impact of an exhaust throat on semi-idealized rotating ...€¦ · national aeronautics and space...

National Aeronautics and Space Administration

www.nasa.govASM 2016 1

SciTech 201654th AIAA Aerospace Sciences Meeting

San Diego, CAJanuary 4-8, 2016

Impact of an Exhaust Throat on Semi-Idealized Rotating Detonation Engine Performance

Daniel E. PaxsonNASA Glenn Research Center

Cleveland, Ohio

https://ntrs.nasa.gov/search.jsp?R=20160010267 2020-04-18T20:22:35+00:00Z



Outline

• Background• Problem Statement• Problem Analysis• Accommodation Strategy• Results• Concluding Remarks


www.nasa.gov 3ASM 2016

BackgroundRotating Detonation Engines (RDE’s) represent an IntriguingApproach to Detonative Pressure Gain Combustion (PGC)

• 1000+ Hz. cycle frequency• No ‘spark’ required• No lossy DDT devices• Compact

PGC: A periodic process, in a fixed volume, whereby gas expansion by heat release is constrained, causing a rise in stagnation pressure and allowing work extraction by expansion to the initial pressure.

Source: Schwer, AIAA 2011-581

Tem

pera

tureP

ress

ure



Problem Statement

• Semi-Ideal Means− Mil. Spec. engine inlet− Combustor (RDE) inlet is lossless− Combustor inlet has no reverse flow (i.e. perfect valve)− Engine exit nozzle is lossless (i.e. perfectly expanded)− Adiabatic− Inviscid− Premixed− Retains fundamental entropy sources associated with RDE’s

Consider a Semi-Ideal, Ram-Based, Stoichiometric Hydrogen Fueled RDE at 37,000 ft., Flying at Mach 1.37

(Note-Flight conditions are illustrative only)

RDEInlet Nozzle



Problem Statement

• RDE 21% above RJ• RDE 22% below PDE

RDEInlet Nozzle

2000

2500

3000

3500

4000

4500

5000

RDE Ramjet PDE

Net

Spe

cific

Impu

lse,

sec

.

Alg

ebra

ic M

odel

CFD

Mod

el

Alg

ebra

icM

odel



Problem Statement

• 7-10% Disparity

3500

4000

4500

5000

RDE RDE w/KEu

RDE w/KEu-Sm

PDE NU PDE

Net

Spe

cific

Impu

lse,

sec

.

Alg

ebra

ic M

odel

CFD Kin

etic

Ene

rgy

Min

orE

ntro

py

Non

-uni

form

Exi

t Flo

w

Contours of Entropy Relative to Algebraic PDE

Entro

py

Where’s All This Blue Coming From and What Can Be Done About it?



Problem AnalysisPrimary Analysis Tool

Quasi-2-Dimensional Euler Solver With Sources• Source Terms Model:

• Chemical Reaction• Friction (not used here)• Heat Transfer (not used here)

• 2 Species Reaction (reactant or product)• Simplified Finite Rate Reaction• High Resolution Numerical Scheme• Coarse Numerical Grid (< 10,000 cells)• Adopts Detonation Frame of Reference

• Time derivatives ultimately vanish and solution is steady• Robust Boundary Conditions

• Sub or supersonic exhaust flow• Optional isentropic exhaust throat• Forward or reverse inlet flow with choking possible (not used here)• Physics based inlet loss model from typical restriction (mostly not used here)

• Runs on a laptop• Approximately 20 sec. per wave revolution

• Validated• Compares well with other semi-idealized numerical results• Compares well with experimental results



Problem AnalysisEffects of Fill Mach Number On 1D PDE

• Algebraic 1D PDE Results Assumed Low Fill Mach Number

• As Fill Mach Increases Post Detonation Entropy Increases and Specific Impulse Decreases

• As Fill Mach Increases PredetonationPressure Drops

• Detonation Does Not Recover Pressure

• So Post-Detonation CJ Pressure Drops

• Less Availability for Thrust Production

4300

4400

4500

4600

4700

4800

4900

5000

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

0.0 0.5 1.0

I ansp

i, se

c.

Entro

py

Fill Mach Number

entropyI_anspientropyIanspi

8

10

12

14

16

18

20

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.5 1.0

p CJ/P

man

p pre

det/P

man

Fill Mach Number

P1/PT1Pcj/PT1ppredet/Pman

pCJ/Pman

16

11162126313641

0.0 0.5 1.0

p/p*

x/L

CJ

Analytical Results for 1D PDE’s Say Fill Mach is the Culprit



Problem AnalysisEffects of Fill Mach Number On RDE

• Fill Mach Number Tricky to Define• Using axial Mach number just prior to

detonation• Axial Mach Number Is High• Post-Detonation Entropy Is High• Fill Mach and Entropy Follow Same Relationship as 1D PDE

CFD Results for RDE’s Suggest Fill Mach is Indeed the Culprit

7.8

7.9

8.0

8.1

8.2

8.3

8.4

8.5

0.0 0.5 1.0

Entro

py

Fill Mach Number

1D CJRDERDE mass-averaged



Accommodation StrategyAdd an Exit Throat

• Rate of Exhaust Affects Rate of Fill• Well established from PDE efforts

• Lower Rate of Fill Yields Higher Pre-detonation Pressure, Higher Post-Detonation Pressure, Lower Entropy, Higher Specific Impulse

It Works! 9.4% Specific Impulse Increase

Aexit/Aannulus=0.75

Log(

pres

sure

)Te

mpe

ratu

re



Accommodation StrategyMore Restriction!

• Throat Sends Strong Waves Upstream

• Waves Affect Inflow• Inflow Changes Affect Detonation Structure

• Detonation Changes Generate Additional Spurious Waves

• Waves Get Reflected• Cascade Established

Unstable Behavior Results

Aexit/Aannulus=0.70

Tem

pera

ture



Accommodation StrategyInlet Restriction With Loss

• Inlet Restriction Creates Total Pressure Loss…• But Damps Unstable Behavior Allowing Smaller Exit Restrictions…• Ultimately Yielding Net Gain

10.3% Specific Impulse Increase

Aexit/Aannulus=0.70; Ain/Aannulus=0.75

Tem

pera

ture

Log(

pres

sure

)



Concluding Remarks

• For an idealized, basic RDE configuration, the fill Mach number can be quite high under representative boundary conditions

• Through the same basic mechanism as the PDE, the high fill Mach limits performance as measured by net specific impulse

• The fill Mach can be reduced by adding a throat to the exit, thereby gaining as much as 9% net specific impulse

• Too much exit restriction yields unstable operation• Adding a ‘lossy’ inlet restriction adds stability and allows for

a 10% specific impulse improvement• Experimental validation (or refutation) is justified



END

impact of an exhaust throat on semi-idealized rotating ...€¦ · national aeronautics and space...

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