A WAVE DISC ENGINE CONCEPT FOR MICRO POWER GENERATION

M. Vagani1, L. Pohořelský

2, G. Sun

1, D. Alemu

3, J.R. Lee

1, R.T. Kelly

1, T.J. Qualman

1,

S.A. Bonner1, D.E. Park

1, F. Iancu

1, P. Akbari

1, J. Piechna

4, and N. Müller

1

1Michigan State University, East Lansing, USA

2Czech Technical University in Prague, Prague, Czech Republic

3Addis Ababa University, Addis Ababa, Ethiopia

4Warsaw University of Technology, Warsaw, Poland

Abstract: Wave disc technology is emerging as a possible replacement for compressors and turbines in engines.

This paper presents a new engine concept, the Wave Disc Engine with internal combustion. This new engine

concept combines the advantages of (a) higher efficiency confined combustion with (b) the high power density

and low maintenance of continuous flow but (c) at a much lower unit cost due to its physical simplicity and

compactness. Furthermore, the geometry of the Wave Disc Engine is especially suited for microfabrication and

micro power generation. Theoretical validation of the engine has been performed using four simulation models. 1-

D and 2-D validations were completed with both in-house and commercial software.

Keywords: Wave Disc Engine, internal combustion, Humphrey cycle, power generation

INTRODUCTION The idea of direct energy exchange between two

media without using mechanical components such as

pistons or vaned impellers started in the early 1900s

[1]. The first functional device was developed in the

1940s when the Brown Boveri Company (now ABB)

designed a pressure-exchange wave rotor.

The wave rotor is a non-steady flow device that

uses shock waves to pressurize fluids by transferring

energy from a high-pressure flow to a low-pressure

flow in a series of channels. The wave rotor consists of

many axial channels in a rotating cylindrical drum,

usually driven by an external motor. For gas turbine

engine applications, the wave rotor employs the hot,

high pressure exhaust gas from combustion to generate

a shock wave that compresses the cooler, lower

pressure air received from the compressor. For car

engine applications, the wave rotor has been used as a

supercharger and was successfully commercialized by

Mazda Company in 1980s and 90s in the serial

production of diesel passenger cars [2].

The Wave Engine The wave engine consists of a wave rotor with

curved blades, used for compression of air and

expansion of exhaust gas, while producing shaft work.

It uses a steady-flow gas turbine type combustor. The

Ruston-Hornsby Turbine Company, in the UK,

developed one such engine in the mid-1950s [1]. This

wave engine, shown in Figure 1 (left), had a 230 mm

diameter and a 76 mm length. The engine worked

successfully for several hundred hours in a wide range

of operating conditions (from 3000 to 18,000 RPM)

and produced up to 26 kW at its design point with a

cycle peak temperature of 1070 K. Accidentally, the

engine was destroyed due to over-speeding from an

improperly connected fuel line, and the project was

canceled.

Figure 1. Assembly of successfully working wave

engine in axial wave rotor configuration [1](left) and

ABB wave rotor combustor cross section [3] (right)

The Wave Combustor The wave combustor is a wave rotor with

combustion occurring inside the rotor channels. This

produces a pressure rise during combustion, unlike a

typical steady-flow combustor used in gas turbines.

ABB and ETH Zurich commenced the design of a full

wave rotor with 36 axial combustor channels in 1992

[3]. Each channel had 165 mm length and 15 x 15 mm

cross section, shown in Figure 1 (right). The 200 mm

inner-diameter rotor was driven by an electric motor

capable of up to 5000 RPM. Spark-plug electric

ignition was used for initial start up. Auto ignition, for

continuous operation, was achieved by injecting hot

gas from the neighboring channels. The fuel injection

and ignition worked well and pressures of 9 bar were

obtained. The project was canceled in 1994, due to the

perception at the time that there was no profitable

market for a 100kW gas turbine unit.

PowerMEMS 2009, Washington DC, USA, December 1-4, 20090-9743611-5-1/PMEMS2009/$20©2009TRF 530

CONCEPT OF THE WAVE DISC ENGINE

WITH INTERNAL COMBUSTION The Wave Disc Engine (WDE) combines the

principles of the wave engine and wave combustor.

While wave rotors use axial flow, the WDE uses a

radial-flow wave rotor, or wave disc [4]. The wave

disc is particularly suited for microfabrication as it has

a simple extruded 2D geometry with a short depth.

The wave disc also allows for curved channels, which

will allow the rotor to extract energy from the flow.

The mechanical simplicity of the engine concept,

with only one rotating part allows it to be miniaturized

without many of the technical issues faced by other

small-scale gas turbine engines [4]. A starter-generator

could be built into the engine similar to that designed

by MIT for micro gas turbines [5].

The WDE, shown in Figure 2 utilizes a typical

engine cycle consisting of compression, combustion,

expansion with work extraction, and heat rejection to

the ambient atmosphere. The cycle however, occurs

completely in the curved disc channels. Using

shockwaves for compression reduces the inertia of the

hardware and promotes a rapid response to load

changes. The compression and expansion are achieved

through shockwaves and expansion waves and the

momentum of the flow is harnessed to drive the rotor.

Rotational

DirectionLoading

Compression

Shock Wave

Constant

Volume

Combustion

Jet

Propulsion

Reflected

Expansion

Wave

Compression

Shock Wave

Expansion

Wave

Scavenging

Fresh Air-Fuel Mixture

Burnt Exhaust Gas

Rotational

DirectionLoading

Compression

Shock Wave

Constant

Volume

Combustion

Jet

Propulsion

Reflected

Expansion

Wave

Compression

Shock Wave

Expansion

Wave

Scavenging

Fresh Air-Fuel Mixture

Burnt Exhaust Gas

Figure 2. Schematic engine model and cycle for a two-

cycle WDE

The schematic in Figure 3 depicts the working

cycle of the internal combustion WDE, briefly

described in the following four steps:

1) The cycle begins with the channel closed on both

sides and filled with a compressed air/fuel mixture.

Constant volume combustion takes place within the

channel, producing a pressure and temperature rise

during the combustion process.

2) As the disk rotates, the exhaust side of the channel

opens to ambient conditions. This sudden opening of

the channel creates an expansion wave propagating

towards the air fuel mixture inlet and scavenging

begins. Torque generation is produced by the fluid

tangential momentum at the outlet (jet propulsion) and

by the change in angular momentum in the channel

(turbomachinery principle).

Figure 3. Schematic for the internal combustion WDE,

incorporating combustion within the shock channels

3) When the inlet port opens the ingestion of fresh

fuel/air mixture into the channels begins. The

expansion wave created in step 2 draws in this mixture

and completes the scavenging process. Centrifugal

fluid forces on the rotating disk assist the scavenging

and loading processes.

4) After the outlet port is suddenly closed, a

“hammer shock” is generated by the deceleration of

the flow to zero velocity. The hammer shock

compresses the fresh air-fuel mixture. It is favorable to

close the inlet port when the hammer shock reaches it.

Another operating cycle starts with the ignition of the

air-fuel mixture (step 1).

Figure 4. Thermodynamic cycle of the WDE in

comparison with the gas turbine engine

Thermodynamically, the WDE operates on the

Humphrey cycle, where combustion ideally occurs at

constant volume, as shown in Figure 4. In the ideal

Brayton cycle for gas turbines, the heat addition occurs

at constant pressure. Additionally, the WDE is

periodically filled with fresh air, cooling the channel

wall temperature. Thus, the WDE can achieve a higher

cycle peak temperature than a typical gas turbine. As a

result, a WDE can be more efficient than a gas turbine

for comparable compression pressure ratios.

531

MATHEMATICAL MODELING AND

PRELIMINARY RESULTS

Ideal Cycle Efficiency of WDE The ideal cycle efficiency does not consider heat

losses across the channel walls, pressure losses during

admission and exhaust, and mechanical friction. It is

an efficiency that can be achieved in an adiabatic

frictionless engine operating with an ideal gas. 0.8

P2/P1

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Diesel

Brayton

Otto

Humphrey

η

0.8

P2/P1

0 5 10 15 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Diesel

Brayton

Otto

Humphrey

η

Figure 5. Thermal efficiencies of ideal

Humphrey, Brayton, Otto, and Diesel cycles as a

function of engine compression pressure ratios

As can be seen in Figure 5, the Humphrey cycle

has the highest efficiency when compared with all gas

power cycles. For instance, a WDE operating on the

Humphrey cycle can have an overall efficiency of 45%

for a compression pressure ratio of 10, assuming 10%

heat losses through the wall, 5% scavenging losses,

and 5% mechanical losses. The mechanical losses are

minimal, as it has only one rotating part.

To evaluate the concept and support the design of

a working WDE prototype, the engine was modeled

and analyzed using four numerical approaches. The

results are presented in the following sections.

t

Velocity

patterns

x

Gas/Air

Interface

t

Velocity

patterns

x

Gas/Air

Interface

t

Velocity

patterns

x

Gas/Air

Interface

t

Velocity

patterns

x

Gas/Air

Interface

Figure 6. WDE wave pattern computed by the

developed Quasi 1-D algebraic algorithm

Quasi 1-D Algebraic Algorithm An analytical algorithm was established to develop

an initial WDE porting geometry and a first estimate

of the flow velocities and wave propagation pattern in

the rotor, shown in Figure 6. It uses the gasdynamic

wave equations and the method of characteristics for

specified boundary conditions, including post-

combustion pressures and temperatures [6]. The

algorithm accounts for the effects of centrifugal force,

channel curvature, and work generated from angular

momentum.

1-D WDE Model in GT-POWER A 1-D model of the WDE was developed in the

commercially available GT-POWER, which has

successfully completed a 1-D wave rotor model [7].

The model describes pressure waves, combustion heat

release, work extraction, friction, heat exchange, and

throttling in the distribution ports during the opening

and closing phases of an individual rotor channel. The

1-D model wave disc engine has 18 channels, a disc

outer diameter of 15 cm, an inlet diameter of 6 cm and

an engine height of 3 cm. Combustion inside the

channel was modeled using the Wiebe heat release

function [8]. The GT-POWER model enables

optimization of the WDE geometry and power output,

using the Quasi 1-D code results as a starting point.

The Euler turbomachinery equation was used to

compute the power generation and modeled by

extracting the same amount from the energy

conservation equation. For this model engine, the

maximal predicted power output was 1.2 kW at 18,000

rpm.

Quasi 2-D CFD Code A Quasi 2-D CFD code was additionally

developed to confirm and improve on the results from

the Quasi 1-D algebraic algorithm. For this code, it is

assumed that the streamlines follow the profile of the

channel wall, so no parameters change over the

channel cross-section. The Wiebe function was again

used to model the heat generation due to combustion

[8].

The 4th order MacCormack Scheme was

employed to solve the continuity equation, Navier-

Stokes equations and the energy equation. The code

calculates the port timing by tracing the waves and the

exhaust scavenging. In addition, it yields velocity,

pressure, density and temperature profiles in the

channel, power generation and engine efficiency and

draws the p-v and T-s diagrams for thermodynamic

analysis.

532

The simulation

results are presented for

a disc of 10 mm outer

diameter, 6 mm inner

diameter, rotating at

200,000 rpm. Figure 7

shows the shape and

locations of the ports,

and Figure 8 the p-v

and T-s diagrams. The

power generation was

found to be 1.189 kW

and the efficiency

0.2647.

0 2 4 6 80

0.5

1

1.5

2

2.5

3x 10

6

Specific volume (kg/m3)

Pressure (Pa)

p-v diagram

-500 0 500 1000 1500 20000

1000

2000

3000

4000

5000

Specific entropy (kJ/(kg*K))

Temperature (K)

T-s diagram

Figure 8. p-v and T-s diagrams given by Q2D code

2-D CFD FLUENT Code Numerical CFD simulations were also performed

using FLUENT 6.2. The 2-D solver was used to model

the flow within the wave disc. In order to model the

wave disc engine, the heat addition in the channels

was achieved by patching a small area of the channel,

the “combustion zone” to the pressure and temperature

expected after combustion. The resulting pressure and

temperature profiles are presented in Figure 9 and

Figure 10.

The FLUENT pressure profiles show that the

pressure and temperature in the channel equalizes

before the exhaust port opens. They confirm that the

wave pattern in the rotor matches the predicted wave

pattern. It also shows that the exhaust gases are

completely scavenged before the beginning of each

cycle. The scavenging actually happens fast enough

that it may be beneficial to close the exhaust port

sooner. This will increase the pressure created by the

“hammer shock” after the closing of the port.

CONCLUSIONS Four separate numerical methods were used to

model the Wave Disc Engine. Each of the preliminary

results confirms that the concept of the engine is

feasible. Further investigations will determine possible

improvements to the engine before the concept is

tested with an experimental prototype.

Rotational

Direction

Temperature [K]

Air/Fuel

Mix Inlet

Scavenging

Exhaust

Outlet

Start of

Combustion

Rotational

Direction

Temperature [K]

Air/Fuel

Mix Inlet

Scavenging

Exhaust

Outlet

Start of

Combustion

Figure 9: FLUENT temperature distribution results

for two cycle WDE

Rotational

Direction

Pressure [Pa]

Air/Fuel

Mix Inlet

Exhaust

Outlet

Start of

Combustion

Compression

Shockwave

Expansion

Wave

Rotational

Direction

Pressure [Pa]

Air/Fuel

Mix Inlet

Exhaust

Outlet

Start of

Combustion

Compression

Shockwave

Expansion

Wave

Figure 10: FLUENT pressure distribution results for

two cycle WDE

REFERENCES [1] Akbari P., Nalim M. R., Mueller N., 2006, “A

Review of Wave Rotor Technology and Its

Applications.” ASME J. of Enineering. for Gas

Turbines and Power, 128-4, 717-735

[2] Pohořelský L., Obernesser P., et al., 2007, “1-D

Model and Experimental Tests of Pressure Wave

Supercharger.” ASME IMECE2007-43427

[3] Akbari P. and Nalim M. R., 2009, “Review of

Recent Developments in Wave Rotor

Combustion Technology.” J. of Propulsion and

Power, 25-4, 833-844

[4] Iancu F., Akbari P., and Müller N., 2004,

"Feasibility Study of Integrating Four-Port Wave

Rotors into Ultra-Micro Gas Turbines." 40th

Joint Propulsion Conference, AIAA 2004-3581

[5] Epstein A.H., 2003, “Millimeter-scale, MEMS

gas turbine engines.” Proc. of ASME Turbo

Expo, GT-2003-38866

[6] Pohořelský L., Sané P. A., et al., 2008, "Wave

Rotor Design Procedure for Gas Turbine Engine

Enhancement." Proc. of ASME Turbo Expo

2008, GT-2008-51354

[7] Pohořelský L., Macek J., Polašek M., Vítek, O.,

2004, “Simulation of a COMPREX Pressure

Exchanger in a 1-D Code.” SAE International

Paper 2004-01-1000, 13

[8] Heywood J.B., 1988, Internal Combustion

Engine Fundamentals, McGraw-Hill

Figure 7. Geometric design

of the WDE calculated by

the Quasi 2-D code

533