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A framework for studying the effect of compliant surfaces on wall turbulence

A framework for studying the effect of compliant surfaces on wall turbulence
A framework for studying the effect of compliant surfaces on wall turbulence
This paper extends the resolvent formulation proposed by McKeon & Sharma (2010) to consider turbulence-compliant wall interactions. Under this formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes, identified via a gain-based decomposition of the Navier-Stokes equations. Compliant surfaces, modeled as a complex wall admittance linking pressure and velocity, affect the gain and structure of these modes. With minimal computation, this framework accurately predicts the emergence of the quasi-2D propagating waves observed in recent direct numerical simulations. Further, the analysis also enables the rational design of compliant surfaces, with properties optimized to suppress flow structures energetic in wall turbulence. It is shown that walls with unphysical negative damping are required to interact favorably with modes resembling the energetic near-wall cycle, which could explain why previous studies have met with limited success. Positive-damping walls are effective for modes resembling the so-called very large-scale motions (VLSMs), indicating that compliant surfaces may be better suited for application at higher Reynolds number. Unfortunately, walls that suppress structures energetic in natural turbulence are also predicted to have detrimental effects elsewhere in spectral space. Consistent with previous experiments and simulations, slow-moving spanwise-constant structures are particularly susceptible to further amplification. Mitigating these adverse effects will be central to the development of compliant coatings that have a net positive influence on the flow.
0022-1120
415-441
Luhar, Mitul
fcdc522c-d1a2-4217-8fcf-411a1f66c8c0
Sharma, Ati S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, Beverley
731f87c6-d84d-4b8e-8f52-87980796f300
Luhar, Mitul
fcdc522c-d1a2-4217-8fcf-411a1f66c8c0
Sharma, Ati S.
cdd9deae-6f3a-40d9-864c-76baf85d8718
McKeon, Beverley
731f87c6-d84d-4b8e-8f52-87980796f300

Luhar, Mitul, Sharma, Ati S. and McKeon, Beverley (2015) A framework for studying the effect of compliant surfaces on wall turbulence. Journal of Fluid Mechanics, 768, 415-441. (doi:10.1017/jfm.2015.85).

Record type: Article

Abstract

This paper extends the resolvent formulation proposed by McKeon & Sharma (2010) to consider turbulence-compliant wall interactions. Under this formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes, identified via a gain-based decomposition of the Navier-Stokes equations. Compliant surfaces, modeled as a complex wall admittance linking pressure and velocity, affect the gain and structure of these modes. With minimal computation, this framework accurately predicts the emergence of the quasi-2D propagating waves observed in recent direct numerical simulations. Further, the analysis also enables the rational design of compliant surfaces, with properties optimized to suppress flow structures energetic in wall turbulence. It is shown that walls with unphysical negative damping are required to interact favorably with modes resembling the energetic near-wall cycle, which could explain why previous studies have met with limited success. Positive-damping walls are effective for modes resembling the so-called very large-scale motions (VLSMs), indicating that compliant surfaces may be better suited for application at higher Reynolds number. Unfortunately, walls that suppress structures energetic in natural turbulence are also predicted to have detrimental effects elsewhere in spectral space. Consistent with previous experiments and simulations, slow-moving spanwise-constant structures are particularly susceptible to further amplification. Mitigating these adverse effects will be central to the development of compliant coatings that have a net positive influence on the flow.

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More information

Accepted/In Press date: 27 January 2015
e-pub ahead of print date: 10 March 2015
Published date: 10 April 2015
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 374189
URI: http://eprints.soton.ac.uk/id/eprint/374189
ISSN: 0022-1120
PURE UUID: 644f99d6-fc7d-4b02-968b-c2f485009a73
ORCID for Ati S. Sharma: ORCID iD orcid.org/0000-0002-7170-1627

Catalogue record

Date deposited: 09 Feb 2015 13:30
Last modified: 08 Jan 2022 03:19

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Contributors

Author: Mitul Luhar
Author: Ati S. Sharma ORCID iD
Author: Beverley McKeon

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