The Effect of Magnetohydrodynamic (MHD) Energy Bypass on Specific Thrust for a Supersonic Turbojet Engine

Summary

This technical memorandum presents a 1-D thermodynamic cycle analysis evaluating the integration of a magnetohydrodynamic (MHD) energy bypass system with a supersonic turbojet engine (such as the Allison J-102). The study demonstrates that applying magnetic fields of 1 to 5 Tesla can augment specific thrust by up to 420 N/(kg/s) in the Mach 2.0 to 3.5 range. Furthermore, the MHD energy bypass system reduces inlet flow enthalpy, potentially extending the operational flight envelope of conventional gas turbine technology up to Mach 7.0 without requiring deadweight secondary engines.

Cover & Front Matter

NASA/TM—2010-216734 AIAA–2010–232

Theresa L. Benyo Glenn Research Center, Cleveland, Ohio

Prepared for the 48th Aerospace Sciences Meeting sponsored by the American Institute of Aeronautics and Astronautics Orlando, Florida, January 4–7, 2010

National Aeronautics and Space Administration Glenn Research Center Cleveland, Ohio 44135

December 2010

Acknowledgments & Notice

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.

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 findings, subject to revision as analysis proceeds.

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

Abstract & Nomenclature

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/ṁa: specific thrust f: fuel-to-air mass flow ratio K: Faraday loading parameter L: length of the MHD generator ṁa: 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 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 Π: 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 & Governing Equations

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 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/ṁa) as derived in Reference 1 is: F / ṁa = [(1 + f) * sqrt((2 * γ * R * T0,6 * (Π - 1)) / ((γ - 1) * Π)) - Ma * sqrt(γ * R * Ta)] + (pe * Ae / ṁa) * (1 - pa / pe) (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: f = (1 - (T0,3 / T0,lim)) / ((ηc * qf / (Cp * T0,lim)) - 1) (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: Π = [1 + ((γ - 1)/2) * Ma^2] * (πp * πd * πg * πb * πe * πa * πn * (pa / pe))^((γ - 1) / γ) (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: πg = [1 - (ηN(g) / ηs(g))]^(γ / (γ - 1)) (4)

and the stagnation pressure ratio for the MHD accelerator is: πa = [1 + ηs(a) * (1 / (1 + f)) * ((1 - χ) * ηN(g) / (1 - χ * ηN(g))) * (T0,a / T0,4)]^(γ / (γ - 1)) (5)

The enthalpy extraction/addition ratio is determined by: ηN(g) = Pelec / (ṁa * Cp * T0,a) (6)

where Pelec = σ * u^2 * B^2 * K * (1 - K) * Ag * L (7)

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 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 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. 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: Π = [1 + ((γ + 1)/2) * Ma^2] * (πp * πd * πg * πc * πb * πt * πe * πa * πn * (pa / pe))^((γ + 1) / γ) (8)

where two additional stagnation pressure ratios are needed to model the supersonic turbojet’s compressor and turbine. The compressor pressure ratio is held constant at 12. The turbine’s stagnation pressure ratio is: πt = [1 - (1 - (T0,5 / T0,4)) / ηt]^(γ / (γ - 1)) (9)

The stagnation pressure ratio of the MHD accelerator is: πa = (1 + ηs(a) * ηN(a))^(γ / (γ - 1)) (10)

where ηN(a) = (T0,6 - T0,5) / T0,5 (11)

Operating Conditions & Parameters

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 (ṁa): 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 m^2
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 & Discussion

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. Results show the performance across 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).

At 1600 K temperature limit (Figures 5 & 6): No specific thrust benefit is seen below Mach 2. With higher conductivity (10 mhos/m) or 10 m length, an increase of 202 N/(kg/s) at 3 Tesla is realized at Mach 2.5 (5.7 kN thrust increase at 28 kg/s flow rate). Positive specific thrust is enabled from Mach 3 to 5.
At 1800 K temperature limit (Figures 7 & 8): Enables positive specific thrust up to Mach 6. At Mach 2.5, specific thrust increases by 144 N/(kg/s) at 3 Tesla (4.0 kN increase), and at Mach 3.0 increases by 337 N/(kg/s) at ~3.75 Tesla (9.4 kN increase).
At 2000 K temperature limit (Figures 9 & 10): Extends operational Mach number range up to Mach 6.5. Specific thrust increases by 106 N/(kg/s) at Mach 2.5 (~3 Tesla, 2.9 kN) and by 263 N/(kg/s) at Mach 3.0 (~3.5 Tesla, 7.4 kN).
At 2200 K temperature limit (Figures 11 & 12): Extends operational range to Mach 7.0. Specific thrust increases by 79 N/(kg/s) at Mach 2.5 (2.5 Tesla, 2.2 kN), 213 N/(kg/s) at Mach 3.0 (3.75 Tesla, 5.9 kN), and 420 N/(kg/s) at Mach 3.5 (~4 Tesla, 11.8 kN thrust increase).

Conclusion & Future Plans

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 (up to Mach 7.0 at 2200 K combustion temperature limit), using magnetic fields between 1 and 5 Tesla and generator lengths between 1 and 10 m.

Benefits include:

Flow enthalpy into the combustor is reduced, allowing efficient addition of energy without exceeding turbine material temperature limits.
Applied electromagnetic body forces enhance off-design inlet performance and reduce total pressure losses.
Electrical power removed can be used for on-board vehicle systems or plasma flow control, while nozzle electromagnetic acceleration augments net thrust.

Future Plans:

Establish optimal operating conditions for a turbojet cycle transferring kinetic energy from inlet air (Mach reduction to 0.8) to downstream locations.
Establish interaction parameter and efficiency for kinetic-to-electrical energy conversion.
Employ Quasi 1-D MHD theory for inlet evaluations using experimentally determined conductivity and interaction parameters.
Conduct interfacing studies between MHD bypass generator, turbojet engine (Allison J-102), and MHD accelerator to ensure flow matching and prevent degradation at higher Mach numbers.

References

Hill, P.G., C.R. Peterson, ‘Mechanics and Thermodynamics of Propulsion,’ Addison-Wesley Publishing Co., Inc., 1965.
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.
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.
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).
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.
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.
J-102 packet includes engine specifications and engine performance envelope from Isaiah Blankson.

Standard Form 298 (Report Documentation Page)

Report Date: 01-12-2010 Report Type: Technical Memorandum Title: The Effect of Magnetohydrodynamic (MHD) Energy Bypass on Specific Thrust for a Supersonic Turbojet Engine Author: Benyo, Theresa, L. Performing Organization: NASA John H. Glenn Research Center at Lewis Field, Cleveland, Ohio 44135-3191 Performing Organization Report Number: E-17311 Work Unit Numbers: WBS 599489.02.07.03.07.02.04; 599489.02.07.03.04.03.01 Sponsoring Agency: NASA Washington, DC 20546-0001 Report Number: NASA/TM-2010-216734 Distribution: Unclassified-Unlimited, Subject Category 07 Subject Terms: Magnetohydrodynamic simulation; Thermodynamics; Jet thrust; Supersonic turbojet