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Theoretical and experimental analysis of liquid layer instability in hybrid rocket engines

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Abstract

The combustion behavior of different hybrid rocket fuels has been analyzed in the frame of this research. Tests have been performed in a 2D slab burner configuration with windows on two sides. Four different liquefying paraffin-based fuels, hydroxyl terminated polybutadiene (HTPB) and high-density polyethylene (HDPE) have been tested in combination with gaseous oxygen (GOX). Experimental high-speed video data have been analyzed manually and with the proper orthogonal decomposition (POD) technique. Application of POD enables the recognition of the main structures of the flow field and the combustion flame appearing in the video data. These results include spatial and temporal analysis of the structures. For liquefying fuels these spatial values relate to the wavelengths associated to the Kelvin Helmholtz Instability (KHI). A theoretical long-wave solution of the KHI problem shows good agreement with the experimental results. Distinct frequencies found in the POD analysis can be related to the precombustion chamber configuration which can lead to vortex shedding phenomena.

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Notes

  1. HTPB fuel sample gratefully provided by SPLab Milan.

  2. Note that the x and z image data arrays are transposed in the POD calculations.

Abbreviations

BM:

Bounded model: (I) Inviscid, (V) Viscous

CB:

Carbon black

DLR:

Deutsches Zentrum für Luft- und Raumfahrt e.V.

ESA:

European Space Agency

FPS:

Frames per second

GOX:

Gaseous oxygen

GR:

Growth rate

HDPE:

High-density polyethylene

HTPB:

Hydroxyl terminated polybutadiene

KHI:

Kelvin Helmholtz instability

NIPALS:

Nonlinear iterative partial least squares algorithm

POD:

Proper orthogonal decomposition

PSD:

Power spectral density

STERN:

Experimental rocket programme for German students

UBM:

Unbounded model: (I) Inviscid, (V) Viscous

\(A,B,C\) :

Constants for boundary conditions

\(G\) :

Mass flux

\(H, h\) :

Height

\(K_{0,1,2}\) :

Dispersion relation constants

\(k\) :

Wave number (\(2 \pi /\lambda\))

\(\dot{m}\) :

Mass flow

\(n\) :

Regression rate exponent

\(p\) :

Pressure

\(p_\mathrm{dyn}\) :

Dynamic pressure

\(\dot{r}\) :

Fuel regression rate

\(t\) :

Time

\(U\) :

Velocity

\(x,z\) :

Coordinates

\(\gamma\) :

Ratio of specific heats

\(\eta\) :

Dynamic viscosity

\(\lambda\) :

Wavelength

\(\mu\) :

Kinetic viscosity

\(\rho\) :

Density

\(\sigma\) :

Surface tension

\(\varphi\) :

Stream function

\(\omega\) :

Frequency

c:

Critical value

ent:

Entrainment

f:

Fuel

G:

Gas

I:

Imaginary part

L:

Liquid

m:

Most amplified value

R:

Real part

s:

Solid

vap:

Vaporization

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Acknowledgments

The authors would like to thank all the persons who supported the presented work in several manners. The cooperation of Prof. De Luca from SPLab in Milan and the exchange of master students, as well as the support of the M11 team at the DLR is greatly acknowledged. Further, we would like to thank Prof. Heislbetz for the helpful discussions and assistance with the KHI theory. Funding of the experiments was gratefully provided by internal resources for fundamental research of the DLR Lampoldshausen.

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Authors and Affiliations

  1. DLR, Institute of Space Propulsion, Lampoldshausen, Germany

    Mario Kobald & Stefan Schlechtriem

  2. Politecnico di Milano, Milan, Italy

    Isabella Verri

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  1. Mario Kobald
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  2. Isabella Verri
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  3. Stefan Schlechtriem
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Correspondence to Mario Kobald.

Additional information

This paper is based on a presentation at the Space Propulsion Conference, May 19-22, 2014, Cologne, Germany.

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Kobald, M., Verri, I. & Schlechtriem, S. Theoretical and experimental analysis of liquid layer instability in hybrid rocket engines. CEAS Space J 7, 11–22 (2015). https://doi.org/10.1007/s12567-015-0076-2

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