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Energy for Propulsion pp 189–215Cite as

Quantification of External Enthalpy Controlled Combustion at Unity Damköhler Number

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Abstract

The use of external enthalpy support (e.g. via heat recirculation) can enable combustion beyond normal flammability limits and lead to significantly reduced emissions and fuel consumption. The present work quantifies the impact of such support on the combustion of lean (\(\varPhi = 0.6\)) turbulent premixed DME/air flames with a Damköhler number around unity. The flames were aerodynamically stabilised against thermally equilibrated hot combustion products (HCP) in a back-to-burnt opposed jet configuration featuring fractal grid generated multi-scale turbulence (\(Re \simeq 18{,}400\) and \(Re_t > 370\)). The bulk strain (\(a_b = 750\) s\(^{-1}\)) was of the order of the extinction strain rate (\(a_q = 600\) s\(^{-1}\)) of the corresponding laminar opposed twin flame with the mean turbulent strain (\(a_I = 3200\) s\(^{-1}\)) significantly higher. The HCP temperature (\(1600 \le T_{HCP}\)(K) \( \le 1800\)) was varied from close to the extinction point (\(T_{q} \simeq 1570\) K) of the corresponding laminar twin flame to beyond the unstrained adiabatic flame temperature (\(T_{ad} \simeq 1750\) K). The flames were characterised using simultaneous Mie scattering, OH-PLIF and PIV measurements and subjected to a multi-fluid analysis (i.e. reactants and combustion products, as well as mixing, weakly reacting and strongly reacting fluids). The study quantifies the (i) evolution of fluid state probabilities and (ii) interface statistics, (iii) unconditional and (iv) conditional velocity statistics, (v) conditional strain along fluid interfaces and (vi) scalar fluxes as a function of the external enthalpy support.

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Abbreviations

a :

Rate of strain [s\(^{-1}\)].

\(\overline{c}\) :

Reaction progress variable [–].

c :

Progress variable; Instantaneous conditioning variable [–].

\(\overline{cu}\) :

Scalar Flux [m s\(^{-1}\)].

D :

Burner nozzle diameter [m].

Da :

Conventional Damköhler number [–].

\(Da_{ign}\) :

Turbulent auto–ignition Damköhler number [–].

\(d_{p,x}\) :

Al\(_2\)O\(_3\) particle diameter x% [m].

e :

Planar rate of strain tensor [s\(^{-1}\)].

H :

Burner nozzle separation [m].

I :

OH signal intensity [–].

\(I^{\ddagger }\) :

Reference signal intensity [–].

Ka :

Conventional Karlovitz number [–].

\(Ka_{ign}\) :

Auto-ignition Karlovitz number [–].

[k]:

Theoretical concentration of species k [mol m\(^{-3}\)].

\(L_{\eta }\) :

Kolmogorov length scale [m].

\(L_I\) :

Integral length scale of turbulence [m].

N :

Total number of images [–].

\({\hat{{\mathbf {n}}}}\) :

Unit vector of the iso-contour normal [–].

\(\dot{Q}\) :

Heat release rate [W m\(^{-3}\)].

\(Re_t\) :

Turbulent Reynolds number [–].

\(S_L\) :

Laminar burning velocity [m s\(^{-1}\)].

\({\hat{{\mathbf {s}}}}\) :

Unit vector of the streamline tangent [–].

T :

Temperature [K].

\(T_{ad}\) :

Adiabatic flame temperature [K].

\(T_{ign}\) :

Auto-ignition temperature [K].

\(T_{HCP}\) :

Lower nozzle hot combustion product temperature [K].

U :

Flow velocity [m s\(^{-1}\)].

\(\overline{U}\) :

Mean unconditional axial velocity [m s\(^{-1}\)].

\(\overline{U_{\dots }}\) :

Mean conditional axial velocity [m s\(^{-1}\)].

u :

Velocity component [m s\(^{-1}\)].

\(\sqrt{u'^2}\) :

Unconditional axial velocity fluctuation [m s\(^{-1}\)].

\(\sqrt{u'^2_{\cdots }}\) :

Conditional axial velocity fluctuation [m s\(^{-1}\)].

\(u_{rms}\) :

Root mean square velocity fluctuation [m s\(^{-1}\)].

\(\overline{U}_s\) :

Slip velocity [m s\(^{-1}\)].

\(\overline{V}\) :

Mean unconditional radial velocity [m s\(^{-1}\)].

\(\dot{V}\) :

Lower nozzle volumetric flow rate [m\(^3\) s\(^{-1}\)].

\(\sqrt{v'^2}\) :

Unconditional radial velocity fluctuation [m s\(^{-1}\)].

\(\sqrt{v'^2_{\cdots }}\) :

Conditional radial velocity fluctuation [m s\(^{-1}\)].

X :

Mole fraction [–].

x :

Axial coordinate [m].

\(x_s\) :

Distance from origin of first thermal alteration [m].

y :

Radial coordinate [m].

\(\beta \) :

Fluid state material surface [–].

\(\delta _f\) :

Laminar fuel consumption layer thickness [m].

\(\varepsilon _r\) :

Rate of dissipation within the reactants [m\(^2\) s\(^{-3}\)].

\(\varLambda \) :

Threshold value [–].

\(\lambda _B\) :

Batchelor scale [m].

\(\lambda _D\) :

Mean scalar dissipation layer thickness [m].

\(\lambda _{MF}\) :

Multi-fluid spatial resolution [m].

\(\lambda _{PIV}\) :

PIV spatial resolution [m].

\(\nu _r\) :

Reactants kinematic viscosity [m\(^2\) s\(^{-1}\)].

\(\omega \) :

Planar vorticity tensor [s\(^{-1}\)].

\(\varPhi \) :

Equivalence ratio [–].

\(\tau _{c}\) :

Chemical timescale [s].

\(\tau _{\eta }\) :

Kolmogorov timescale [s].

\(\tau _{ign}\) :

Auto-ignition delay time [s].

\(\tau _{I}\) :

Integral timescale of turbulence [s].

\(\xi \) :

Blending fraction [%\(_{vol}\)].

0:

Alignment at the origin; initial value.

\(^\ddagger \) :

Reference value.

BTB :

Back-to-burnt configuration.

b :

Bulk flow motion.

d :

Total.

FS :

Fluid state.

HCP :

Hot combustion products.

I :

Integral scale; turbulent.

i, j:

Pixel index.

k :

Velocity component.

M :

Mixing fluid iso-contour.

m :

Mixing fluid.

n :

Instantaneous image; normal.

NE :

Nozzle exit.

p :

Product fluid.

q :

Extinction conditions.

R :

Reactant fluid iso-contour.

r :

Reactant fluid.

SR :

Strongly reacting fluid iso-contour.

s :

Strongly reacting (flamelet) fluid.

T :

Dependency on HCP temperature.

t :

Tangential.

WR :

Weakly reacting fluid iso-contour.

w :

Weakly reacting fluid.

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Acknowledgements

The authors would like to acknowledge the support of the AFOSR and EOARD under Grant FA9550-17-1-0021 and thank Dr. Chiping Li and Dr. Russ Cummings for encouraging the work. The US Government is authorised to reproduce and distribute reprints for Governmental purpose notwithstanding any copyright notation thereon. The authors would also like to thank Dr. Robert Barlow for his support.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Imperial College, London, SW7 2AZ, UK

    Fabian Hampp & Rune Peter Lindstedt

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  1. Fabian Hampp
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Correspondence to Rune Peter Lindstedt .

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Editors and Affiliations

  1. ACRI, The CFD Innovators, Los Angeles, California, USA

    Akshai K. Runchal

  2. Department of Mechanical Engineering, University of Maryland, Department of Mechanical Engineering, College Park, Maryland, USA

    Ashwani K. Gupta

  3. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, Uttar Pradesh, India

    Abhijit Kushari

  4. Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Department of Aerospace Engineering, Kanpur, Uttar Pradesh, India

    Ashoke De

  5. Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Department of Mechanical Engineering, Chicago, Illinois, USA

    Suresh K. Aggarwal

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Hampp, F., Lindstedt, R.P. (2018). Quantification of External Enthalpy Controlled Combustion at Unity Damköhler Number. In: Runchal, A., Gupta, A., Kushari, A., De, A., Aggarwal, S. (eds) Energy for Propulsion . Green Energy and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-7473-8_8

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  • DOI: https://doi.org/10.1007/978-981-10-7473-8_8

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