶ

൅ Uቁ ൌ െસ ∙ ሺܞpሻ ൅ j ∙ E (3)

Current: 

સ  ∙  j ൌ 0 (4) 

Ohm’s Law: 

j ൌ σሺE ൅ v ൈ Bሻ െ னத

|୆|

j ൈ B (5) 

Axisymmetric 1-D MHD Equations 

The above simplified 3-D equations are reduced to a 1-D axisymmetric form for the annular geometry 

and coordinate system shown in Figure 2 and using the following assumptions. This is similar to a mean 

line flow calculation in a turbomachine. 

1. Azimuthal symmetry 

2. Large radius approximation, with functions of z only: p(z), v(z), vz(z), j(z), jz(z), T(z), (z), 

Ez(z) 

3. Constant terms: Br,  

4. Zero terms: B, Bz, vr, jr, E, Er

 
NASA/TM—2011-217210 5 

Axial Momentum: 

ρvz

dvz

dz  ൌ ‐jBr‐

dp

dz (6) 

Angular Momentum: 

ρvz

dv

dz ൌ jzBr (7) 

Axial Ohm’s Law: 

j

z ൌ σBr

1+(ωτ)

2 ቂ

Ez

Br

െ v஘ ൅ னத୆౨

|୆| vzቃ (8) 

Angular Ohm’s Law: 

j

 ൌ σBr

1+(ωτ)

2 ቂvz െ ω߬

Ez

|୆|

൅ னத୆౨

|୆| v஘ቃ (9) 

Energy: 

ρvz

d

dz ቀ

v

మାvz

2

2 ൅ hቁ ൌ jzEz (10) 

Continuity: 

ρvzA ൌ mሶ (11) 

Conservation of Current: 

jzA ൌ I (12) 

Electrical power: 

Pୣ ൌ IV (13) 

Ideal gas equation of state: 

ρ ൌ

୔౩

ୖ୘౩

 (14) 

Calorically perfect gas: 

C୮T୭ ൌ C୮Tୱ ൅ ୴౰

మ

ଶ

൅ ୴ಐ

మ

ଶ (15) 

Entropy of perfect gas: 

dSൌCp

d୘౥

୘౥

െ R d୔౥

୔౥

 (16) 

1-D Annular MHD Calculation Procedure 

The above axisymmetric 1-D equations describe a pure Hall type device, since the applied tangential 

electrical field E is zero by short circuit around the annulus. In order to numerically evaluate these 

equations, the Hall parameter  is related to macroscopic properties of the plasma. The following 

definition is used 

ωτ ൌ ୣ|୆|

୫౛୬୕ୡ౛

 (17) 

Here we use a two temperature model of the plasma where the electron temperature Te is much higher 

than the bulk gas static temperature Ts. Such nonequilibrium plasmas can be generated experimentally in 

high speed flows using high voltage pulsed nanosecond discharges (Ref. 19). Numerical modeling of such 

discharges places the electron temperature at Te = 1ev, i.e., Te = 11605 K (Ref. 20). The mean random 

thermal velocity of the electrons, ce is calculated to be ce = 6.692107

 cm/sec from 

cୣ ൌ ට଼୩୘౛

஠୫౛

 (18) 

The electron—molecule momentum transfer cross section for air is estimated (Ref. 17) to be 

Q = 810–16 cm2

. The number density n for air at the local static pressure Ps and local static temperature 
NASA/TM—2011-217210 6 

Ts is found from the Loschmidt Number of 2.691019 molecules/cm3 at standard temperature and 

pressure. 

The externally applied electric field Ez is defined using the Hall loading parameter Kh as follows: 

K୦ ൌ ∝୉౰

னத୴౰୆౨

 (19) 

where  is the fraction of discharge energy going into Joule heating of the gas. This number has been 

shown to be as low as 0.02 in electrical discharges in nitrogen (Ref. 21). The rest of the discharge energy 

fraction, as high as 0.98, goes into vibrational excitation of the gas and is trapped inside the vibrational 

states of the molecules. As such, it does not contribute to the bulk gas translational temperature which 

also determines entropy rise. The relevant  depends strongly on the gas composition and is especially 

sensitive to the presence of water molecules. Experimental measurements (Ref. 19) indicate that 

= 0.1 in dry air and rises to = 0.4 in moist air. The  in combustion products can be expected to be 

even higher. Energy deposited in vibrational states of molecules is known to have relaxation times on the 

order of milliseconds (Ref. 22), which may be enough time to transit the MHD generator and accelerator 

and affect their performance, but probably not enough time to transit the entire cycle. This effect of  has 

not been considered in the calculations presented in this paper, i.e., the assumed = 1.0. 

One of the goals of this analysis is to determine the magnitudes of the electrical conductivity, 

magnetic field, and length of flow path that are required for the enthalpy extraction and addition 

operations. These parameters are therefore inputs to the calculation. In order to solve the above set of 

equations, ((6) to (19)), one more parameter such as the flow area must be specified. It was found to 

facilitate the numerical analysis to specify 

ୢሺ஡୴౰ሻ

ୢ୸ ൌ constant (20) 

instead of specifying the flow geometry. An annular Hall generator/accelerator concept is shown in Figure 3 

where the ionized flow in the annulus interacts with a vector current j composed of components jz and j

which forms a spiral in the annulus. Electrodes providing the pulsed nanosecond discharges for ionization 

are shown placed at several axial positions to maintain the conductivity and the current jz is withdrawn 

through the inlet and exit electrodes and flows through the external power extraction/addition circuit. 
NASA/TM—2011-217210 7 

MHD Energy Bypass Turbojet Cycle Analysis 

A preliminary cycle analysis was conducted in order to derive gas dynamic inlet parameters for the 

MHD generator and accelerator. It was conducted iteratively with the spike inlet and turbojet until a flow 

path area variation similar to that shown in Figure 4 was attained. A T-s (temperature-entropy) diagram 

for the cycle flying at M = 7 at 30 km altitude is shown in Figure 5. This cycle is estimated to have a 

positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at 

an aggressive 2200 K. Note that the inlet total temperature of 2453 K exceeds this allowable combustor 

temperature. The MHD generator reduces this total temperature to 930 K by extracting 1.6 MW-s/kg 

from the flow. The turbojet at this altitude is estimated to have only a compression ratio of only 1.09, so 

only 31 kW-s/kg is transferred from the turbine to the compressor. Heat addition in the combustor raises 

the total temperature to 2200 K and the 1.4 MW-s/kg (generator minus ionizer power) energy bypass to 

the MHD accelerator raises the total temperature of the exit flow to 3633 K. 

The annular MHD Hall generator is L = 3 m in length with a Br = 5 Tesla magnetic field, a 

conductivity = 5 mho/m and a loading parameter Kh = –0.09. The derivative of the product d(vz)dz = 

–21.0 kg/m3-s is held constant allowing an area variation in the flow path calculation. The Mach number 

reduction from 5.0 to 2.1 and area variation from 0.013 to 0.086 m2

-s/kg in the generator is shown in 

Figure 6. The total temperature drop from 2530 to 930 K is shown in Figure 7. This corresponds to an 

enthalpy extraction ratio, Ng = 0.63, defined as the ratio of the total enthalpy decrease divided by the 

inlet total enthalpy. This enthalpy extraction results in two orders of magnitude drop in total pressure Po 

from 2350 to 18 kPa as shown in Figure 7. This corresponds to an isentropic efficiency of 84 percent. The 

Hall parameter and axial electric field are given in Figure 8. Keeping the Hall parameter above 20 by 

maintaining low static pressure is important for the enthalpy extraction process indicating that high 

altitude operation is preferable. The total voltage across the 3 m long generator is V = 55.8 kV, i.e., the 

integral of the axial electric field. Total current flow in the generator is I = 28.7 Amp-s/kg. 
NASA/TM—2011-217210 8 

 

 

The turbojet is primarily a high altitude combustor since it’s compression ratio is only 1.09. The 

fuel/air ratio needed to raise the temperature to 2200 K in the combustor is 0.0286 using fuel with a 

heating value of 45000 kJ/kg. Heat addition in frictionless flow in which the flow area is increased in 

such a way that static pressure is held constant in the combustor is employed in the analysis. 

Following a small expansion downstream of the turbine, the annular MHD accelerator receives the 

flow at an inlet Mach Number of M = 1.1, static pressure Ps = 58.6 torr and static temperature 

Ts = 1790 K. Based on these conditions, the inlet Hall parameter = 51.9. The annular MHD Hall 

accelerator is L = 3 m in length with a magnetic field Br = 5 Tesla, a conductivity = 1.0 mho/m, and a 

loading parameter Kh = 0.08. The derivative of the product d(vz)dz = –1.3 kg/m3

-s is held constant 

allowing an area variation in the flow path calculation. The Mach number increase from 1.1 to 3.1 and 

area variation from 0.069 to 0.094 m2

-s/kg in the accelerator is shown in Figure 9. The total temperature 

rise from To = 2240 to 3640 K is shown in Figure 10. This corresponds to an enthalpy addition ratio 

Na = 0.62, defined as the ratio of the total enthalpy increase divided by the inlet total enthalpy. This 

enthalpy addition results in a total pressure rise of Po from 17 to 72 kPa as shown in Figure 10. This 

corresponds to an isentropic efficiency of 81 percent. The Hall parameter and axial electric field are given 

in Figure 11. The Hall parameter is above 50 because of the low static pressure and high static 

temperature enabling the efficient enthalpy addition process. The total voltage across the 3 m long 

accelerator is V = 204.9 kV, i.e., the integral of the axial electric field. Total current flow in the 

accelerator is I = 6.7 Amp-s/kg. 

Performance maps of generators and accelerators can be derived by solving Equations (6) through 

(20) for the specified inlet conditions and plotting the exit parameters. When one does this, one finds that 

exit parameters can be plotted against the combination of parameters LB, indicating that conductivity , 

length L, and magnetic field Br can be traded off against one another such that the product is constant for 

the same performance. A plot of generator isentropic efficiency sg is plotted against LB for various Kh

in Figure 12 for d(vz)/dz = –21 kg/m3

-s. The operating point at sg = 0.84 and LB = 75 on the loading 
NASA/TM—2011-217210 9 

 

 

 

curve Kh = –0.09 is shown by the circle point. Note that there is no higher performance without increasing 

 or L or Br. A similar plot of generator isentropic efficiency sg is plotted against LB for various 

d(vz)/dz in Figure 13 for Kh = –0.09. Again the operating point is shown by the circle point on the 

d(vz)/dz = –21 kg/m3

-s curve. Note that higher performance is available at more negative d(vz)/dz, but 

this performance comes at the expense of increasing exit area as shown on Figure 14. The power 

generated by the MHD generator is plotted in Figure 15 as a function of LB and Kh for d(vz)/dz 

= –21 kg/m3

-s with the operation point shown at 1.6 MW-s/kg. This power minus a fraction used in the 

ionizers is passed on to the MHD accelerator. 
NASA/TM—2011-217210 10 

 

Power used by the accelerator is plotted in Figure 16 as a function of LB and Kh for d(vz)/dz 

= –1.3 kg/m3

-s with the operating point of 1.4 MW-s/kg determined by the power passed to it by the 

generator. Operation on the Kh = 0.08 loading parameter at LB = 15 was chosen. A plot of accelerator 

isentropic efficiency sa is plotted against LB for various Kh in Figure 17 for d(vz)/dz = –1.3 kg/m3

-s. 

The operating point at sg = 0.81 and LB = 15 on the loading curve Kh = 0.08 is shown by the circle 

point. Note that higher performance is available at lower Kh, but higher  or L or Br is required. A similar 

plot of accelerator isentropic efficiency sa is plotted against LB for various d(vz)/dz in Figure 18 for 

Kh = 0.08. Again the operating point is shown by the circle point on the d(vz)/dz = –1.3 kg/m3

-s curve. 

Note that some higher performance is available for less negative d(vz)/dz, but this component 

performance is limited by an expansion to match the exit static pressure at the altitude of flight. 

An assessment of the electron number density necessary to achieve the required electrical 

conductivity is derived from the following equation: 

σ ൌ  ୬౛ୣమ

୫౛୬୕ୡ౛

 (21) 

The ionization fraction, ne/n that results in electrical conductivity = 1.0 mho/m can be determined from 

the equation for . Substituting Q = 810–16 cm2

 for the estimated electron-molecule momentum transfer 

cross section for air given previously and ce = 6.692107

 cm/sec for the mean random thermal velocity of 

the electrons at an electron temperature of Te = 1ev, i.e., Te=11605 K (Ref. 20), we get 

σ ൌ 5.2510ହ ୬౛

୬ (22) 
NASA/TM—2011-217210 11 

For a conductivity of = 1.0 mho/m an ne/n = 1.9010–6 is required, and for = 5.0 mho/m an 

ne/n = 9.5210–6 is required. Ionization fractions were estimated in weakly ionized plasmas using pulsed 

nanosecond, high-voltage discharges sustained by a lower DC voltage (Ref. 15). The calculations were 

based on the slope of the DC voltage—current in the sustainer circuit. The reported ionization fractions 

were relatively constant at ne/n = 1.210–8 over the static pressure range of 10 to 50 torr of interest here. 

Two to three orders of magnitude higher ionization fraction is required than is currently estimated in the 

measurements. 

Conclusions 

This paper lays a foundation for exploring the thermodynamic benefits of MHD energy bypass in 

hypersonic propulsion with turbojet engines. The equations for a 1-D, axisymmetric MHD 

generator/accelerator which can be used in an integrated combined cycle propulsion system analysis 

incorporating a turbojet are derived and numerically integrated to determine the generator/accelerator 

performance characteristics. MHD power generation and enthalpy extraction in low-temperature, 

nonequilibrium supersonic air flows is explored, with the primary application being an MHD inlet 

diffuser and energy bypass around a turbojet to an MHD accelerator. The annular flowpath geometry of a 

turbojet suggests the desirability of annular type MHD power extraction/addition devices. The concept 

offers a shockless means of interacting with high speed inlet flows and potentially offers variable inlet 

geometry performance without the complexity of moving parts simply by varying the generator loading 

parameter. The 1-D axisymmetric model of this flow describing the interaction for modeling purposes 

uses the assumptions/approximations of the more generalized 3-D MHD equations for steady-state flow. 

A preliminary cycle analysis was conducted in order to derive gas dynamic inlet parameters for the MHD 

generator and accelerator. It was conducted iteratively with the spike inlet and turbojet flying at M = 7 at 

30 km altitude. This cycle is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The 

turbojet allowable combustor temperature is set at an aggressive 2200 K. Performance maps of 

generators and accelerators were derived for the specified inlet conditions. It was found that exit 

parameters can be plotted against the combination of parameters LB, indicating that conductivity , 

length L, and magnetic field B can be traded off against one another such that the product is constant for 

the same performance. The annular MHD Hall generator is L = 3 m in length with a Br = 5 Tesla 

magnetic field and a conductivity of = 5 mho/m. The Mach number reduction is from 5.0 to 2.1 and 

area variation is from 0.013 to 0.086 m2

-s/kg in the generator. The total temperature drop from 2530 to 

930 K. This corresponds to an enthalpy extraction ratio, Ng = 0.63. This enthalpy extraction results in 

two orders of magnitude drop in total pressure Po from 2350 to 18 kPa. This corresponds to an isentropic 

efficiency of 84 percent. The annular MHD Hall accelerator is L = 3 m in length with a magnetic field 

Br = 5 Tesla and a conductivity = 1.0 mho/m. The Mach number increase is from 1.1 to 3.1 and area 

variation is from 0.069 to 0.094 m2

-s/kg in the accelerator. The total temperature rise from To = 2240 to 

3640 K. This corresponds to an enthalpy addition ratio Na = 0.62. This enthalpy addition results in a 

total pressure rise of Po from 17 to 72 kPa. This corresponds to an isentropic efficiency of 81 percent. An 

assessment of the ionization fraction necessary to achieve a conductivity of = 1.0 mho/m is ne/n 

= 1.9010–6, and for = 5.0 mho/m is ne/n = 9.5210–6. 

Future Work 

Cycle analysis using this approach should continue with a computational method set up to rapidly 

establish the performance maps of the generator and accelerator as a function of inlet conditions and 

control parameters. The method should iterate with the performance of a turbojet to establish and 

optimize the cycle performance as a function of flight regime. The magnetic field Br, the load factor Kh, 

and the conductivity  are all variables that can be varied without any change in geometry. Mass bypass 

around the turbojet may prove beneficial and can be incorporated with geometric change. The analysis 
NASA/TM—2011-217210 12 

should follow the established dynamic pressure corridor of the airframe. Once a 1-D axisymmetric design 

of a generator and accelerator is established, the large radius approximation should be relaxed going into 

a 2-D axisymmetric analysis to calculate hub to tip variations in the flow. Finally a full 3-D analysis 

should be conducted, allowing for 3-D variations in the vectors B, E, , and j. 

Since the conductivity of the working fluid in the cycle analysis is based on a two temperature gas 

model with a nonequilibrium ionization process, a higher fidelity analysis should be established in which 

the plasma is considered as a mixture of ions, electrons, and neutral particles that is neutral overall. This 

analysis would use the “kinetic theory of plasmas” to follow the relaxation time of the high temperature 

electrons and the resulting loss of conductivity. The analysis should also look at energy transfer from the 

electrons into the vibrational states of the neutrals and their subsequent relaxation times.

Experimentally, the pulsed nanosecond discharge method of ionization needs to be developed with 

the goal of delivering a higher ionization fraction than that currently estimated. Methods of measuring this 

ionization fraction and the attendant electron temperature distribution function need to be established. 

Also, methods of measuring the fraction of discharge energy  going into Joule heating of the gas need to 

be established along with the variability of  as a function of gas composition, especially air with water 

vapor and carbon dioxide present. Proof of concept generator and accelerator tests need to be designed for 

wind tunnel testing. These tests should be conducted in parallel with the analysis which would seek to 

reproduce experimental results analytically. 

References 

1. Gurijanov, E.P., and Harsha, P.T.: “AJAX: New Directions in Hypersonic Technology,” AIAA-96-

4609, Seventh Aerospace Planes and Hypersonics Technology Conference, Norfolk, VA, 1996. 

2. Bruno, C., Czysz, P.A., and Murthy, S.N.B., “Electro-magnetic Interactions in a Hypersonic 

Propulsion System,” AIAA 97-3389, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 

Seattle, WA, July 6–9, 1997. 

3. Litchford, R.J., Cole, J.W., Bityurin, V.A., and Lineberry, J.T., “Thermodynamic Cycle Analysis of 

Magnetohydrodynamic-Bypass Hypersonic Airbreathing Engines,” NASA/TP—2000-210387, 

July 2000. 

4. Murthy, S.N.B. and Blankson, I.M., “MHD Energy Bypass for Turbojet-Based Engines,” IAF-00-5-

5-05, 51st International Astronautical Congress, Rio de Janeiro, Brazil, October 2-6, 2000. 

5. Adamovich, I.V., Rich, J.W., Schneider, S.J., and Blankson, I.M., “Magnetogasdynamic Power 

Extraction and Flow Conditioning for a Gas Turbine,” AIAA–2003–4289, 34th AIAA 

Plasmadynamics and Lasers Conference, Orlando, FL, June 23-26, 2003. 

6. Blankson, I.M. and Schneider, S.J., “Hypersonic Engine Using MHD Energy Bypass with a 

Conventional Turbojet: A Progress Report,” AIAA–2003–6922, 12th AIAA International Space 

Planes and Hypersonic Systems Conference, Norfolk, VA, December 15-19, 2003. 

7. Shumlak, U., Jarboe, T. and Sprenger, R., “Physics of the Hall Thruster,” AIAA Paper 97-3048, 33rd 

AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Seattle, WA, July 6-9, 1997. 

8. Karlovitz, B. and Halasz, D., “History of the K and H Generator and Conclusions Drawn from 

Experimental Results,” 3rd Symposium on Engineering Aspects of Magnetohydrodynamics, 1964, 

pp. 187–203. 

9. Schmidt, G.R., Patterson, M.J., and Benson, S.W., “The NASA Evolutionary Xenon Thruster 

(NEXT): Nasa’s Next Step for U.S. Deep Space Propulsion,” IAC-08-C4.4.2, 59th International 

Astronautical Congress, Glasgow, Scotland, UK, Sept. 29 - Oct. 3, 2008. 

10. Manzella, D.H., Kamhawi, H., Peterson, P.Y., and Yim, J.T., “Progress on the Development of a Hall 

Thruster for NASA Science Missions,” Proceedings of the Joint Army-Navy-NASA-Air Force 

(JANNAF) Spacecraft Propulsion Subcommittee (SPS) Meeting; Denver, CO, May 14–17, 2007, 

Also NASA/TM—2007-215004. 
NASA/TM—2011-217210 13 

11. Murray, R.C., Zaidi, S.H., Carraro, M.R., Vasilyak, L., Macheret, S.O., Shneider, M.N., and Miles, 

R.B., “Investigation of a Mach 3 Cold Air MHD Channel,” AIAA–2003–4282, 34th AIAA 

Plasmadynamics and Lasers Conference, Orlando, FL, June 23–26, 2003. 

12. Shang, J.S., Kimmel, R., Hayes, J., Tyler, C., and Menart, J., “Hypersonic Experimental Facility for 

Magnetohydrodynamic Interactions,” Journal of Spacecraft and Rockets, Vol. 42, No. 5, SeptemberOctober 2005, pp. 780–789. 

13. Nishihara, M., Jiang, N., Rich, J.W., Lempert, W.R., and Adamovich, I.V., “Low-temperature 

Supersonic Boundary Layer Control Using Repetitively Pulsed Magnetohydrodynamic Forcing,” 

Physics of Fluids 17, 106102, 2005. 

14. Bobashev, S.V., Erofeev, A.V., Lapushkina, T.A., Poniaev, S.A., Vasileva, R.V., and Van Wie, D.M., 

“Effect of Magnetohydrodynamics Interaction in Various Parts of Diffuser on Inlet Shocks: 

Experiment,” Journal of Propulsion and Power, Vol. 21, No. 5, September-October, 2005, 

pp. 831–837. 

15. Schneider, S.J., Kamhawi, H., and Blankson, I.M., “Efficient Ionization Investigation for Flow 

Control and Energy Extraction,” AIAA–2009–1050, 47th AIAA Aerospace Sciences Meeting, 

Orlando, FL, January 5–8, 2009. 

16. Pai, Shih-I, Magnetogasdynamics and Plasma Dynamics, Springer-Verlag, Vienna, Prentice-Hall, 

Inc., Englewood Cliffs, NJ 1962. 

17. Rosa, R.J., Magnetohydrodynamic Energy Conversion, McGraw-Hill Book Company, NY, 1968. 

18. Chambers, H.F., “Aerospace Applications of the DOE MHD Program Results, Part II: MHD Plasma 

Physics and Power Generation,” AIAA–2008–1389, 46th AIAA Aerospace Sciences Meeting, Reno, 

NV, January 7–10, 2008. 

19. Nishihara, M., Rich, J.W., Lempert, W.R. and Adamovich, I.V., “Low-temperature M=3 Flow 

Deceleration by Lorentz Force,” Physics of Fluids 18, 086101, 2006. 

20. Nishihara, M. and Adamovich, I.V., “Numerical Simulation of a Crossed Pulser-Sustainer Discharge 

in Transverse Magnetic Field,” IEEE Transactions on Plasma Science, Vol. 35, No. 5, pp. 1312–

1324, October, 2007. 

21. Raizer, Y.P., Gas Discharge Physics, Springer-Verlag, Berlin, New York, 1997. 

22. Gordiets, B.F., Osipov, A.I., and Shelepin, L.A., Kinetic Processes in Gases and Molecular Lasers, 

Gordon and Breach Science Publishers, New York, 1988. 
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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated assuming weakly ionized flows 

obtained from pulsed nanosecond discharges. The equations for a 1-D, axisymmetric MHD generator/accelerator are derived and 

numerically integrated to determine the generator/accelerator performance characteristics. The concept offers a shockless means of 

interacting with high speed inlet flows and potentially offers variable inlet geometry performance without the complexity of moving parts 

simply by varying the generator loading parameter. The cycle analysis conducted iteratively with a spike inlet and turbojet flying at M = 7 at 

30 km altitude is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at 

an aggressive 2200 °K. The annular MHD Hall generator/accelerator is L = 3 m in length with a Br

 = 5 Tesla magnetic field and a 

conductivity of σ = 5 mho/m for the generator and σ = 1.0 mho/m for the accelerator. The calculated isentropic efficiency for the generator 

is ηsg = 84 percent at an enthalpy extraction ratio, ηNg = 0.63. The calculated isentropic efficiency for the accelerator is ηsa = 81 percent at 

an enthalpy addition ratio, ηNa = 0.62. An assessment of the ionization fraction necessary to achieve a conductivity of η = 1.0 mho/m is ne

/n 

= 1.90×10-6, and for σ = 5.0 mho/m is ne

/n = 9.52×10-6.

15. SUBJECT TERMS

Magnetohydrodynamics; Plasma-electromagnetic interaction; Hypersonic inlets 

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