Skip to main content
SpringerLink
Log in

Uncertainty quantification of a generic scramjet engine using a probabilistic collocation and a hybrid approach

  • Original Paper
  • Published:
CEAS Aeronautical Journal Aims and scope Submit manuscript

Abstract

A hybrid probabilistic model was developed and used to investigate a generic scramjet engine at flight conditions (Mach 8, 30 km altitude). To assess the robustness of the design, uncertainties in boundary conditions and modelling were considered. The full-system model is composed of three parts, which were modelled separately: inlet with isolator, combustion chamber and nozzle. The inlet and the nozzle were resolved using two-dimensional calculations solving the Reynolds averaged Navier Stokes equations, while the combustion chamber modelling was based on an one-dimensional stream tube approach. Flight properties and injection parameters were considered aleatoric in nature. Uncertainties introduced by different averaging approaches at the model interface were presumed to be epistemic. The uncertainties were propagated using probabilistic collocation if feasible and Monte Carlo simulation if necessary. The more recent probabilistic collocation approach allows a reduction of the necessary number of evaluations. Hence, a more detailed model can be employed. However, as this polynomial chaos approach is only valid for smooth transformations, it fails to predict singular hazardous events, e.g. discontinuities such as thermal choking of the combustor. To consider these events, a Monte Carlo simulation had to be applied. The hybrid model and the full probabilistic collocation model showed equivalent results. But the hybrid model acquired additional information at overall lower calculation expanses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

\(\beta \) :

Nozzle thrust vector (–)

\(\gamma \) :

Ratio of specific heats (–)

\(\delta \) :

Boundary layer height (m)

\(\zeta \) :

Vector of random variables (–)

\(\eta \) :

Efficiency (–)

\(\Theta \) :

Angle (\(\circ \))

\(\mu \) :

Mean value

\(\rho \) :

Density (kg/m\(^3\))

\(\sigma \) :

Standard deviation

\(\sigma ()\) :

Variation coefficient (–)

\(\phi \) :

Base of random variables (–)

b :

Width (m)

c :

Expansion coefficients (–)

F :

Net Force (N)

f :

Factor for Pulsonetti correlation (–)

h :

Height (m)

l :

Length (m)

Ma :

Mach number (–)

M :

Standard normal distributed random variable (–)

n :

Number of Samples (–)

P :

Degree of Polynomial Chaos expansion (–)

p :

Pressure (Pa)

r():

Correlation coefficient (–)

r :

Recovery factor (–)

T :

Temperature (K)

u :

Random variable (–)

v :

Velocity (m/s)

w :

Mass fraction (–)

x, y, z :

Coordinates (m)

\(\mathbf {X}\) :

Vector of random variables (–)

0:

Ambient conditions

\(\infty \) :

Infinity value

c:

Combustion

central:

Central injector position

i:

Control variable

inj:

Injector

L:

Lift direction

mix:

Mixing

rel:

Reliability

T:

Thrust direction

t,tot:

Total

var:

Variables

w:

Wall

wall:

Wall injector position

AoA:

Angle of attack

CFD:

Computational fluid dynamics

CI:

Central injector

CMES:

Conserved mass/energy/entropy method

CMME:

Conserved mass/momentum/energy method

ER:

Equivalence ratio

Lang:

Langley distortion methodology

LHS:

Latin Hypercube Sampling

Mawe:

Mass flux-weighting

PCM:

Probabilistic collocation method

QoI:

Quantities of interest

RANS:

Reynolds averaged Navier Stokes Equations

SERN:

Single expansion ramp nozzle

WI:

Wall injector

References

  1. Baurle, R., Gaffney, R.: The art of extracting one-dimensional flow properties from multi-dimensional data sets. In: 45th AIAA Aerospace Sciences Meeting and Exhibit (2007). https://doi.org/10.2514/6.2007-639

  2. Eldred, M.S., Giunta, A.A., Brown, S.L., Adams, B.M., Dunlavy, D.M., Eddy, J.P., Gay, D.M., Griffin, J.D., Hart, W.E., Hough, P.D., Kolda, T.G., Martinez-Canales, M.L., Swiler, L.P., Watson, J.P., Williams, P.J.: Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis—version 6.4 reference manual (2016)

  3. Fuhrmann, T.: Auslegung und Betriebsverhalten von SCRamjet-Antriebssystemen für Raumtransporter-Hyperschallflugzeuge: Techn. Univ., Diss.–München, 2009, 1. aufl. edn. Luftfahrt. Verl. Dr. Hut, München (2009)

  4. Gerhold, T., Galle, M., Friedrich, O., Evans, J.: Calculation of complex three-dimensional configurations employing the dlr-tau-code. In: 35th Aerospace Sciences Meeting and Exhibit (06 January 1997–09 January 1997). https://doi.org/10.2514/6.1997-167

  5. Gerlinger, P., Möbus, H., Brüggemann, D.: An implicit multigrid method for turbulent combustion. Journal of Computational Physics 167(2), 247–276 (2001). https://doi.org/10.1006/jcph.2000.6671

    Article  Google Scholar 

  6. Goodwin, D.G., Harry K. Moffat, Raymond L. Speth: Cantera: An object-oriented software toolkit for chemical kinetics, thermodynamics, and transport processes (2016)

  7. Häberle, J., Gülhan, A.: Investigation of two-dimensional scramjet inlet flowfield at mach 7. Journal of Propulsion and Power 24(3), 446–459 (2008). https://doi.org/10.2514/1.33545

    Article  Google Scholar 

  8. Hannemann, K., Karl, S., Martinez Schramm, J., Steelant, J.: Methodology of a combined ground based testing and numerical modelling analysis of supersonic combustion flow paths. Shock Waves 20(5), 353–366 (2010). https://doi.org/10.1007/s00193-010-0269-8

    Article  Google Scholar 

  9. Heiser, W.H., Pratt, D.T.: Hypersonic airbreathing propulsion. AIAA education series. American Institute of Aeronautics and Astronautics, Washington, D.C (1994)

    Book  Google Scholar 

  10. Hirschen, C.M., Gruhn, P., Gülhan, A.: Influence of heat capacity ratio on the interaction between the external flow and nozzle flow of a scramjet. In: 14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference (2006). https://doi.org/10.2514/6.2006-8095

  11. Hosder, S., Bettis, B.: Uncertainty and sensitivity analysis for reentry flows with inherent and model-form uncertainties. J. Spacec. Rockets 49(2), 193–206 (2012). https://doi.org/10.2514/1.A32102

    Article  Google Scholar 

  12. Hosder, S., Walters, R., Balch, M.: Efficient sampling for non-intrusive polynomial chaos applications with multiple uncertain input variables. In: 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (23 April 2007–26 April 2007). https://doi.org/10.2514/6.2007-1939

  13. Huan, X., Safta, C., Sargsyan, K., Geraci, G., Eldred, M., Vane, Z., Lacaze, G,. Oefelein, J., Najm, H.,: Global Sensitivity Analysis and Estimation of Model Error, Toward Uncertainty Quantification in Scramjet Computations. AIAA J. 56(3), 1170–1184 (2018). https://doi.org/10.2514/1.J056278

    Article  Google Scholar 

  14. Johnson, D.L.: Terrestrial environment (climatic) criteria guidelines for use in aerospace vehicle development. 2008 revision (2008)

  15. Karl, S., Laurence, S., Martinez Schramm, J., Hannemann, K.: Cfd analysis of unsteady combustion phenomena in the hyshot-ii scramjet configuration. In: 18th AIAA/3AF International Space Planes and Hypersonic Systems and Technologies Conference (2012). https://doi.org/10.2514/6.2012-5912

  16. Kliche, D., Mundt, C.: Progress in multidisciplinary analysis and evaluation of supersonic combustion ramjets. In: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference (2011). https://doi.org/10.2514/6.2011-2281

  17. Krause, M., Ballmann, J.: Numerical simulations and design of a scramjet intake using two different rans solvers. In: 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (2007). https://doi.org/10.2514/6.2007-5423

  18. Langener, T., Steelant, J., Roncioni, P., Natale, P., Marini, M.: Preliminary performance analysis of the lapcat-mr2 by means of nose-to-tail computations. In: 18th AIAA/3AF International Space Planes and Hypersonic Systems and Technologies Conference (2012). https://doi.org/10.2514/6.2012-5872

  19. Loeven, G.J.A., Witteveen, J.A.S., Bijl, H.: Probabilistic collocation: An efficient non-intrusive approach for arbitrarily distributed parametric uncertainties. In: 45th AIAA Aerospace Sciences Meeting and Exhibit (2007). https://doi.org/10.2514/6.2007-317

  20. Mack, A., Hannemann, V.: Validation of the unstructured dlr-tau-code for hypersonic flows. In: 32nd AIAA Fluid Dynamics Conference and Exhibit (24 June 2002–26 June 2002). https://doi.org/10.2514/6.2002-3111

  21. Mantis, G.C., Mavris, D.N.: A bayesian approach to non-deterministic hypersonic vehicle design. In: World Aviation Congress & Exposition, SAE Technical Paper Series. SAE International400 Commonwealth Drive, Warrendale, PA, United States (2001). https://doi.org/10.4271/2001-01-3033

  22. Mcbride, B.J., Gordon, S.: Computer program for calculating and fitting thermodynamic functions (1995)

  23. Meiss, J.H., Schröder, W., Meinke, M.: Numerical investigation to enhance the thrust vector of a scramjet nozzle. In: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference (2011). https://doi.org/10.2514/6.2011-2346

  24. Menter, F.R., Kuntz, M., Langtry, R.: Ten years of industrial experience with the sst turbulence model. Turbul. Heat Mass Transf. 4, 625–632 (2003)

    Google Scholar 

  25. Miller, D.S.: Internal flow systems, BHRA Fluid Engineering Series, vol. 5. BHRA Fluid Engineering, Cranfield (1984)

    Google Scholar 

  26. National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, U. S. Air Force: U.s. standard atmosphere (1976)

  27. Ogawa, H., Alazet, Y., Pudsey, A., Boyce, R., Isaacs, A., Ray, T.: Full flow-path optimization of axisymmetric scramjet engines. In: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference (2011). https://doi.org/10.2514/6.2011-2347

  28. Pulsonetti, M., Erdos, J., Early, K.: An engineering model for analysis of scramjet combustor performance with finite rate chemistry. In: 24th Joint Propulsion Conference (11 July 1988–13 July 1988). https://doi.org/10.2514/6.1988-3258

  29. Scheuermann, T., Chun, J., Wolfersdorf, J.V.: Experimental investigations of scramjet combustor characteristics. In: 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference (28 April 2008–01 May 2008). https://doi.org/10.2514/6.2008-2552

  30. Scheuermann, T., Chun, J., Wolfersdorf, J.V.: One-dimensional modelling of a scramjet combustor reacting flow. In: 15th AIAA International Space Planes and Hypersonic Systems and Technologies Conference (28 April 2008–01 May 2008). https://doi.org/10.2514/6.2008-2643

  31. Schütte, G., Staudacher, S.: Probabilistic aspects of scramjet design. J. Propuls. Power 25(2), 281–288 (2009). https://doi.org/10.2514/1.38195

    Article  Google Scholar 

  32. Sobol, I.M.: Sensitivity estimates for nonlinear mathematical models. Math. Modell. Comput. Exp. 1993(14), 407–414 (1993)

    MathSciNet  MATH  Google Scholar 

  33. Tang, G., Iaccarino, G., Eldred, M.S.: Using stochastic expansion methods in evidence theory for uncertainty quantification. In: 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (2010). https://doi.org/10.2514/6.2010-2589

  34. Vellaramkalayil, J.J., Scheuermann, T., Wolfersdorf, J.V.: Analysis of a two-staged supersonic combustion chamber using experiments and simulations. In: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference (2011). https://doi.org/10.2514/6.2011-2247

  35. Weigand, B., Gaisbauer, U.: An overview on the structure and work of the dfg research training group grk 1095: ’aero-thermodynamic design of a scramjet propulsion system’. In: 16th AIAA/DLR/DGLR International Space Planes and Hypersonic Systems and Technologies Conference (2009). https://doi.org/10.2514/6.2009-7276

  36. Witteveen, J.A.S., Duraisamy, K., Iaccarino, G.: Uncertainty quantification and error estimation in scramjet simulation. In: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference (2011). https://doi.org/10.2514/6.2011-2283

  37. Xiu, D.: Numerical methods for stochastic computations: a spectral method approach. Princeton University Press, Princeton (2010)

    MATH  Google Scholar 

Download references

Acknowledgements

The present work was created as part of the Research Training Group GRK1095/2. The authors want to thank the German Research Foundation (DFG) for providing financial support.

Author information

Authors and Affiliations

  1. Institute of Aircraft Propulsion Systems, University of Stuttgart, Stuttgart, Germany

    Markus Feil & Stephan Staudacher

Authors
  1. Markus Feil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephan Staudacher
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markus Feil.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Feil, M., Staudacher, S. Uncertainty quantification of a generic scramjet engine using a probabilistic collocation and a hybrid approach. CEAS Aeronaut J 9, 649–659 (2018). https://doi.org/10.1007/s13272-018-0303-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13272-018-0303-6

Keywords

Search

Navigation