# Direct numerical simulations of Taylor-Couette turbulence: The effects of sand grain roughness

Pieter Berghout*, Xiaojue Zhu, Daniel Chung, Roberto Verzicco, Richard J.A.M. Stevens, Detlef Lohse

*Corresponding author for this work

1 Citation (Scopus)

### Abstract

Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor-Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from $Ta=1.0\times 10^{7}$ (corresponding to $Re-{\unicode[STIX]{x1D70F}}=82$) to $Ta=1.0\times 10^{9}$ ($Re-{\unicode[STIX]{x1D70F}}=635$). We focus on the influence of the roughness height $k-{s}^{+}$ in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from $k-{s}^{+}=5$ up to $k-{s}^{+}=92$. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport $Nu-{\unicode[STIX]{x1D714}}$ and by the friction factor $C-{f}$. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness $k-{s}^{+}$ is calculated to be $1.33k$, where $k$ is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (VDI-Forsch., vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer $h-{r}$ with $h-{r}=2.78k-{s}$.

Original language English 260-286 27 Journal of fluid mechanics 873 24 Jun 2019 https://doi.org/10.1017/jfm.2019.376 Published - 25 Aug 2019

### Fingerprint

Direct numerical simulation
direct numerical simulation
sands
Turbulence
roughness
Sand
Surface roughness
turbulence
friction drag
Friction
pipe flow
friction factor
skin friction
Skin friction
Open systems
Pipe flow
Angular velocity
fluid dynamics
angular velocity
Fluid dynamics

### Keywords

• UT-Hybrid-D
• Taylor-Couette flow
• turbulent boundary layers
• plumes/thermals

### Cite this

title = "Direct numerical simulations of Taylor-Couette turbulence: The effects of sand grain roughness",
abstract = "Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor-Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from $Ta=1.0\times 10^{7}$ (corresponding to $Re-{\unicode[STIX]{x1D70F}}=82$) to $Ta=1.0\times 10^{9}$ ($Re-{\unicode[STIX]{x1D70F}}=635$). We focus on the influence of the roughness height $k-{s}^{+}$ in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from $k-{s}^{+}=5$ up to $k-{s}^{+}=92$. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport $Nu-{\unicode[STIX]{x1D714}}$ and by the friction factor $C-{f}$. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness $k-{s}^{+}$ is calculated to be $1.33k$, where $k$ is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (VDI-Forsch., vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer $h-{r}$ with $h-{r}=2.78k-{s}$.",
keywords = "UT-Hybrid-D, Taylor-Couette flow, turbulent boundary layers, plumes/thermals",
author = "Pieter Berghout and Xiaojue Zhu and Daniel Chung and Roberto Verzicco and Stevens, {Richard J.A.M.} and Detlef Lohse",
note = "Cambridge UP deal",
year = "2019",
month = "8",
day = "25",
doi = "10.1017/jfm.2019.376",
language = "English",
volume = "873",
pages = "260--286",
journal = "Journal of fluid mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

In: Journal of fluid mechanics, Vol. 873, 25.08.2019, p. 260-286.

TY - JOUR

T1 - Direct numerical simulations of Taylor-Couette turbulence

T2 - The effects of sand grain roughness

AU - Berghout, Pieter

AU - Zhu, Xiaojue

AU - Chung, Daniel

AU - Verzicco, Roberto

AU - Stevens, Richard J.A.M.

AU - Lohse, Detlef

N1 - Cambridge UP deal

PY - 2019/8/25

Y1 - 2019/8/25

N2 - Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor-Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from $Ta=1.0\times 10^{7}$ (corresponding to $Re-{\unicode[STIX]{x1D70F}}=82$) to $Ta=1.0\times 10^{9}$ ($Re-{\unicode[STIX]{x1D70F}}=635$). We focus on the influence of the roughness height $k-{s}^{+}$ in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from $k-{s}^{+}=5$ up to $k-{s}^{+}=92$. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport $Nu-{\unicode[STIX]{x1D714}}$ and by the friction factor $C-{f}$. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness $k-{s}^{+}$ is calculated to be $1.33k$, where $k$ is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (VDI-Forsch., vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer $h-{r}$ with $h-{r}=2.78k-{s}$.

AB - Progress in roughness research, mapping any given roughness geometry to its fluid dynamic behaviour, has been hampered by the lack of accurate and direct measurements of skin-friction drag, especially in open systems. The Taylor-Couette (TC) system has the benefit of being a closed system, but its potential for characterizing irregular, realistic, three-dimensional (3-D) roughness has not been previously considered in depth. Here, we present direct numerical simulations (DNSs) of TC turbulence with sand grain roughness mounted on the inner cylinder. The model proposed by Scotti (Phys. Fluids, vol. 18, 031701, 2006) has been modified to simulate a random rough surface of monodisperse sand grains. Taylor numbers range from $Ta=1.0\times 10^{7}$ (corresponding to $Re-{\unicode[STIX]{x1D70F}}=82$) to $Ta=1.0\times 10^{9}$ ($Re-{\unicode[STIX]{x1D70F}}=635$). We focus on the influence of the roughness height $k-{s}^{+}$ in the transitionally rough regime, through simulations of TC with rough surfaces, ranging from $k-{s}^{+}=5$ up to $k-{s}^{+}=92$. We analyse the global response of the system, expressed both by the dimensionless angular velocity transport $Nu-{\unicode[STIX]{x1D714}}$ and by the friction factor $C-{f}$. An increase in friction with increasing roughness height is accompanied with enhanced plume ejection from the inner cylinder. Subsequently, we investigate the local response of the fluid flow over the rough surface. The equivalent sand grain roughness $k-{s}^{+}$ is calculated to be $1.33k$, where $k$ is the size of the sand grains. We find that the downwards shift of the logarithmic layer, due to transitionally rough sand grains exhibits remarkably similar behaviour to that of the Nikuradse (VDI-Forsch., vol. 361, 1933) data of sand grain roughness in pipe flow, regardless of the Taylor number dependent constants of the logarithmic layer. Furthermore, we find that the dynamical effects of the sand grains are contained to the roughness sublayer $h-{r}$ with $h-{r}=2.78k-{s}$.

KW - UT-Hybrid-D

KW - Taylor-Couette flow

KW - turbulent boundary layers

KW - plumes/thermals

UR - http://www.scopus.com/inward/record.url?scp=85068080088&partnerID=8YFLogxK

U2 - 10.1017/jfm.2019.376

DO - 10.1017/jfm.2019.376

M3 - Article

AN - SCOPUS:85068080088

VL - 873

SP - 260

EP - 286

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

ER -