Characteristics of Scalar Frequency-Wave Spectrum of Wall Pressure Fluctuations at Gradient-Free Turbulent Boundary Layer

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Abstract

An analysis of the basic properties of the scalar frequency-wave spectrum of turbulent pressures, representing the total energy of the wave components of the turbulent pressure field with a given wave vector modulus, has been carried out. Consideration of the scalar spectrum, which has independent applied significance, allows us to visualize the energy distribution of turbulent pressures in a wide range of frequencies and wave numbers. Based on well-known vector wave field models, relations are proposed for estimating the reduced scalar spectrum. The degree and nature of the parametric influence of the Mach and Reynolds numbers are determined.

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About the authors

E. B. Kudashev

Space Research Institute, Russian Academy of Sciences

Author for correspondence.
Email: fmkdshv@gmail.com
Russian Federation, Moscow

L. R. Yablonik

Polzunov Scientific and Development Association on Research and Design of Power Equipment

Email: yablonik@gmail.com
Russian Federation, St. Petersburg

References

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Supplementary files

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2. Fig. 1. Qualitative analysis of the properties of the scalar wave spectrum; 1 – curves of equal values of the frequency-wave spectrum; 2 – convective ridge (maximum values); 3 – integration contour corresponding to the maximum value of the scalar wave spectrum

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3. Fig. 2. The given spectral dependences for different values of the dimensionless frequency. Models: (a) Smolyakova–Tkachenko [3]; (b) modified Efimtsova [2]; (c) Friendly–Zhang [4]. Values : 1 – 10; 2 – 1.0; 3 – 0.1. Curves:         ; —— ; ---- ; ••••••

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4. Fig. 3. Curves of equal levels of the reduced scalar spectrum. The values of 10lgφ are shown. Models: (a) – Smolyakova–Tkachenko [3]; (b) – modified Efimtsova [2]; (c) – Friendly–Zhang [4]; (d) – approximation (10)

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5. Fig. 4. Curves of equal levels of a dimensionless scalar spectrum. The values of 10lg are shown. Models: (a) – Smolyakova–Tkachenko [3]; (b) – modified Efimtsov [2]; (c) – Friendly–Zhang [4]; (d) – scalar model (10)

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6. Fig. 5. Influence numbers Mach on dimensionless Urgell scalar Urgell spectrum . Wide model Chase [5]. Numerical values: (a) – 0.01 (dotted-0); (b – - 0.1; (C) - 0.3; (D) - 0.5

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7. Fig. 6. The effect of the Reynolds number on a dimensionless scalar spectrum. Scalar model (10). RT values: -- 300; ---- 30

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