Turbulence in a transient channel flow with a wall of pyramid roughness

M. Seddighi, S. He, D. Pokrajac, T. O'Donoghue, A. E. Vardy

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Abstract

A direct numerical simulation investigation of a transient flow in a channel with a smooth top wall and a roughened bottom wall made of close-packed pyramids is presented. An initially stationary turbulent flow is accelerated rapidly to a new flow rate and the transient flow behaviour after the acceleration is studied. The equivalent roughness heights of the initial and final flows are k+s = 14.5 and 41.5, respectively. Immediately after the acceleration ends, the induced change behaves in a ‘plug-flow’ manner. Above the roughness crests, the additional velocity due to the perturbation flow is uniform; below the crest, it reduces approximately linearly to zero at the bottom of the roughness elements. The interaction of the perturbation flow with the rough wall is characterised by a series of events that resemble those observed in roughness-induced laminar–turbulent transitions. The process has two broad stages. In the first of these, large-scale vortices, comparable in extent to the roughness wavelength, develop around each roughness element and high-speed streaks form along the ridge lines of the elements. After a short time, each vortex splits into two, namely (i) a standing vortex in front of the element and (ii) a counter-rotating hairpin vortex behind it. The former is largely inactive, but the latter advects downstream with increasing strength, and later lifts away from the wall. These hairpin vortices wrap around strong low-speed streaks. The second stage of the overall process is the breakdown of the hairpin vortices into many smaller multi-scale vortices distributed randomly in space, leading eventually to a state of conventional turbulence. Shortly after the beginning of the first stage, the three components of the r.m.s of the velocity fluctuation all increase significantly in the near-wall region as a result of the vortical structures, and their spectra bear strong signatures of the surface topology. During the second stage, the overall turbulence energy in this region varies only slightly, but the spectrum evolves significantly, eventually approaching that of conventional turbulence. The direct effect of roughness on the flow is confined to a region up to approximately three element heights above the roughness crests. Turbulence in the core region does not begin to increase until after the transition near the wall is largely complete. The processes of transition over the smooth and rough walls of the channel are practically independent of each other. The flow over the smooth wall follows a laminar–turbulent transition and, as known from previous work, resembles a free-stream turbulence-induced boundary layer bypass transition
Original languageEnglish
Pages (from-to)226-260
Number of pages35
JournalJournal of Fluid Mechanics
Volume781
Early online date16 Sep 2015
DOIs
Publication statusPublished - Oct 2015

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channel flow
Channel flow
pyramids
Turbulence
roughness
Surface roughness
turbulence
Vortex flow
horseshoe vortices
vortices
Confined flow
perturbation
wrap
uniform flow
bypasses
free flow
Direct numerical simulation
plugs
bears
direct numerical simulation

Keywords

  • transient channel flow
  • roughness-induced transition
  • bypass transition

Cite this

Turbulence in a transient channel flow with a wall of pyramid roughness. / Seddighi, M.; He, S.; Pokrajac, D.; O'Donoghue, T.; Vardy, A. E.

In: Journal of Fluid Mechanics, Vol. 781, 10.2015, p. 226-260.

Research output: Contribution to journalArticle

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abstract = "A direct numerical simulation investigation of a transient flow in a channel with a smooth top wall and a roughened bottom wall made of close-packed pyramids is presented. An initially stationary turbulent flow is accelerated rapidly to a new flow rate and the transient flow behaviour after the acceleration is studied. The equivalent roughness heights of the initial and final flows are k+s = 14.5 and 41.5, respectively. Immediately after the acceleration ends, the induced change behaves in a ‘plug-flow’ manner. Above the roughness crests, the additional velocity due to the perturbation flow is uniform; below the crest, it reduces approximately linearly to zero at the bottom of the roughness elements. The interaction of the perturbation flow with the rough wall is characterised by a series of events that resemble those observed in roughness-induced laminar–turbulent transitions. The process has two broad stages. In the first of these, large-scale vortices, comparable in extent to the roughness wavelength, develop around each roughness element and high-speed streaks form along the ridge lines of the elements. After a short time, each vortex splits into two, namely (i) a standing vortex in front of the element and (ii) a counter-rotating hairpin vortex behind it. The former is largely inactive, but the latter advects downstream with increasing strength, and later lifts away from the wall. These hairpin vortices wrap around strong low-speed streaks. The second stage of the overall process is the breakdown of the hairpin vortices into many smaller multi-scale vortices distributed randomly in space, leading eventually to a state of conventional turbulence. Shortly after the beginning of the first stage, the three components of the r.m.s of the velocity fluctuation all increase significantly in the near-wall region as a result of the vortical structures, and their spectra bear strong signatures of the surface topology. During the second stage, the overall turbulence energy in this region varies only slightly, but the spectrum evolves significantly, eventually approaching that of conventional turbulence. The direct effect of roughness on the flow is confined to a region up to approximately three element heights above the roughness crests. Turbulence in the core region does not begin to increase until after the transition near the wall is largely complete. The processes of transition over the smooth and rough walls of the channel are practically independent of each other. The flow over the smooth wall follows a laminar–turbulent transition and, as known from previous work, resembles a free-stream turbulence-induced boundary layer bypass transition",
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note = "Acknowledgements The authors acknowledge funding from the UK Engineering and Physical Science Research Council (EP/G068925/1 and EP/G069441/1). We are grateful to Professor P. Orlandi for his advice on the numerical methods. This work made use of the facilities of the N8 HPC, provided and funded by the N8 consortium and EPSRC (grant no. EP/K000225/1), as well as the UK National Supercomputer ARCHER sponsored by EPSRC through the UK Turbulence Consortium (UKTC) (grant no. EP/L000261/1).",
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T1 - Turbulence in a transient channel flow with a wall of pyramid roughness

AU - Seddighi, M.

AU - He, S.

AU - Pokrajac, D.

AU - O'Donoghue, T.

AU - Vardy, A. E.

N1 - Acknowledgements The authors acknowledge funding from the UK Engineering and Physical Science Research Council (EP/G068925/1 and EP/G069441/1). We are grateful to Professor P. Orlandi for his advice on the numerical methods. This work made use of the facilities of the N8 HPC, provided and funded by the N8 consortium and EPSRC (grant no. EP/K000225/1), as well as the UK National Supercomputer ARCHER sponsored by EPSRC through the UK Turbulence Consortium (UKTC) (grant no. EP/L000261/1).

PY - 2015/10

Y1 - 2015/10

N2 - A direct numerical simulation investigation of a transient flow in a channel with a smooth top wall and a roughened bottom wall made of close-packed pyramids is presented. An initially stationary turbulent flow is accelerated rapidly to a new flow rate and the transient flow behaviour after the acceleration is studied. The equivalent roughness heights of the initial and final flows are k+s = 14.5 and 41.5, respectively. Immediately after the acceleration ends, the induced change behaves in a ‘plug-flow’ manner. Above the roughness crests, the additional velocity due to the perturbation flow is uniform; below the crest, it reduces approximately linearly to zero at the bottom of the roughness elements. The interaction of the perturbation flow with the rough wall is characterised by a series of events that resemble those observed in roughness-induced laminar–turbulent transitions. The process has two broad stages. In the first of these, large-scale vortices, comparable in extent to the roughness wavelength, develop around each roughness element and high-speed streaks form along the ridge lines of the elements. After a short time, each vortex splits into two, namely (i) a standing vortex in front of the element and (ii) a counter-rotating hairpin vortex behind it. The former is largely inactive, but the latter advects downstream with increasing strength, and later lifts away from the wall. These hairpin vortices wrap around strong low-speed streaks. The second stage of the overall process is the breakdown of the hairpin vortices into many smaller multi-scale vortices distributed randomly in space, leading eventually to a state of conventional turbulence. Shortly after the beginning of the first stage, the three components of the r.m.s of the velocity fluctuation all increase significantly in the near-wall region as a result of the vortical structures, and their spectra bear strong signatures of the surface topology. During the second stage, the overall turbulence energy in this region varies only slightly, but the spectrum evolves significantly, eventually approaching that of conventional turbulence. The direct effect of roughness on the flow is confined to a region up to approximately three element heights above the roughness crests. Turbulence in the core region does not begin to increase until after the transition near the wall is largely complete. The processes of transition over the smooth and rough walls of the channel are practically independent of each other. The flow over the smooth wall follows a laminar–turbulent transition and, as known from previous work, resembles a free-stream turbulence-induced boundary layer bypass transition

AB - A direct numerical simulation investigation of a transient flow in a channel with a smooth top wall and a roughened bottom wall made of close-packed pyramids is presented. An initially stationary turbulent flow is accelerated rapidly to a new flow rate and the transient flow behaviour after the acceleration is studied. The equivalent roughness heights of the initial and final flows are k+s = 14.5 and 41.5, respectively. Immediately after the acceleration ends, the induced change behaves in a ‘plug-flow’ manner. Above the roughness crests, the additional velocity due to the perturbation flow is uniform; below the crest, it reduces approximately linearly to zero at the bottom of the roughness elements. The interaction of the perturbation flow with the rough wall is characterised by a series of events that resemble those observed in roughness-induced laminar–turbulent transitions. The process has two broad stages. In the first of these, large-scale vortices, comparable in extent to the roughness wavelength, develop around each roughness element and high-speed streaks form along the ridge lines of the elements. After a short time, each vortex splits into two, namely (i) a standing vortex in front of the element and (ii) a counter-rotating hairpin vortex behind it. The former is largely inactive, but the latter advects downstream with increasing strength, and later lifts away from the wall. These hairpin vortices wrap around strong low-speed streaks. The second stage of the overall process is the breakdown of the hairpin vortices into many smaller multi-scale vortices distributed randomly in space, leading eventually to a state of conventional turbulence. Shortly after the beginning of the first stage, the three components of the r.m.s of the velocity fluctuation all increase significantly in the near-wall region as a result of the vortical structures, and their spectra bear strong signatures of the surface topology. During the second stage, the overall turbulence energy in this region varies only slightly, but the spectrum evolves significantly, eventually approaching that of conventional turbulence. The direct effect of roughness on the flow is confined to a region up to approximately three element heights above the roughness crests. Turbulence in the core region does not begin to increase until after the transition near the wall is largely complete. The processes of transition over the smooth and rough walls of the channel are practically independent of each other. The flow over the smooth wall follows a laminar–turbulent transition and, as known from previous work, resembles a free-stream turbulence-induced boundary layer bypass transition

KW - transient channel flow

KW - roughness-induced transition

KW - bypass transition

U2 - 10.1017/jfm.2015.488

DO - 10.1017/jfm.2015.488

M3 - Article

VL - 781

SP - 226

EP - 260

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -