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On spectral linear stochastic estimation

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Abstract

An extension to classical stochastic estimation techniques is presented, following the formulations of Ewing and Citriniti (1999), whereby spectral based estimation coefficients are derived from the cross spectral relationship between unconditional and conditional events. This is essential where accurate modeling using conditional estimation techniques are considered. The necessity for this approach stems from instances where the conditional estimates are generated from unconditional sources that do not share the same grid subset, or possess different spectral behaviors than the conditional events. In order to filter out incoherent noise from coherent sources, the coherence spectra is employed, and the spectral estimation coefficients are only determined when a threshold value is achieved. A demonstration of the technique is performed using surveys of the dynamic pressure field surrounding a Mach 0.30 and 0.60 axisymmetric jet as the unconditional events, to estimate a combination of turbulent velocity and turbulent pressure signatures as the conditional events. The estimation of the turbulent velocity shows the persistence of compact counter-rotating eddies that grow with quasi-periodic spacing as they convect downstream. These events eventually extend radially past the jet axis where the potential core is known to collapse.

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Notes

  1. Refer to Eq. (8) of Ewing and Citriniti (1999).

  2. The Arndt et al. (1997) analysis was more recently revisited by Coiffet et al. (2006) to show the existence of interference patterns between the reactive and propagative components of the pressure field.

  3. A more indepth discussion pertaining to pressure–velocity field coupling can be found in Ko and Davies (1971), Tinney et al. (2005), Hall et al. (2005) and Jordan et al. (2005).

Abbreviations

u :

Fluctuating velocity

\(\tilde{u}\) :

Estimate of u

x′:

Vector field over which the conditional event is investigated

x :

Vector field over which the unconditional event is investigated

p :

Fluctuating pressure

t :

Time

f :

Frequency

k :

Wave number

ρ:

Gas density

t :

Time

τ:

Time lag

U cl :

Jet centerline exit velocity

δx :

Spatial separation between unconditional and conditional events

R, D :

Jet radius and diameter, respectively

r :

Radial coordinate of the jet from the jet axis

r s :

Radial coordinate from the center of the jet shear layer

x :

Axial coordinate of the jet from the jet exit

\(St_{{D}}\) :

Strouhal number \((St_{{{D}}}={{fD}\over {U_{{{{\rm cl}}}}}})\) based on jet diameter

R ij :

Reynolds stresses

Δt :

Time step increment

f 1 :

High-pass frequency

f 2 :

Low-pass frequency

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Acknowledgments

The authors are grateful to Program Manager Dr. John Schmisseur from the Air Force Office of Scientific Research, the Central New York AGEP Program from the National Science Foundation, and NYSTAR, for funding the Syracuse University portions of this study.

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Authors and Affiliations

  1. Laboratoire d’Etudes Aérodynamiques, UMR CNRS 6609, Université de Poitiers, 43 rue de l’aerodrome, 86036, Poitiers Cedex, France

    C. E. Tinney, J. Delville & P. Jordan

  2. Department of Mechanical Engineering, Florida State University, Tallahassee, FL, USA

    F. Coiffet

  3. Department of Mechanical & Aerospace Engineering, Syracuse University, Syracuse, NY, USA

    A. M. Hall & M. N. Glauser

Authors
  1. C. E. Tinney
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  2. F. Coiffet
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  3. J. Delville
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  4. A. M. Hall
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  5. P. Jordan
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  6. M. N. Glauser
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Correspondence to C. E. Tinney.

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Tinney, C.E., Coiffet, F., Delville, J. et al. On spectral linear stochastic estimation. Exp Fluids 41, 763–775 (2006). https://doi.org/10.1007/s00348-006-0199-5

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