Theresa L. Benyo

Glenn Research Center, Cleveland, Ohio

The Effect of Magnetohydrodynamic (MHD) 

Energy Bypass on Specifi c Thrust for a 

Supersonic Turbojet Engine

NASA/TM—2010-216734

December 2010

AIAA–2010–232
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Theresa L. Benyo

Glenn Research Center, Cleveland, Ohio

The Effect of Magnetohydrodynamic (MHD) 

Energy Bypass on Specifi c Thrust for a 

Supersonic Turbojet Engine

NASA/TM—2010-216734

December 2010

AIAA–2010–232

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

48th Aerospace Sciences Meeting

sponsored by the American Institute of Aeronautics and Astronautics

Orlando, Florida, January 4–7, 2010
Acknowledgments

 Theresa L. Benyo thanks Dr. Isaiah Blankson and Dr. Steve Schneider of NASA Glenn Research Center 

for their guidance and encouragement throughout this research.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://gltrs.grc.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2010-216734 1

The Effect of Magnetohydrodynamic (MHD) Energy Bypass on 

Specific Thrust for a Supersonic Turbojet Engine 

Theresa L. Benyo 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

This paper describes the preliminary results of a thermodynamic cycle analysis of a supersonic 

turbojet engine with a magnetohydrodynamic (MHD) energy bypass system that explores a wide range of 

MHD enthalpy extraction parameters. Through the analysis described here, it is shown that applying a 

magnetic field to a flow path in the Mach 2.0 to 3.5 range can increase the specific thrust of the turbojet 

engine up to as much as 420 N/(kg/s) provided that the magnitude of the magnetic field is in the range of 

1 to 5 Tesla. The MHD energy bypass can also increase the operating Mach number range for a 

supersonic turbojet engine into the hypersonic flight regime. In this case, the Mach number range is 

shown to be extended to Mach 7.0. 

Nomenclature 

Ae cross sectional area of the nozzle exit 

Ag cross sectional area of the MHD generator 

B magnetic field intensity 

Cp constant pressure specific heat 

F thrust 

F/ ma  specific thrust

f fuel-to-air mass flow ratio 

K Faraday loading parameter 

L length of the MHD generator 

ma  mass flow rate of the air at the entry of the MHD generator 

Ma flight Mach number 

pa freestream static pressure 

pe static pressure at the nozzle exit 

Pelec power output of the MHD generator 

qf fuel heating value 

R gas constant for air 

T0,3 stagnation temperature at entrance to the burner 

T0,4 stagnation temperature at the exit of the burner 

T0,5 stagnation temperature at the exit of the turbine 

T0,6 stagnation temperature at the exit of the MHD accelerator 

T0,a freestream total temperature 

T0,lim stagnation temperature limit of the engine 

Ta freestream static temperature 

u flow velocity 

γ specific heat ratio for air 

ηc combustion efficiency 

ηN(a) enthalpy extraction/addition ratio of the MHD accelerator 

ηN(g) enthalpy extraction/addition ratio of the MHD generator 
NASA/TM—2010-216734 2

ηs(a) isentropic efficiency for the MHD accelerator

ηs(g) isentropic efficiency for the MHD generator 

πa stagnation pressure ratio of the MHD accelerator 

πb stagnation pressure ratio of the burner 

πc stagnation pressure ratio of the compressor 

πd stagnation pressure ratio of the diffuser 

πe stagnation pressure ratio of the expansion section 

πg stagnation pressure ratio of the MHD generator 

πn stagnation pressure ratio of the nozzle 

πp stagnation pressure ratio of the pre-ionizer 

πt stagnation pressure ratio of the turbine 

П global stagnation pressure ratio 

σ electrical conductivity 

χ fraction of generator power diverted to pre-ionizer 

Introduction 

A 1–D thermodynamic cycle analysis (Ref. 1) was completed for a supersonic turbojet engine with a 

MHD energy bypass system which consists of a MHD generator and MHD accelerator for flow control 

and energy bypass capability. For many years, MHD technology has been studied and recognized as a 

viable technology for increasing the performance of supersonic and hypersonic flight vehicles. 

Electromagnetic fields are used to enhance flow features in supersonic/hypersonic inlets for flow control 

and combustor energy bypass. Expanding flows in high speed nozzles may also be accelerated by means 

of electromagnetic forces to augment the thrust generated. The overall objective of this paper is to 

establish the feasibility and demonstrability of a kinetic energy bypass from the inlet air-stream of a jet 

engine that has been weakly ionized by an external means to a downstream location using MHD 

interaction with the ionized air stream. 

This paper describes a previous 1–D thermodynamic cycle analysis (Ref. 2) of a ramjet/scramjet and 

describes an extension of this analysis to a turbojet by exploring a range of MHD enthalpy extraction 

parameters using a previous (Ref. 3) enthalpy extraction/addition ratio derivation. It should be noted that 

these results are preliminary and require further study. The analysis is a point-to-point 1–D 

thermodynamic cycle analysis where only energy bypass is considered. This analysis additionally does 

not take into consideration any variable cross sectional areas. The Mach 3.3 condition at the J-102 inlet 

needs to be maintained at the higher free-stream Mach numbers. Maintaining these constraints would 

normally require an iterative procedure, which this analysis does not have. Even so, this analysis produces 

results that are encouraging enough to continue to explore the use of MHD bypass for supersonic and 

hypersonic flight. 

Background 

A 1–D thermodynamic cycle analysis previously completed (Ref. 2) was studied and the results were 

verified. The analysis assumes a constant stagnation pressure ratio for each element of the MHD energy 

bypass ramjet/scramjet engine which is illustrated in Figure 1. The MHD energy bypass system 

incorporated into a conventional gas turbine technology is a revolutionary concept which offers three 

distinct advantages. It allows turbomachinery to operate continuously over the entire range of Mach 0 to 7 

where no deadweight engines are carried aloft. This revolutionary concept only uses hydrocarbon fuel 

where the plasma in the weakly ionized flow may be used to reform the hydrocarbon fuel into hydrogen. 

And finally, there is high potential for increased specific impulse. 

A MHD energy bypass system bypasses kinetic energy from the inlet stream and uses it downstream 

to generate more thrust or reduce drag on the vehicle. This energy bypass is accomplished by using weak 

ionization of the inlet stream by an external means and MHD interaction with the ionized gas. The key 
NASA/TM—2010-216734 3

feature of the engine lies in the additional hardware surrounding the jet engine. There are three main 

components of a MHD energy bypass system; the pre-ionizer, the MHD generator and the MHD 

accelerator. 

The pre-ionizer is positioned in the inlet where it ionizes the incoming flow which, in conjunction 

with applying a magnetic field to the flow, provides the benefits of flow control. The flow is ionized by 

the high voltage nanosecond discharge method (Ref. 4) where high-voltage, short pulse duration, high 

pulse repetition rate discharges generate ionization in supersonic cold flows (T0 = 300 K). 

The MHD generator towards the front of the engine acts as a flow control device and provides power 

to the pre-ionizer and MHD accelerator. The electromagnetic fields produced by the MHD generator are 

used to enable variable inlet flow control that is similar to that controlled by variable geometry. The MHD 

generator is a non-obstructing means of total temperature reduction that can be controlled by applied 

magnetic fields and load parameter adjustment. The MHD accelerator at the back of the engine 

accelerates the flow exiting the engine by applying electromagnetic forces to ionized flow which work 

together to augment the thrust generated. 

In order to fully understand the current work described in this paper, it is essential to document the 

equations used in the previous analyses. The specific thrust of an engine can be derived by coupling the 

first and second laws of thermodynamics with elementary gasdynamic relationships. The calculation for 

the specific thrust (F/݉ሶ ௔ሻ as derived in Reference 1 is 

ி

௠ሶ ೌ

ൌ ቈሺ1൅݂ሻටଶஓோ்బ,లሺஈିଵሻ

ሺஓିଵሻஈ

െ ܯ௔ඥγܴܶ௔቉ ൅ ௣೐஺೐

௠ሶ ೌ

ቀ1 െ ௣ೌ

௣೐

ቁ (1) 

Notice that as long as the ratio of pa/pe is 1, the additive term contributes nothing to the specific thrust 

calculation. Two main contributors to the specific thrust calculation are the fuel-to-air mass flow rate (f) 

and the freestream Mach number,(Ma). In Equation (1), f is the fuel-to-air mass flow rate and is further 

expressed as 

݂ ൌ ଵି൫்బ,య⁄்బ,೗೔೘൯

൫ఎ೎௤೑⁄஼೛்బ,೗೔೘൯ିଵ (2) 

Another important contributor to Equation (1) is the global stagnation pressure ratio. This ratio takes into 

account the pressure ratios of the pre-ionizer, the diffuser, the MHD generator, the burner, the expansion, 

the MHD accelerator and the nozzle. The global stagnation pressure ratio parameter is further expressed 

as 
NASA/TM—2010-216734 4

Π ൌ ቀ1 ൅ ஓାଵ

ଶ

௔ܯ

ଶቁ ቀπ௣πௗπ௚π௕π௘π௔π௡

௣ೌ

௣೐

ቁ

ሺஓିଵሻ⁄ஓ

 (3) 

where the individual stagnation pressure ratios of each component are either computed using efficiency 

parameters or held at constant values. The pressure ratios of particular interest in this analysis are the 

pressure ratios for the MHD generator and MHD accelerator. The stagnation pressure ratio for the MHD 

generator is 

 π௚ ൌ ൬1 െ ஗ಿሺ೒ሻ

஗ೞሺ೒ሻ ൰

ಋ

ಋషభ (4) 

and the stagnation pressure ratio for the MHD accelerator is 

π௔ ൌ ൤1൅η௦ሺ௔ሻ ቀ ଵ

ଵା௙ቁ ሺଵି஧ሻ஗ಿሺ೒ሻ

ଵି஧஗ಿሺ೒ሻ

்బ,ೌ

்బ,ర൨

ಋ

ಋషభ (5) 

The analysis studied produces results indicated in Figure 2 wherein the enthalpy extraction parameter 

of the MHD generator was held constant at five different levels; 0, 0.25, 0.5, 0.65, and 0.75. This 

parameter is the ratio of the stagnation enthalpy change in the MHD generator device to the entrance 

stagnation enthalpy. For each parameter level, the specific thrust was calculated for all Mach numbers 

from 1 to 12. As indicated in the figure, as the MHD generator enthalpy extraction increases, the 

operating range of the engine expands into Mach numbers above Mach 8. For example, if one wants to fly 

at Mach 8, the MHD generator enthalpy extraction percentage would have to be at least 25 percent. In 

order to fly at Mach 10, a MHD generator enthalpy extraction percentage of at least 50 percent is 

required. It is noted however, that the maximum specific thrust achieved is decreased as a result of using 

the MHD energy bypass system. Even though the analysis shows a maximum potential performance 

decrease, with the application of the MHD energy bypass system (i.e., creating an environment where the 

MHD generator enthalpy can be changed), the aircraft has the potential of operating at higher Mach 

 Figure 2.—Results of 1–D thermodynamic cycle analysis for a ramjet/ 

scramjet from Litchford et al. with added ηN(g) values of 0.65 and 0.75 

Specific thrust as a function of flight Mach number for ηN(g) = 0, 0.25, 0.5, 

0.65, and 0.75. 

1 2 3 4 5 6 7 8 9 10 11 12

0

0.2

0.4

0.6

0.8

1

Specific Thrust Characteristics vs. Flight Mach Number

Flight Mach Number, Ma

F/ma (kN sec/kg)

Enthalpy extraction fraction = 0

Enthalpy extraction fraction = 0.25

Enthalpy extraction fraction = 0.5

Enthalpy extraction fraction = 0.65

Enthalpy extraction fraction = 0.75
NASA/TM—2010-216734 5

numbers. Therefore, the result of the analysis indicates that there are flight envelope benefits and should 

be researched more vigorously. 

As derived in Reference 2, the enthalpy extraction/addition ratio is determined by the output power 

produced by the MHD generator and the enthalpy input through the ‘inlet’ of the MHD generator. This 

ratio is portrayed in the following equation: 

ηேሺ௚ሻ ൌ 

௉೐೗೐೎

௠ሶ ೌ஼೛்బ,ೌ

 (6) 

where Pelec is the power output of the MHD generator (in Watts) and T0,a is the total temperature of the 

freestream air and ݉ሶ ௔ is the mass flow rate of the air coming into the MHD generator. Equation (6) 

allows a calculation of a variable MHD generator enthalpy extraction parameter. The expression for the 

power output, Pelec also derived in Reference 2 was used to calculate the power output of the MHD 

generator. That equation is expressed as: 

ܲ௘௟௘௖ ൌ σݑଶܤଶܭሺ1 െ ܭሻܣ௚ܮ) 7 (

where σ is the conductivity of the ionized air, u is the velocity of flow entering the MHD generator in m/s, 

B is the applied magnetic field in Tesla, K is the Faraday loading parameter (usually held at 0.5) for the 

generator, Ag is the cross sectional area of the MHD generator in m2

, and L is the length of the generator 

in meters. 

Current Analysis with a Turbojet 

This analysis builds upon previous work performed (Ref. 2) with a ramjet/scramjet and uses a variable 

MHD generator enthalpy extraction parameter coupling details of the MHD generator design into the 

analysis (Ref. 3) to further enhance a thermodynamic cycle analysis of a supersonic turbojet engine. The 

MHD generator is used to augment turbojet performance mainly by extending the operating range to 

higher Mach numbers. 

The geometry used for this analysis is shown in Figures 3 and 4. The concept engine is a MHD driven 

energy bypass supersonic turbojet engine (Ref. 5). The MHD generator may be employed in the inlet, 

nozzle, and another duct, individually and in combination. The possibility of electromagnetically 

extracting part of the turbojet inlet air kinetic energy is the key feature. The concept potentially offers 

variable inlet 

Figure 3.—General arrangement of MHD controlled turbojet for high-speed propulsion. 
NASA/TM—2010-216734 6

geometry performance without the complexity of moving inlet parts. Three primary aeropropulsion 

purposes are served by the concept. Firstly, the flow enthalpy into the combustor is reduced allowing 

more efficient addition of energy in the combustor without exceeding temperature limitations on the 

turbine materials. Secondly, the applied electromagnetic fields and their body forces can enhance offdesign performance by manipulating the flow features in the supersonic/hypersonic inlets thereby 

reducing total pressure losses and entropy changes for the same level of flow compression by other 

means. Thirdly, electrical power removed can be used for various on-board vehicle requirements 

including plasma flow control around the vehicle. In addition, the expanding flow in the high-speed 

nozzle may also be augmented by electromagnetic forces to generate more thrust. 

Because a supersonic turbojet engine is being used in this case instead of a ramjet/scramjet, a 

different expression for the global stagnation pressure ratio is needed. Equation (8) expresses the new 

global stagnation pressure ratio. 

   

















          

 



     

1

2

2

1 1 e

a a p d g c b t e a n p

p M (8) 

where two additional stagnation pressure ratios are needed to model the supersonic turbojet’s compressor 

and turbine. The stagnation pressure ratio of the compressor in this case is held constant at a well-known 

value. The turbine’s stagnation pressure ratio is computed in the normal manner and expressed as: 

  1

0,4

0,5 1 1 





















    t

T

T

t (9) 

In addition, because of the turbine, a new stagnation pressure ratio of the MHD accelerator was 

needed. The equation used for this pressure ratio is: 

  1   1



a   s a N a (10) 

where the efficiency parameter for the MHD accelerator is computed by the following equation: 

  0,5

0,6 0,5

T

T T

N a

   (11) 

Figure 4.—Schematic of MHD controlled turbojet for high-speed propulsion. 
NASA/TM—2010-216734 7

In this study, the focus was on a supersonic turbojet engine like the Allison J-102 with a MHD energy 

bypass system and the following operating conditions (Refs. 6 and 7): 

System 

Stagnation temperature limit (T0,lim): 1600, 1800, 2000, and 2200 K 

Freestream temperature (Ta): 233 K 

Turbojet engine length: about 1.2 m 

Pre-ionizer 

Stagnation pressure ratio (πp): 1 

Diffuser 

Stagnation pressure ratio (πd): 0.7 

MHD Generator 

Mass flow rate of air (݉ሶ

௔): 28 kg/s 

Electrical conductivity (σ): 1 mhos/m and 10 mhos/m 

Magnetic field (B): varies from 0 to 20 Tesla 

Length (L): 1 and 10 m 

Cross sectional area (Ag): 0.5 m2 

Isentropic efficiency: 0.9 

Fraction of generator power diverted to pre-ionizer (χp): 0.05 

Faraday loading parameter (K): 0.5 

Compressor 

Isentropic efficiency: 0.77 

Stagnation pressure ratio (πc): 12 

Combustor 

Combustion efficiency (ηc): 1 

Fuel heating value (qf): 45,000 kJ/kg 

Turbine 

Isentropic efficiency: 0.79 

Stagnation pressure ratio (πt): varies to match compressor power 

Expansion 

Stagnation pressure ratio (πe): 1 

MHD Accelerator 

Isentropic efficiency: 0.9 

Nozzle 

Stagnation pressure ratio (πn): 0.98 

Results for a Turbojet 

For this study, the specific thrust was calculated for a range of Mach numbers from 1 to 7. The MHD 

generator’s enthalpy extraction ratio varied with a magnetic field range of 0 to 20 Tesla. Figures 5 to 12 
NASA/TM—2010-216734 8

show the results at four combustion temperature limits (1600, 1800, 2000, and 2200 K), two MHD 

lengths (1 and 10 m), and two conductivity levels (1 and 10 mhos/m). 

The data in Figures 5 and 6 are for a 1600 K temperature limit. Note that there is no specific thrust 

benefit with the application of magnetic fields below Mach 2. The application of magnetic fields enables 

positive specific thrust from Mach 3 to 5. 

Figure 6.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). 

Results are the same if the MHD generator length is 1 m and 

conductivity of the flow field is 10 mhos/m. 

0 2 4 6 8 10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 10 meters

with a combustion temperature limit of 1600 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0

Figure 5.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). 

0 5 10 15 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 1 meters

with a combustion temperature limit of 1600 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0
NASA/TM—2010-216734 9

In the data shown in Figure 5, a high magnetic field of over 7 Tesla is required for any specific thrust 

benefit to be realized with a low combustion temperature limit of 1600 K, a moderate flow conductivity 

of 1 mhos/m, and a MHD generator length of 1 m. If either the flow conductivity or the MHD generator 

length increases by tenfold, the required magnetic field drops by a factor of three as shown in Figure 6. 

An increase of 202 N/(kg/s) at a magnetic field of 3 Tesla is realized at the Mach 2.5 level. This 

corresponds to a thrust increase of 5.7 kN at a 28 kg/s flow rate at Mach 2.5. This affords a fairly good 

increase in performance of a supersonic turbojet engine. 

If we allow the combustion temperature limit to increase to levels of 1800, 2000, and 2200 K; higher 

Mach number flight is enabled. We can potentially increase the operating range into the hypersonic flight 

regime by using MHD energy bypass. 

Figures 7 and 8 show results with a combustion temperature limit of 1800 K. Note again that there is 

no specific thrust benefit with the application of magnetic fields below Mach 2. The application of 

magnetic fields in this case enables positive specific thrust up to Mach 6. If either the length of the MHD 

generator or flow conductivity is increased by tenfold, the required applied magnetic field decreases 

again by a factor of three. As seen in Figure 8, the specific thrust is increased by 144 N/(kg/s) at the 

Mach 2.5 level with an applied magnetic field of 3 Tesla. Even better, the specific thrust is increased by 

337 N/(kg/s) at Mach 3.0 with an applied magnetic field of about 3.75 Tesla. This corresponds to a 

thrust increase of 4.0 and 9.4 kN respectively at a 28 kg/s flow rate. 

If we increase the combustion temperature limit to 2000 K, even better results are achieved and are 

shown in Figures 9 and 10. The possible Mach numbers that show specific thrust improvements are now 

up into the Mach 6.5 range. As indicated in Figure 10 at Mach 2.5, the specific thrust is shown to increase 

by 106 N/(kg/s) with an applied magnetic field of just under 3 Tesla. Similarly, an increase in specific 

thrust of 263 N/(kg/s) is realized at Mach 3.0 with a magnetic field of about 3.5 Tesla. This corresponds 

to a thrust increase of 2.9 and 7.4 kN respectively at a 28 kg/s flow rate. 

Figure 7.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). 

0 5 10 15 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 1 meters

with a combustion temperature limit of 1800 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0

Mach 5.5

Mach 6.0
NASA/TM—2010-216734 10

The final two figures (Figs. 11 and 12) show results with a combustion temperature limit of 2200 K. 

At this temperature limit, the range of possible Mach numbers further increases to Mach 7. Along with 

the wider Mach number range, an increased specific thrust is now realized between Mach numbers 2 to 

3.5. Figure 12 shows that at the Mach 2.5 level, the specific thrust increases by 79 N/(kg/s) with a 

magnetic field of about 2.5 Tesla. A larger increase in performance occurs at the Mach 3.0 level where 

Figure 9.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). 

0 5 10 15 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 1 meters

with a combustion temperature limit of 2000 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0

Mach 5.5

Mach 6.0

Mach 6.5

Mach 7.0

Figure 8.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). The 

results are the same if the MHD generator length is 1 m and the 

conductivity of the flow field is 10 mhos/m.

0 2 4 6 8 10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 10 meters

with a combustion temperature limit of 1800 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0

Mach 5.5

Mach 6.0
NASA/TM—2010-216734 11

the specific thrust grows by 213 N/(kg/s) with an applied magnetic field of around 3.75 Tesla. Still larger 

specific thrust can be found at Mach 3.5 where a 420 N/(kg/s) increase can be realized with a magnetic 

field of just below 4 Tesla. This corresponds to a thrust increase of 2.2, 5.9 and 11.8 kN respectively at a 

flow rate of 28 kg/s.

Figure 11.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). 

0 5 10 15 20

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 1 meters

with a combustion temperature limit of 2200 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0

Mach 5.5

Mach 6.0

Mach 6.5

Mach 7.0

Figure 10.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). The 

results are the same if the MHD generator length is 1 m and the 

conductivity of the flow field is 10 mhos/m. 

0 1 2 3 4 5 6 7 8 9 10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 10 meters

with a combustion temperature limit of 2000 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0

Mach 5.5

Mach 6.0

Mach 6.5

Mach 7.0
NASA/TM—2010-216734 12

Conclusion 

Through the new analysis described here, it is shown that applying a magnetic field to a supersonic 

flow path in the Mach 2 to 3.5 range will increase the specific thrust up to 420 N/(kg/s). It also shows that 

by using a MHD energy bypass system, a supersonic aircraft’s operating envelope may be increased into 

the hypersonic flight regime. All this is shown with a magnetic field between 1 to 5 Tesla and the length 

of the MHD generator between 1 and 10 m. 

As evidenced by the above results, MHD technology is a valuable addition to supersonic and 

hypersonic flight and should be studied further and in progressively more detail. As it stands, this analysis 

has shown that better specific thrust performance can be realized for an operating range of Mach 2 to 

Mach 3.5 and that there is high potential for an expanded operating envelope up to Mach 7.0 provided 

that suitable conditions are present and allow the supersonic turbojet to operate at combustion 

temperatures of 2200 K. In addition, it is hoped that future work can discover the conditions necessary for 

the required magnetic field to be in the more desired range of 1 to 2 Tesla. 

By working the areas listed above, it is desired that MHD technology can fully make its way into 

high-speed flight and reap the following benefits of this technology. 

 The flow enthalpy into the combustor is reduced allowing more efficient addition of energy in the 

combustor without exceeding temperature limitations on the turbine materials. 

 The applied electromagnetic fields and their body forces can enhance off-design performance by 

manipulating the flow features in the supersonic/hypersonic inlets thereby reducing total pressure 

losses, and entropy changes for the same level of flow compression by other means. 

 The electrical power removed can be used for various on-board vehicle requirements including 

plasma flow control around the vehicle. In addition, the expanding flow in the high speed nozzle 

may also be augmented by the electromagnetic forces to generate more thrust.

Figure 12.—Results of 1–D thermodynamic cycle analysis for a turbojet. 

Specific thrust as a function of magnetic field for variable ηN(g). The 

results are the same is the MHD generator length is 1 m and the 

conductivity of the flow field is 10 mhos/m. 

0 2 4 6 8 10

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Specific Thrust Characteristics vs Magnetic Field for MHD Length of 10 meters

with a combustion temperature limit of 2200 Kelvin and conductivity of 1 mhos/m.

Magnetic Field, T

F/ma (kN sec/kg)

Mach 1.0

Mach 1.5

Mach 2.0

Mach 2.5

Mach 3.0

Mach 3.5

Mach 4.0

Mach 4.5

Mach 5.0

Mach 5.5

Mach 6.0

Mach 6.5

Mach 7.0
NASA/TM—2010-216734 13

This analysis also confirmed previous work completed by Litchford, et al. as evidenced by the figures 

showing the expanded Mach number range that is possible. 

Future Plans 

It is planned to conduct cycle analyses to properly match the flows between the pre-ionizer, the MHD 

generator, the turbojet engine and the MHD accelerator and to establish the operating conditions for a jet 

engine cycle that are optimal for kinetic energy transfer from inlet air to a downstream location in the 

engine. It is also desired to establish a model for a jet engine with MHD energy bypass and determine the 

design and operating conditions in which the thrust-to-weight ratio, thrust per unit mass of fuel 

consumption, and effectiveness of energy utilization are maximized. 

Specific future work in this area of full engine cycle analyses using MHD technology includes: 

 Establish the operating conditions for a turbo-jet engine cycle, that are optimal for kinetic energy 

transfer from inlet air (Mach reduction to 0.8) to a downstream location in the engine in a bypass 

mode. 

 Establish the interaction parameter and efficiency for MHD conversion of kinetic energy of the 

ionized gas to electrical energy. 

 Quasi 1–D MHD theory will be employed to conduct inlet analysis evaluations using 

experimentally determined conductivity, interaction parameters, and the mass flow captured at 

the inlet. 

 Conduct interfacing studies between the MHD bypass generator, the turbojet engine, and the 

MHD accelerator. Perform a thermal analysis to properly match the flows from an inlet 

employing an MHD generator to a supersonic turbojet engine such as the Allison J-102 engine. 

Working with various operating conditions (such as flow mass, magnetic field, combustion 

temperature limit, and length of the MHD generator and accelerator) should help accomplish flow 

matching and extend operation to higher Mach numbers before performance degradation occurs. 

References 

1. Hill, P.G., C.R. Peterson, “Mechanics and Thermodynamics of Propulsion,” Addison-Wesley 

Publishing Co., Inc., 1965. 

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

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

3. Murthy, S.N.B and I.M. Blankson, “MHD Energy Bypass Turbojet-Based Engines,” presented at the 

51st International Astronautical Congress, October 2000, Rio de Janeiro, Brazil, IAF–00–5–5–05. 

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

Deceleration by Lorentz Force,” Phys. Fluids 18, 086101 (2006). 

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

Extraction for a Gas Turbine,” presented at the 34th AIAA Plasmadynamics and Lasers Conference, 

June 2003, AIAA–2003–4289. 

6. Blankson, I.M., S. Schneider, “Hypersonic Engine using MHD Energy Bypass with a Conventional 

Turbojet,” presented at the 12th AIAA International Space Planes and Hypersonic Systems and 

Technologies, December 2003, AIAA–2003–6922. 

7. J-102 packet includes engine specifications and engine performance envelope from Isaiah Blankson. 
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The Effect of Magnetohydrodynamic (MHD) Energy Bypass on Specific Thrust for a 

Supersonic Turbojet Engine 

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Benyo, Theresa, L. 

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599489.02.07.03.04.03.01

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14. ABSTRACT

This paper describes the preliminary results of a thermodynamic cycle analysis of a supersonic turbojet engine with a magnetohydrodynamic 

(MHD) energy bypass system that explores a wide range of MHD enthalpy extraction parameters. Through the analysis described here, it is 

shown that applying a magnetic field to a flow path in the Mach 2.0 to 3.5 range can increase the specific thrust of the turbojet engine up to 

as much as 420 N/(kg/s) provided that the magnitude of the magnetic field is in the range of 1 to 5 Tesla. The MHD energy bypass can also 

increase the operating Mach number range for a supersonic turbojet engine into the hypersonic flight regime. In this case, the Mach number 

range is shown to be extended to Mach 7.0. 

15. SUBJECT TERMS

Magnetohydrodynamic simulation; Thermodynamics; Jet thrust; Supersonic turbojet 

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