Rotary wave-ejector enhanced pulse detonation engine - M. R. Nalim.pdf

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Shock Waves (2012) 22:2338

DOI 10.1007/s00193-011-0348-5

ORIGINAL ARTICLE

Rotary wave-ejector enhanced pulse detonation engine

M. R. Nalim

Z. A. Izzy

P. Akbari

Received: 27 December 2010 / Revised: 7 June 2011 / Accepted: 24 August 2011 / Published online: 3 December 2011

Springer-Verlag 2011

Abstract The use of a non-steady ejector based on wave

rotor technology is modeled for pulse detonation engineperformance improvement and for compatibility with tur-

bomachinery components in hybrid propulsion systems. The

rotary wave ejector device integrates a pulse detonation pro-

cess with an efficient momentum transfer process in spe-

cially shaped channels of a single wave-rotor component.

In this paper, a quasi-one-dimensional numerical model is

developed to help design the basic geometry and operating

parameters of the device. The unsteady combustion and flow

processes are simulated and compared with a baseline PDE

without ejector enhancement. A preliminary performance

assessment is presented for the wave ejector configuration,

considering theeffect of keygeometricparameters, which are

selected for high specific impulse. It is shown that the rotary

wave ejector concept has significant potential for thrust aug-

mentation relative to a basic pulse detonation engine.

Keywords Wave ejector Wave rotor

Pulse detonation engine Shock waves

1 Introduction

Considerable work has been done on the development of the

pulse detonation engine (PDE) in the past decades, focused

Communicated by F. Lu.

M. R. Nalim Z. A. Izzy

Department of Mechanical Engineering,

Indiana University-Purdue University Indianapolis (IUPUI),

Indianapolis, IN 46202-5132, USA

P. Akbari (B)

Department of Mechanical Engineering, Columbia University,

New York, NY 10027, USA

e-mail: [email protected]

on many aspects of the PDE including ignition and detona-

tioninitiation,fuelmixing, valving,intake, andnozzle design[1]. The application of a PDE was usually envisioned for

aircraft and missile propulsion [24] when used as a direct

thrust device, taking advantage of a nearly constant-volume

combustion process and gas acceleration in the PDE tube.

A single-tube PDE produces intermittent high-temperature

high-velocity jets of exhaust, separated by longer periods of

dribbling or no outflow. This concentration of momentum

and energy stems from the fundamental mechanics of det-

onation and the mixture detonability limits, and causes low

propulsive efficiency, diminishing the benefits of high ther-

mal efficiency. The use of an external ejector to redistribute

momentum to a larger mass flow is an effective and rec-

ognized remedy [5,6], boosting thrust and specific impulse

significantly. MostPDE configurations alsouse multiple det-

onation tubes [79] that breathe and fire sequentially, using

a rotary valve or other type of valving. This tends to reduce

inlet and nozzle non-steadiness and flow losses, but does not

eliminate flow stagnation in individual feed distribution and

exhaust collection ducts.

Multi-tube PDE technology could also benefit gas turbine

engines [1013] inhybrid-PDE systems byreplacingthe con-

ventional pressure-loss combustor with a pressure-gain PDE

combustor. However, the detonation-generatedpressure fluc-

tuations and peak temperatures are generally deleterious to

turbines, even while high average gas pressure is desirable.

Therefore, the highly concentrated and intermittent energy

of the PDE exhaust compromises the fundamental thermo-

dynamic superiority of nearly constant-volume combustion.

Multi-tube PDE configurations also typically need multiple

high-repetition detonation initiation devices, and complex,

high-speed valving for purge gas, fuel, oxidant (or enrich-

ment). Furthermore,cyclically loaded valve partsor bearings

transmit pressure and thrust, which reduces durability by

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24 M. R. Nalim et al.

creating vibration and noise. The concept described here

addresses these issues with the innovative approach of rotat-

ing a drum of multiple PDE tubes. It is applicable to hybrid-

PDE systems with downstream components that impose

temperature and uniformity requirements on the PDE, and

to direct thrust augmentation at moderate flight speeds.

2 Rotary PDE: wave rotor concept

The principle of the present concept is to rotate the multi-

ple detonation tubes and keep all other parts stationary under

continuous flow [14]. Such a device, called a rotary PDE

is one form of a wave-rotor combustor (WRC) [1517] that

takes advantage of automatic valving at each end and cre-

ates a confined combustion process for the rotating tubes, as

schematically shown in Fig. 1. In this figure, relative motion

betweencombustors andturbomachinerycomponentsaccom-

plishes sequential filling, firing, and purging in a WRC, as

illustrated notionally by an upward moving direction. In a

periodic operation, each combustor alignswith theflow from

the compressor and flow to the turbine with a time lag set

by rotational speed. At any moment, some combustors pass

flow with thecompressor andturbine, while othersareclosed

and firing under volumetric confinement. Wave rotors were

originally employed for exchanging pressures between dif-

ferentfluids in a more complex geometry calledthepressure-

exchange wave rotor [1820]. They have been successfully

operated as superchargers for diesel engines [21], a shock-

wave repeater for a high-enthalpy wind tunnel [22], and have

Combustor 4

contains high pressure hot gas

Combustor 1

filling low pressure air

Compressor

Turbine

Combustor 2

contains low pressure air + fuel

Combustor 3constant volume combustion

Combustor 5

discharging high pressure gas

Fig. 1 Conceptual layout for a WRC

beentested for propulsionandpower generationsystems [23]

in pressure-exchange and combuster versions.

The geometry of a WRC is illustrated in Fig. 2, show-

ing the inlet and exit ports and the end walls functioning as

valves when the clearance gaps between the rotational tubes

and stationary end walls (exaggerated here) are tightly con-

trolled to minimize leakage. As each rotating channel aligns

with the inlet port, it receives reactant mixture. After bothends of each channel are closed, combustion occurs through

an igniter mounted at one or both end walls. Finally, the out-

let port discharges the burned gas as the channels rotate past

the partial-annular outlet port. The length and height of com-

bustion channels, the placement and circumferential size of

the inlet and exit ports, and the rotational speed of the rotor

are optimally designed to control the cyclic flow processes,

internal wave processes, and confined combustion.

Figure 3 is a more detailed illustration of Fig. 1, being

specificallya developed (unwrapped) view of the rotaryPDE

where the circular motion of the channels is represented on

paper by a vertical translatory motion. The hatched shad-ing on the each side of the channels represent end walls that

establish the portion of the cycle over which the inlet and

outlet ports are closed. The relative locations of the inlet and

outlet ports connected to the turbomachinery components

will be shown to be related by pressure wave motion. Pos-

sible locations of the fuel injectors and the ignition initiator

are also depicted. The inlet port is divided into segments by

a few partitions and fuel is added to the incoming air only

through a few of these segments. The first segment prefera-

bly introduces only air into the inlet forming a non-combus-

tible region within the respective chamber. This provides a

buffer from previously existinghot gases in thechannel,thus,

inhibiting premature ignition.Each fuel injector is capable of

introducing fuel at a different rate, leading to stratification of

combustible gases within the rotating chambers. Such strati-

fication aids in establishing proper conditions for detonative

combustion [24]. While there are several possible methods

to ignite the combustible gas, the ignition initiator shown is

a combustion-torch ignition method, which simply injects a

hot gas into each channel [25]. The complicated gasdynamic

wave processes are simply represented via schematic waves

and will be discussed in detail in the next sections.

3 Rotary wave ejector concept

While the rotary PDE obtains internally the same funda-

mental detonation process and combustion stoichiometry as

other PDEs, it would have essentially steady inlet and noz-

zle flows with relatively little flow stagnation or pulsation,

high-frequency operation without pulsed ignition, no mov-

ing parts that transmit thrust, and automatic valveless purg-

ing and mixture stratification as needed. While numerical

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Rotary wave-ejector enhanced pulse detonation engine 25

End-Wall Seal Plates

Igniter

Inflow (air + fuel)

From Compressor

Outflow to

TurbineInlet Duct

Rotation

Fig. 2 Schematic of a WRC or rotary PDE

Fuel

Air

Rotation

Exhaust

Expansion wave

Shock

Detonation

Fig. 3 Schematic of exit-valved rotary PDE with synchronized wave

motion

simulations [2630] have indicated a relatively uniform exit

profile for such a configuration, overall outflow temperature

and velocity remain high, as with any PDE. An integrated

ejector can improve the propulsive efficiency of a direct-

thrust PDE, and lower the output temperature of a gas-gen-

erator PDE [5,6]. Ejectors have been widely used for aug-

menting thrust in propulsion applications. In an ejector, the

energy and momentum of a driving primary fluid are redis-

tributed by entrainment of a driven secondary fluid. The sec-

ondary flow is drawn into a duct with primary fluid usually

flowing in parallel with the incoming jet as schematically

shown in Fig. 4. This action distributes energy and momen-

tum to a larger mass, resulting in lower overall exit velocity

and greater propulsive efficiency and thrust. While most past

work focused on steady-flow ejectors designs [31,32], inter-

est in non-steady ejectors has grown to address the needs of

PDE and similar non-steady flow thrusters. Non-steady ejec-

tors that accomplish work exchange between fluids by the

action of pressure forces are potentially more efficient than

steady ejectors that rely on dissipative viscous momentum

exchange alone [33]. They have been designed and tested

for various configurations of PDEs [5,6,34] and pulsejets

[3538]. A typical non-steady ejector consists of a duct of

Fig. 4 Schematic of an ejector

larger diameter at the exit of the non-steady device, designed

to accept the intermittent exhaust and entrain the secondary

flow from a bypass duct or the atmosphere. Such an ejector

harnesses theenergyandmomentum of detonation processes

to maximize performance. A significant challenge for PDE-

driven ejectors is that the strong shock waves driven out of

the exhaust disrupt the secondary flow and tend to propa-

gate upstream into the bypass duct, which negates thrust.

The concept of a rotary wave ejector combined with a rotary

PDE introduced here canavoid this problem [3941]. Asdis-

cussedin this article, the rotarywave ejector effectivelyshuts

in the shock pressure from the secondary flow and allows the

ejector to maximize thrust augmentation.

A rotary-wave-ejector PDE can be visualized as a rotary

wave ejector longitudinally integrated with a particular con-

figuration of a rotary PDE with varying radial height of the

rotor channels in the middle section of the rotor. Air flow that

bypasses the primary inlet enters in the middle section, pre-

dominantly in axial direction. Figure 5 shows four sketched

views of a rotary PDE integrated with a rotary wave ejec-

tor: (a) partially shrouded rotor without housing or ducts, (b)

the housing and primary inlet ducting for the rotor, (c) front

view of assembled engine, and (d) rear view of assembled

engine. Therotor and itschannels consist of three main parts:

the detonation channels (narrow forward section), partially

or completely unshrouded flow merging channels (transition

middle section), and pressure-exchange channels (wide rear

section). The channels are continuous through the three sec-

tions,and thefrontand rear sectionsarecompletelyshrouded.

The transition section and the aft sections have as many or

fewer channels that have higher radial height and circum-

ferential width than the forward ones. The transition middle

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Fig. 5 Multiple views of rotary

wave ejector PDE

section joins the forward combustion passages to the rear

combustion channels and communicates with a source of

bypass air to provide a rotary wave ejector. In the transition

section, the height of channels increase gradually along the

length of the rotor and it is mostly or completely unshrouded

to allow the secondary flow to enter the transition section. In

the figure, there are two sets of inlet ducts from which the pri-

mary airfuel mixture is introduced to the forward section.

This implies two cycles of operation over one revolution,

which is more suitable for balancing mechanical loads and

engine applications. The inlet port has a helical shape to pro-

vide required rotational velocity to the rotor. The bypass or

secondary air inlet duct is not shown for clarity. Figure 6

shows schematic side view of the assembly where the com-

busted gases flow from the forward combustion passages

through the transitional and rear passages to an exhaust port.

Possible variations of the rotary wave ejector PDE concept

are described by Nalim [42].

Thesequenceof combustion events occurringin oneoper-

ating cycle of the rotary wave ejector is illustrated in Fig. 7,

for a representative combustion chamber of Fig. 3 at differ-

ent stages of its rotation. Starting after closure of the inlet

port, the forward channel contains detonable mixture, while

the remainder of the chamber contains only air (I). Here,

employing optional partitions in the inlet duct may provide

a stratified reactant mixture and an air buffer layer preceding

the detonable mixture in the channels as discussed in Fig. 3.

Detonation is initiated at the inlet end wall at left (II), by a

presumedrapidmechanism. A detonationwavemoves super-

sonically, pressurizing and accelerating the burned gas until

ForwardSection

Transition Section

Rear

Section

Bypass Air

Inflow (air + fuel)

Outflow (burned gas)

Fig. 6 Schematic side view of rotary wave ejector PDE (from [42])

the detonation wave reaches non-combustible mixture and

converts to a shock wave (III). Propagating the shock wave

through the large area change of the transition section causes

first expansion waves formedand travel back to the inlet side,

while the shock wave continues to propagate to the exit side.

Gas is expelled through the open exit end, while the shock

wave reflects as a secondary expansion wave that propagates

towards the inlet end (IV). Meanwhile, the first expansion

waves arrive at the closed inlet end and reflect off the wall,

reducing the rotor pressure sufficiently for the primary inlet

to be opened, admitting a buffer of unfueled air followed by

fresh detonable mixture. Concurrently, the secondary expan-

sion wavearrivesat theinletendand is reflected back towards

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Fuel/Air Mixture

Fresh AirBurned Gases

Detonation

I

II

III

IV

V

VI

I

II

III

IV

V

VI

Exhaust

Shock WaveFirst Expansion Fans

Hammer Shock

Bypass Flow

First Reflected Expansion FansSecond Expansion Fans

2nd Reflected Expansion Fans

Time

Fig. 7 Operation of rotary wave ejector PDE cycle, corresponding to

Fig. 3

the outlet end forming a second reflected wave. This expan-

sion wave reduces pressure in the transition section, further

which byrotationcomes into communication with thebypass

airduct (not shown), admittingbypass airinto therear section

now also at low pressure (V). At various times, the primary

andsecondary inlet ports areclosedby rotation,avoidingany

flow reversal as local pressures change. The exit port may

also be closed when necessary, whereupon a hammer shock

is generated at the exit wall (VI). The charged combustionchamber is then ready for another operating cycle.

It is expected that the shock wave and its reflections pro-

vide thedominantmechanismfor entrainmentofandmomen-

tum transfer to bypass air. This is in contrast with steady and

non-steady ejectors that rely on viscous shear layers and vor-

tex formation for their working mechanism. In addition, it

is known that the macroscopic gasdynamics of detonations

is well predicted by a one-dimensional (ZND) model. With

this assumption, thebasic fluid dynamics anddetonation pro-

cesses of the rotary wave ejector PDE can be estimated well

by a quasi-one-dimensional gasdynamic model that includes

the effects of detonative combustion, secondaryair injection,and area variation of the channel. Such a model is described

next, in which important multi-dimensional effects are mod-

eled as source terms in the governing equations.

4 Computational methodology

The modeling presented here uses an experimentally vali-

dated wave rotor simulation code under the assumption of

quasi-one-dimensional flow of an ideal gas. The numeri-

cal code, originally developed [4345] at NASA has been

applied to a broad range of non-unsteady flow devices such

as pressure dividers [46], wave augmented diffusers [47],

four-port pressure-exchange wave rotors [48,49], pulsejets

[36,50], premixed gas turbine combustors [51,52], PDEs

[29,30,5355], andcombustionwave rotors[24,26,56].Some

analyses considered uniform cross-section chambers, andsome considered area variation [47,53,57]. Details of the

code including algorithm, numerical approach, loss mod-

eling, and boundary condition implementations have been

described in the above references. A brief description

emphasizing aspects relevant to this study is provided

here.

The code simulates flow in one channel of a wave rotor as

it passesover various ports.Ports are specified by their repre-

sentative pressures, temperatures, composition, and theircir-

cumferential locations on the wave rotor casing. To simulate

theoperation process of PDE-drivenrotarywaveejectors,the

original code was modified to model mass addition into thetransition channels (middle section). Gradual area variation

of the middle section is assumed in a sinusoidal form. The

type and number of boundary conditions required are based

on the direction and Mach number of flow and are discussed

in detail by Paxson [43]. For subsonic flow, inflow requires

specification of upstream stagnation conditions, and outflow

requires downstream pressure. For reacting gases, the code

solvesone-dimensionalflow equationsalong withthespecies

equation for fuel represented by a reaction progress variable

(z), varying from unity for pure reactants to zero (0 z 1)

for products as combustion occurs. The combustion process

is represented by a simple, one-step, premixed reaction with

calorically perfect gas, with constant specific heat ratio ( ).

Thecombustioninitiation is simulatedby exposingthetermi-

nal computational cell to a high-pressure high-temperature

gas injection port. The code is capable of modeling both def-

lagration and detonation combustion modes. A turbulence

model in the form of an eddy diffusivity is activated when

deflagration is considered. The rate of reaction is assumed

zero below the threshold temperature (Tign). Building on the

earlier non-reacting code [46,48], all major loss mechanisms

in combustion wave rotors, including friction, heat transfer,

leakage, partial (gradual) channel opening/closing, mixing

phenomena in the ports, and flow incidence, are available

in the code as sub-models, but require dimensional infor-

mation that is not considered in the current work. For sim-

plicity, several assumptions and simplifications are used to

model the rotary PDE-driven rotary wave ejector as listed

below:

The flow is quasi-one-dimensional, adiabatic, inviscid,

and is everywhere a pure calorically perfect gas, with

specific heat ratio = 1.3.

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Wall viscous drag, heat transfer, the interaction effect

among channels, circumferentialvelocity of the rotor and

leakage at the gaps are neglected in the calculations.

Thechannel ends areopenedandclosedvery rapidly with

no partial-opening losses, presuming a large number of

channels.

For generality, a particular fuel is not specified; the adia-

batic flame temperature fora stoichiometric fuelair mix-ture is 9.35 times primary inlet stagnation temperature,

The detonation initiation occurs very rapidly upon expo-

sure of the channel to a high-pressure, high-temperature

gas, and the deflagration to detonation transient (DDT)

process is not included.

Thechannels cross sections areassumed rectangular with

constant mean width, but varying height.

Stagnation pressure, and stagnation temperature are

assumed known for primary and secondary inlets, while

static pressure is assumed known for the outlet. If flow

reversal occurs at the outlet, gas properties are estimated

from conditions of thegasoutflow preceding thereversal.

The code uses a shock-capturing flow solver to integrate the

governing equations of mass, momentum, energy, and spe-

cies. The non-dimensional equations are expressed in vector

format with conserved variable w, flux F and source term S

defined alongside:

w

t+

F(w)

x= S(w) (1)

where:

w =

H

uHpH

(1)+

Hu2

2+ Hzqc

zH

(2)

F =

uHpH

+ Hu2

uH

p(1)

+u2

2+ zqc

uHz

(3)

S(w,x) =

urel

p dHdx + u2rel cos

urel

Tcav1

zK0

1, Ti > Tign0, Ti > Tign

(4)

Non-dimensionalization of pressure (p), density (), and

velocity (u) is based on a reference statep, , and sound

speed a, while channel height, H, and distance x are based

on total rotor length, L, and timebasedon L/a. The specific

heat ratio, and specific heat of reactionqc areassumed con-

stants, and internal energy is expressed as 11

p

.

The source vector S(w,x) includes contributions from

entrainment of secondary flow, area variation, and combus-

tion. Other source terms present in the original code and

deactivated in thepresent study arenot shown here: turbulent

eddy diffusion, wall viscous forces, and wall heat transfer,

and a deflagrative combustion rate model. The secondary air

flow is assumed to enter a specified section of the channel

from a stagnation cavity at pressure Pcav, temperature Tcav,

at a specified incidence angle . The inflow velocity of the

secondary flow urel is computed from isentropic expansion

to the local channel pressure, and the coefficient is the

projection of the secondary flow direction on the local chan-

nel surface orientation. The cosine factor in the momentum

equation captures the axial component of momentum from

the secondary flow, thus taking a loss on the kinetic energy

of the radial component of the flow. The detonative combus-

tion is represented by a finite-rate, single-step reaction, with

a reaction rate constant K0, when a threshold ignition tem-

perature Tign is exceeded. Based on prior experience with

detonation simulations [24], K0 = 100 and Tign = 2.5 were

set,withno significant sensitivity of performance predictions

to these small variations of values for the grid spacing used.

The equations are numerically integrated using a Lax

Wendroff scheme that utilizes Roes approximate Riemann

solver [43]. Second-order central differencing is applied to

derivatives in thesource terms.Previous work using this code

predicted key gas dynamic effects with a grid of 1050 cells,

or fewer [46,48]. Grid sensitivity tests specifically for det-

onative combustion computations have indicated [26] that

detonation speed and cycle performance measures arenearly

independent of grid size varied from 50 to 200, provided the

solution are converged, but peak pressure may vary. Wave

speed accuracy is important for valve timing andcyclic oper-

ation. Real detonation structure is fundamentally three-

dimensional and cannot be captured in this one-dimensional

numerical model, which is intended to predict the conse-

quent gasdynamics and system performance without sensi-

tivity to local detonation structure. The von Neumann peak

pressure of the classical one-dimensional detonation model

is approached with fine grids and large K0, but there is no

significant correlation of performance predictions with peak

pressure. Grid sensitivity tests for the typical simulations

of this study are presented below after presentations of the

results.

Paxson andLindau[57] used this code to study waverotor

flowswith differentchannel heightprofiles andcomparedthe

results with both the exact solutions and two-dimensional

unsteady CFD results. Their results justify the use of this

quasi-one-dimensional code for channel height ratio used

here in the range of 1.22.0.

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5 Performance prediction

In this section, modeling andanalysisof PDEs with andwith-

out rotarywave ejectors are presented. First, simulations will

be presented (Sect. 5.1) for a rotary PDE (no mass addition

and no area variation) with and without exit valve to ver-

ify simple PDE simulation. This discussion will also demon-

strate theadvantageof incorporating an exit valve to a simplePDE, which is much easier in the rotating case. In Sect. 5.2,

a particular PDE cycle will be selected as the baseline engine

for benchmarking theperformance of the rotary wave ejector

PDE. Next, simulations performed for a rotary PDE-driven

ejector without and with an exit valve will be demonstrated

(Sects. 5.3 and 5.4). Finally, preliminary performance eval-

uation of rotary wave ejector PDE without an exit valve is

presented (Sect. 5.5) in terms of calculated specific impulse

and pressure gain, and comparative performance measures

are discussed. Detailed parametric investigation and design

are presented in Ref. [58,59].

5.1 PDE cycle without and with exit valve

The first results presented here are based on a previous study

[30] investigating the flow field of rotary PDEs of a partic-

ular design, for illustration of major features. The rotor has

20 channels; each has a length of 77.5 cm with height and

width of about 6.35 cm. It operates under rotational speed

of 4,100 revolutions per minute ( f = 68 Hz) with inlet gas

pressure of 1.43 atm. Configurations without and with an

exit valve were considered, as shown in the top and bottom

of Fig. 8, respectively, in plots of key non-dimensional gas

properties in a representative channel, as a function of time

over one converged cycle of operation. A converged solu-

tion is defined as the situation that after several cycles of

time-marching computation, the wave pattern and operation

process will be very closely the same for successive cycles.

Velocity profiles in the inlet (blue line) and exit planes (red

lines) are shown on the leftmost plots as functions of time.

The three xt contour plots on the right show temperature,

pressure (in logarithmic scale), and fuel concentration as a

function of time (vertical axis) and position (horizontal) in

the channel frame of reference. The color scheme represents

lowest values in blue and highest in red, for non-dimensional

quantities shown.The white stripson the left sidesof thetem-

perature plots represent the portion of the cycle over which

the inlet and outlet ports are closed (end walls). The loca-

tion of detonation initiator is shown with a black arrow on

the top left side of the temperature plots. In these scenar-

ios, the air/fuel mixture is detonated directly when channel

gas is exposed briefly to the small high-pressure high-tem-

perature ignition gas port placed after closing the inlet port,

as described before. Typically, the mass of gas injected is

less than 1% if the total mass flow. It is assumed that the

mixture in the channel is detonable for the channel size and

conditions. There is evidence that hot gas injection is a fea-

sible direct method of detonation initiation; other methods

like spark ignition may be used if sufficient time is provided

for deflagration to detonation transition (DDT), but is not

considered here for ejector-enhanced and conventional PDE

(baseline)simulations.DDTprocessesscale accordingto tur-

bulent and multi-dimensional flow physics that are beyondthe models used here, and must beshort relativeto the overall

time of the cycle gas dynamics. This assumption simplifies

the assessment of ejector performance.

For the configuration without an exit valve (top of Fig. 8),

the exit velocity plot (red dashed line) indicates a signifi-

cantly non-uniform profile with intermittent flow reversal.

The inlet velocity (blue full line) shows gradual velocity

change during the partially open period, considered in this

particular case. Note the small peak due to the detonation

initiator. The inlet port opens when the channel pressure has

fallen below the inlet port pressure, admitting cooler fresh

air followed by the detonable mixture, as seen in the temper-ature and fuel fraction plots. As the inflowing gas is stopped

by closing the inlet, it generates an expansion wave that

depresses thechannel pressure (circled region in the pressure

plot), with consequent loss of thermodynamic performance.

Immediately following initiation, the detonation wave con-

sumes the fuel rapidly and overtakes the expansion wave,

as seen in the temperature, pressure, and fuel concentra-

tion plots. The detonation wave becomes a shock wave upon

reaching non-fueled air. The temperature plot also indicates

the movement of the contact interface between hot gas in the

channels and fresh cold mixture received at the inlet port.

For the exit-valved rotary PDE (bottom), portions of the

exit end are covered by an end wall where exit velocity is

expected to be low. The detonation initiator is located such

that the detonation wave does not hit the exit end wall, and

create additionalshock reflections. Thedetonation-generated

shock wave reflects at the open but choked exhaust port as

a reflected shock wave. Relatively more uniform velocity

profiles are seen at the exhaust port, with no flow rever-

sal. Further, by closing the exit end wall, a hammer shock

wave is generated inside the rotor channels that stops the

inflow and favorably increases the pressure and temperature

of the detonable mixture, in contrast to the pressure drop in

the previous case. Because this pre-compression wave stops

the channel gas motion, no further expansion wave is gener-

ated when the inlet port closes. This causes the exit-valved

cycle to have significantly better thermodynamic performa-

nce. More details of these two casesareavailable in Ref. [30].

5.2 Baseline PDE cycle

For consistent comparison with rotary wave ejector designs,

another particular and typical PDE cyclewith no exit valving

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Fig. 8 Flow field of rotary PDE without, top, and with exit valve, bottom, (from [30])

is selected as a baseline cycle. Such a rotary PDE is assumed,like all other rotary wave ejector PDE designs discussed

here, to have a sufficiently large number of channels that the

inflowsandoutflows areapproximatelysteady, althoughgen-

erally not uniform, This baseline allows self-consistency in

the analysis of rotary PDE designs, and avoids comparisons

among the many different types of valving provided in var-

ious stationary PDE designs. To provide a baseline cycle of

this type with a high performance, care was taken to time the

inlet valveto createa channel wavepattern that avoids a com-

pression wave upon opening the inlet port, or an expansionwave upon closing the inlet port, or any backflow. This maxi-

mizes the efficiency of thefilling process. A minimal amount

of purge air is supplied for the first one-fifth of the inlet open

time. Figure 9 indicates 40 wave diagrams and computed

Mach number and pressures at the inlet and exit planes for

two successive cycles of the baseline cycle, illustrating con-

verged solution on a repeating cycle. Based on the desired

rotor frequencyand adequate time fora complete combustion

process, the cycle time is set to 4.8, non-dimensionalized by

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-1 0 1 214

15

16

17

18

19

20

21

22

23

24

Mach No

Time

InletOutlet

-0.5 0 0.5 1 1.514

15

16

17

18

19

20

21

22

23

24

Log Pressure

InletOutlet

Inlet

Exit

Inlet

Fig. 9 Flow field of baseline PDE without exit valve (from [40])

the reference transit time. Ignition occurs at the beginning of

each cycle.

The specific impulse for the baseline cycle is calculated

to be 1.11 a/s, where a is the reference state speed of

sound, s is the stoichiometric fuelair ratio, and the con-

stant specific heat ratio is = 1.3. For sea-level atmospheric

inlet with a = 345 m/s and typical hydrocarbon fuel with

s = 15,this gives a baselinecycle Isp of1,510 s.It is empha-

sized that this value is based on homogenization of the out-

flow feeding a nozzle, and thus reflects pressure gain rather

than momentum change in the PDE. In contrast, many PDE

performance estimates are based on the raw time-unsteady

momentum and pressure balance of a single tube or multiple

tubes without regard to the need for steady flow and homo-

geneity in a flow supplied to a jet nozzle or turbine.

5.3 Rotary wave ejector PDE cycle with equal pressure

inlets and without exit valve

In this section, selected simulations of the rotary wave ejec-

tor rotary PDE are presented. Total pressures and tempera-

tures of the primary and bypass inlet ports are all at standard

atmospheric conditions. Geometric and timing parameters

are set based on preliminary experience to assure detonation

combustion within channels, but detailed parametric investi-

gation can be found in Ref. [58,59] where the potential for

further improvements by geometric parameter optimization

is indicated. The channel height ratio between the rear and

forward sections is set at 2.0, with a smooth sinusoidal tran-

sition from the small to the larger diameter. The bypass duct

start and end angles in the radial plane are set at 30 as illus-

trated in Fig. 10 where L is the rotor total length and H1 is

the forward combustion channel height.

Figure 11 presents [3941] simulations of a rotary wave

ejector PDE without an exit valve where the outlet port

Bypass Air

Primary Air

andFuel

2

1

H1H2

X1

X2

SX1

SX2

Fuel

H1H2

X1

Passage Outflow Height, H2 = 2.0 H1

Area Transition Start Location, X1 = 0.2 LArea Transition End Location, X2 = 0.5 L

Secondary Duct Start Location, SX1 = 0.3 L

Secondary Duct End Location, SX2 = 0.6 LSecondary Duct Start Angle, 1 = 30

Secondary Duct End Angle, 2 = 30

Fig. 10 Dimensions used for simulations (from [3941])

remains open for the entire cycle at one atmosphere static

pressure. Appropriate boundary conditions and time is pro-

vided for each of the phases of operation described in Fig. 7.

The non-dimensional cycle time of 2.95 and other timings

appear to be shorter only because they are referenced to the

nominal wave transit time for the entire rotor length, longer

than the detonation section. The primary inlet port is parti-

tioned into five sectors of selected circumferential width, to

allow non-uniform mixtures. Typically, the first sector was

left unfueled to provide a non-combustible buffer, and had a

width of 15% of the inlet.

As shown in the Mach number plot, the primary inlet port

remains open from time 1.0 to 2.3 (blue full line). In the

exit flow (red dashed line), a short duration of backflow is

observed in a highly non-uniform flow. The pressure pro-

file indicates that the channel pressure during the primary

123


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-0.5 0 0.5 1 1.50

0.5

1

1.5

2

2.5

3

Mach No

Tim

e

Inlet

Outlet

-0.5 0 0.5 10

0.5

1

1.5

2

2.5

3

Log Pressure

Inlet

Outlet

Inlet

Exit

Fig. 11 Flow field of rotary PDE without exit valve (from [3941])

inlet port opening is belowatmosphere, as required to receive

the inlet flow at the forward section. The sub-atmospheric

pressure is the outcome of reflected expansion waves as dis-

cussed in Fig. 7. The peak pressure at the outflow indicatestheshock wave leaving therotor. Thetrajectory of detonation

wave and transmitted shock wave appears sharply near the

bottom of the pressure xtplot.

The significant feature of the rotary wave ejector is the

entrainment of fresh air in the transition section, with the

bypass inlet port located at non-dimensional axial location

0.30.55. This is seen most clearly in the temperature plot,

which shows the initial injection of colder secondary air

(dark/blue) beginning about time 1.0 along this region. The

secondary flow terminates at time 2.6, but this is less evident

as the flow rate diminishes and the primary air flow sweeps

along the channel. The closing of the secondary air inlet port

may occur after or before closing the inlet port; the timing

of closure has ranged from 1.6 to 2.95 in attempted simu-

lations. Typically, the timing is chosen to avoid significant

backflow into the bypass and to achieve a high performance.

The green region in the fuel fraction graph indicates dilution

by the bypass air (blue) from the full strength mixture (red).

5.4 Rotary wave ejector PDE cycle with pressurized

primary inlet, and with exit valve

For a hybrid-PDE configuration with upstream compression,the primary inlet pressure could exceed the secondary inlet

pressure.Forprimary-to-secondarypressureratios more than

about 1.2, visual inspection of wave patterns showed signifi-

cant backflow into the rotor. To prevent backflow and obtain

other benefits, the exhaust is closed for a time period, in this

exit-valved configuration. As discussed in Fig. 8 for a simple

PDE, the partial closing of the exhaust can also improve the

performance of the engine.

Figure 12 shows [41] wave diagrams and predicted flow

properties at the inlet andexit planesforan exit-valved rotary

wave ejector PDE. Now, the primary inlet total pressure is

set to 4.0 atm while other ports are kept at the standard atmo-

spheric conditions. The Mach number plot shows that the

primary inlet and exhaust ports are open from 1.6 to 2.0 and

from 0.2 to 0.7, respectively. The plot clearly shows that

compared with the full annular exit configuration discussed

before, both the primary inlet and exhaust flows indicate a

more uniform velocity profile without any backflow at the

-1 0 1 20

0.5

1

1.5

2

2.5

3

Mach No

Time

Inlet

Outlet

-1 0 1 20

0.5

1

1.5

2

2.5

3

Log Pressure

Inlet

OutletInle

t

Exit

Fig. 12 Flow field of rotary PDE with exit valve (from [41])

123


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exit. The inward motion of the fueled region (red) is initially

stopped byclosing of theexhaustport anda backwardmotion

is observed later due to propagations of waves inside the

rotor channels. In this simulation, the bypass duct remained

open from time 0.2 to 0.7, before the opening of the higher-

pressure primary flow, and the colder fluid may be observed

(darker blue) in the temperature plot.

5.5 Performance evaluation

To evaluate the rotary wave ejector for enhancing PDE per-

formance, a detailed performance investigation was made

[3941]. Performance results are presented in the form of net

pressure gain across the wave ejector PDE and augmentation

ratios for specific impulse as functions of entrainment ratio.

The results are obtained for an exit-valved rotary PDE inte-

grated with a rotary wave ejector. Port timings are selected

basedon matching waveevents, using theresults of a detailed

parametric design investigation using the design-of-experi-

ments statistical methodology presented in Ref. [58,59].

For hybrid-PDE application to gas turbine engines, pres-

sure gain is defined as the ratio of the port-average stagna-

tion pressures, exhaust to inlet. The averaging calculation

preserves the time-integrated mass, momentum, and energy

flux in the port, and assumes that each port is in commu-

nication with a large number of rotating channels, so that

it has a steady flow of gas regardless of the unsteady pro-

cesses in each channel. The numerical procedure takes into

account the mixing loss associated with homogenizing the

port properties [46]. The pressure gain measures the perfor-

mance of hybrid-PDE systems because their overall effect

is to increase the turbine inlet pressure, resulting in higher

cycle efficiency. For the exit-valved rotary PDEs, the ham-

mer shock discussed in Fig. 8 enhances the pressure gain due

to the pre-compression prior to the combustion.

Fordirect thrustapplications, performance is measured by

augmentation of specific impulse, defined as the thrust per

unit mass rate of fuel. For the rotary waveejector PDE, thrust

is computed by assuming an isentropic expansion of the

homogenized exhaust gas to atmospheric pressure. Neglect-

ing the inlet flow velocity compared with the exit flow veloc-

ity, the ideal thrust (F) can be calculated by [59]:

F = mexit

2cpTtwee1

Pa

Ptwee

1

(5)

where subscript a indicates the ambient state which sets

the nozzle discharge static pressure, and wee indicates

the wave ejector exit state supplying the nozzle. Subscript

t stands for stagnation condition. It should be noted that

this thrust is not the same as that calculated from a sim-

ple pressure and momentum balance on the detonation tube.

1

2

3

4

5

0 1 2 3 4 5 6 7 8

Entrainment Ratio

Temp

eratureRatio

HR = 1.2

HR = 1.35

HR = 1.5

HR = 1.8

HR = 2.0

HR = 2.2

HR = 2.5

Fig. 13 Temperature ratio versus entrainment ratio (from [41])

Because mexit = minlet + mbypass, the specific impulse is

calculated as:

Isp =F

mfuel=

1 +

mbypassmprimary

mfuelmprimary

F

mexit=

1 + ER

primary

2cpTtwee1

Pa

Ptwee

1

(6)

whereER isentrainment ratio,defined as themassflow rate

ratio of the bypass air and the primary inlet flow. Parameter

primary is the fuelair mass ratio in the primary inlet port,

and hence defines its energy content. In this study, the results

are presented in the form of the specific impulse augmenta-

tion ratio, which is defied as the ratio of the non-dimensional

specific impulse of the rotary wave ejector PDE to the non-

dimensional specific impulse of thebaseline rotaryPDE with

no bypass flow.

The overall energy balance requires that the average out-

flow enthalpy, as measured by the stagnation temperature

ratio, reflect the average energy in the primary and second-

ary inlet, including fuel enthalpy, regardless of the details of

the system design and design parameters. If it is assumed

that the primary zone fuelair ratio does not change, the

overall fuelair ratio will depend directly on the entrain-

ment ratio. To verify this, the stagnation temperature ratio

across the rotary wave ejector PDE is plotted as a func-

tion of entrainment ratio in Fig. 13. Entrainment ratio was

changed by varying the bypass opening and closing timings.

Port locations and other geometric parameters were kept the

same. Outflow temperature falls hyperbolically with entrain-

ment ratio regardless of height ratio (HR) in the range 1.2

2.5, as expected. The observed fluctuations may reflect small

variations in the primary mixture fuelair ratio, which is due

to wave-induced velocity fluctuations.

123


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1

1.1

1.2

1.3

1.4

1.5

1 2 3 4 5

Temperature Ratio

Pre

ssureRatio

HR = 1.2

HR = 1.35

HR = 1.5

HR = 1.8

HR = 2.0

HR = 2.2

HR = 2.5

Fig. 14 Pressure ratio versus temperature ratio (from [41])

The variation of overall pressure gain with temperature

ratio is indicated in Fig. 14 for different height ratios. Thisplot is a common representation of the performance of

pressure-gain combustors. Overall energy balance and ther-

modynamicmodels [60,61] show that themaximum pressure

gain increaseswith temperatureratio, butactual performance

can vary considerably depending on design features. It

appears that height ratio has moderate but possibly complex

impact on pressure gain.

The specific impulse for the baseline cycle is calculated to

be 2.87 a/s using the constant specific heat ratio

= of 1.3. It is emphasized that thrust and impulse calcula-

tions for this baseline andforejector enhanced designs in this

paper all include a mixingloss associated with homogenizingthe multi-tube exhaust prior to nozzle expansion. For other

cases, the calculated specific impulse is divided by this value

to express an augmentation ratio. The variation of specific

impulse augmentation with entrainment ratio for the previ-

ousheight ratiosis shownin Fig. 15. Considerable thrust aug-

mentation is observed, even for small entrainment ratios, but

there is significant scatter associated with the direct effects

ofHR variation and indirect effects via the overall fuelair

ratio and entrainment ratio responses to wave dynamics at

the inlets. The performance generally increases with entrain-

ment ratio, and impulse augmentation up to a factor of two

appears possible.

6 Optimization using design-of-experiments

To optimize the rotary wave ejector design for maximum Isp,

the most influential seven parameters were examined. Of the

selected seven, the effect of fill fraction FF is relatively obvi-

ous and strong, as it corresponds to partial filling in a PDE.

Therefore, FF was separated from the analysis, and two sets

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5 6 7 8

Entrainment Ratio

SpecificImpulseAugmentation

HR = 1.2

HR = 1.35

HR = 1.5

HR = 1.8

HR = 2.0

HR = 2.2

HR = 2.5

Fig. 15 Specific impulse augmentation ratio versus entrainment ratio

(from [41])

of experimentswereconductedbasedon settingsof FF = 0.6

and FF = 0.8. The non-linear effects of the remaining sixvariable parameters were sought using a three level analysis,

applying the BoxBehnken design-of-experiments structure

to minimize experimental effort.

Based on the design-of-experiments prediction, the opti-

mal design without exit valving is shown of Table 1. In this

table, X2 and X3 represent transition middle section forward

and middle offsets, respectively. ANG refers to the bypass

duct angel relative to the rotor. When FF is 0.8, the non-

dimensional Isp for the rotary wave ejector is 2.01. In com-

parison, for the PDE baseline case with FF set at 0.8, Isp was

calculated as 1.11. Thus, a specific impulse augmentation

ratio of 1.83 is obtained. When FF is 0.6, Isp is 2.29., and Ispaugmentation becomes 2.1.

Figure 16 is a sketch of the resultingoptimal rotarywave

ejector geometry model for FF = 0.6, which was also found

to give nearly optimal Isp for FF = 0.8, with the optimal

parameter settings given in Table 2. POT and SOT represent

primary and bypass ducts opening time, respectively. PCT

and SCT are used for the primary and bypass ducts closing

time, respectively. P5 is the back pressure and X4 is transi-

tion middle section rear offset. It is emphasized that in this

design, parameters were selected for their weak or strong

influence on specific impulse alone, without regard to other

Table 1 Design of experimentsbased optimaldesign simulation results

Designofexperimentspredictions

of the optimal settings for design

parameters

FF Isp prediction

HR Cycle X2 X3 ANG

2 3.95 0 0.3 30 0.8 2.01

2 3.95 0.05 0.3 30 0.6 2.29

123


13/16


H

30

2H

L

L/5 3L/10

35

L/20

Fig. 16 Optimal rotary wave ejector model based on Isp

Table 2 Optimal design parameter values

POT PCT SOT SCT P5 Cycle FF

1.1 2.3 0.7 2.5 1 3.95 0.6

X1 X2 X3 X4 ANG1 HR

0.2 0 0.3 0.05 30 2

performance measures. Other measures such as thrust den-

sity, rotorweight,size,and costshouldbeconsidered together

with Isp to generate a feasible design.

6.1 Exit valving for backflow control

It was observed that some backflow occurs at the rotary

wave ejector exit, generally in the low-speed phase of each

cycle. This may be explained by the fact that improved Ispat the near-optimal design state corresponds to high levels

of entrainment, with concomitant low exit velocity as the

momentum of the detonation is distributed over increasedmass. Backflow is computed in the model according to the

pressure difference across the exit, and an averaged outflow

temperature is assigned to the returning fluid. The opportu-

nity was presented to prevent backflow by valving the exit,

andfurther improvethe Isp. Theexitport timingwasmodified

to open only from 0.36 to 3.9 in non-dimensional time, and

backflow is reduced but not eliminated, as shown in Fig. 17

forthecaseofFF = 0.6. Isp is calculated tobe increasedfrom

2.29 to 2.63. Exit port timing could involve two or more addi-

tional parameters, which were not included as design param-

eters in thecurrent research,but shouldbe included in further

investigation.Figure 18 shows the Isp augmentationfor variousparamet-

ric cases considered in the design-of-experiments approach

of Ref. [58,59], for the case of FF = 0.8. It included a

two-level FFD and three-level BoxBehnken sets of simula-

tions. It illustrates that Isp is strongly correlated with entrain-

ment ratio, as expected. The optimal settings had the highest

Isp among all the runs, justifying the design-of-experiment

approach to an optimal rotary wave ejector model. Figure 19

is a plot ofIsp augmentation against the overall temperature

ratio, where in addition to the baseline, several partial-fill

Fig. 17 Optimized rotary wave

ejector simulation (exit-valved,

FF = 0.6)

123


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0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

0 1 2 3 4 5 6

Entrainment Ratio

IspAugmentation

PDE Baseline FF=0.8

"RWE (2-level FFD)"

"RWE (Box-Behnken)"

"Optimal RWE - open exit"

"Optimal RWE - exit-valved"

Fig. 18 Isp augmentationas a functionof entrainment ratio (FF = 0.8)

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

1 3 5 7 9

Overall Temperature Ratio

IspAugmentation

PDE baselinePDE LF1 FF=0.6

PDE LF2 FF=0.5PDE LF3 FF=0.4

PDE LF4 FF=0.3"RWE Box-Behnken FF=0.6"

"RWE Box-Behnken FF=0.8""RWE exit-valved FF=0.6""RWE exit valved FF=0.8"

Fig. 19 Isp augmentation as a function of overall temperature ratio

straight-channel PDE simulations are included: ranging from

FF = 0.8 to FF = 0.3. PDE designs with FF < 0.3 could

not be simulated with stable solutions, and it is likely that

practical PDE systems would not be able to control fuel

distribution at such low fill fractions. All PDE simulations

assume a multi-channel rotary design with the same loss

assumptions, other than the ejector feature. Isp is generally

higher for straight channel PDE with the same overall air

to fuel ratio and the same exit temperature, as a straight

channel PDE does not suffer some of the losses of an

ejector or rotary wave ejector, in particular the momentum

loss as secondary air is entrained at an incidence

angle.

When compared for the same fuel fraction in its primary

zone, the rotary wave ejector almost doubled the Isp. This is

because segregation of the main mixture in the primary zone

allows the rotary wave ejector to reach much lower over-

all fuelair ratio than effectively possible with partial fill or

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 100 200 300 400 500

No. of Computational Cells

Non-Dim

ensionalMetric

Specific Impulse

Thrust Density

Entrainment Ratio

Fig. 20 Grid sensitivity of non-dimensional performance metrics and

entrainment ratio

other means, and thus reach a greater thrust augmentation,

as indicated by the specific impulse augmentation achievedby the optimal cases.

6.2 Grid sensitivity verification

All simulations in this study use 100 uniform computational

cells over length L. As the cycle presented here includes

features such as secondary mass inflow that is not present in

previous analysis,a grid sensitivitystudy was conductedspe-

cifically for the typical configuration presented in Sect. 5.3

and illustrated in Fig. 11. The simulation was repeated with

200and 400cells.Thepropertyfieldsandprofiles were indis-

tinguishable from Fig. 11, and the results indicated that grid

refinementbeyond 100cells didnot changeany performance

predictions more than 1%, nor entrainment ratio more than

2%, as shown in Fig. 20.

7 Conclusion

By combining the rotary PDE with a non-steady ejector

device, the rotary wave ejector is envisioned to enhance PDE

performance and address some existing challenges in PDE

technology. A time-unsteady quasi-one-dimensional model

has been created for the analysis of the rotary wave ejector

concept. Simulations are presented for several rotary con-

figurations of a multi-tube PDE with and without the rotary

wave ejector. A preliminary investigation of exit valving and

one of the important geometrical parameters of the model

is presented in this paper. This analysis indicates that exit

valving has significant benefit and a rotary PDE with rotary

wave ejector has potential for doubling the specific impulse

relative to a rotary PDE with a conventional operating cycle.

The performance predictions are sensitive to ejector geome-

123


15/16


try and entrainment ratio, and these effects were investigated

to obtain the best performance.

The large entrainment ratio corresponding to the optimal

design was observed to result in slight backflow at the exit,

suggesting exit valving to reduce backflow. When exit val-

ving was applied to a design that had been previously opti-

mized for an open exit, the rotary wave ejector significantly

increasedmaximum Isp to2.37 times that of thePDE baselinecase, suggesting that this concept has potential for high effi-

ciency propulsion technology. Factors that increase entrain-

ment tend to increase specific impulse, but may compromise

thrust density.

Acknowledgments This work was partially supported by grant

NAG3-2325 from the NASA Glenn Research Center, monitored by

G. Welch. The authors acknowledge D. E. Paxson for assisting with the

code modifications.

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