Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session Q24: Surface Roughness: ComputationsBoundary Layers Micro

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Chair: Mostafa Toloui, University of Minnesota Room: 703 
Tuesday, November 21, 2017 12:50PM  1:03PM 
Q24.00001: Roughness topographical effects on mean momentum and stress budgets in developed turbulent channel flows Mostafa Aghaei Jouybari, Junlin Yuan Direct numerical simulations of turbulent channel flows are carried out over two surfaces: a synthesized sandgrain surface and a realistic turbine roughness that is characterized by more prominent largescale surface features. To separate the effects of wallnormal variation of the roughness area fraction from the (true) variation of flow statistics, the governing equations are areaaveraged using intrinsic averaging, contrary to the usually practice based on the total area (i.e., superficial averaging). Additional terms appear in the meanmomentum equation resulted from the wallnormal variation of the solid fraction and play a role in the nearwall balance. Results from surfaces with a step solidity function (e.g., cubes) will also be discussed. Compared to the sand grains, the turbine surface generates stronger forminduced fluctuations, despite weaker dispersive shear stress. This is associated with more significant forminduced productions (comparable to shear production) in Reynolds stress budgets, weaker pressure work, and, consequently, more anisotropic redistribution of turbulent kinetic energy in the roughness sublayer, which potentially leads to different turbulent responses between the two surfaces in nonequilibrium flows. [Preview Abstract] 
Tuesday, November 21, 2017 1:03PM  1:16PM 
Q24.00002: Effective Boundary Conditions for Viscous Incompressible Flow Over Rough Boundaries Sean Carney, Bjorn Engquist The direct numerical simulation of viscous flow over a rough boundary is challenging due to the large number of degrees of freedom required to adequately resolve the flow structures near the boundary. Previous mathematical analysis of the problem in the laminar regime has shown that replacing the noslip condition on the rough boundary with a Navierslip condition on a smooth boundary captures the average effect of roughness on the flow near the boundary, where the slip length is given by the average to a solution of an auxiliary cell problem. We describe a numerical multiscale method designed to estimate the slip length by coupling a coarse scale computation in the full domain with a high resolution computation localized to patches along the rough boundary. The method reproduces the proper slip length from the mathematical theory where it is applicable, and numerical results demonstrate the utility of the method even where the theory is no longer valid. We will also briefly comment on the application of this coupling strategy as a wall model in a high $Re$ LES. The physics is of course very different than the laminar regime considered here, but there are preliminary indications (Sandham et al, 2017) that this approach can successfully produce accurate turbulent flow statistics. [Preview Abstract] 
Tuesday, November 21, 2017 1:16PM  1:29PM 
Q24.00003: Modeling roughwall turbulent channel flow with principal component analysis enhanced amplitude modulation Sicong Wu, Kenneth Christensen, Carlos Pantano Direct numerical simulation of turbulent channel flows over rough surfaces, formed from hexagonallypacked arrays of hemispheres on both walls, were performed at friction Reynolds numbers $Re_\tau = 200$, $400$, and $600$. The inner normalized roughness height $k^+=20$ was maintained for all Reynolds numbers while the spacing between hemispheres was varied from $d/k=24$. The interactions between the nearwall smallscale fluctuations and outer layer largescale turbulence were studied by amplitude modulation (AM) analysis that has been modified to include principal component analysis (PCA). Based on these interactions, a PCAadapted predictive innerouter model was developed to address the modeling of anisotropic effects near the roughness and effectively predict the nearwall statistics up to $4^{th}$ order moments of all velocity fluctuations, including cross terms. The predictions based on the PCAadapted model were shown to agree excellently with the original statistics from the DNS with better predictions of the statistics of $v$ compared to model without the PCA. [Preview Abstract] 
Tuesday, November 21, 2017 1:29PM  1:42PM 
Q24.00004: Turbulent flow over `hydrodynamically smooth' longitudinal grooves Yixuan Li, Krishnan Mahesh Direct numerical simulations (DNS) are used to study turbulent channel flow at $\textit{Re}_\tau = 400$ over longitudinal grooves whose size is within the hydrodynamically smooth regime. Simulations are performed for flatwall channel and three different groove geometries. It is found that despite identical bulk velocity when the size of the groove is comparable to the viscous sublayer thickness, the slip effect of the longitudinal grooves causes some differences within the viscous sublayer. The spectra of the velocity and pressure fluctuations inside and outside the grooves are presented. It is found that the grooves suppress the energy at low frequencies. The filtering effect of the grooves is investigated using an analytical approach and a set of numerical experiments. The local effect of the grooves is associated to the turbulent channel flow by a nondimensional parameter $\omega L^2/\nu$, where $\omega$ is the frequency of outside turbulent signal, $L$ is half size the groove and $\nu$ is the kinematic viscosity. The analytical solution shows good agreement with the DNS data and helps explain the filtering mechanism of the grooved surfaces. [Preview Abstract] 
Tuesday, November 21, 2017 1:42PM  1:55PM 
Q24.00005: Large eddy simulation of the atmospheric boundary layer above a forest canopy Jahrul Alam A goal of this talk is to discuss large eddy simulation (LES) of atmospheric turbulence within and above a canopy/roughness sublayer, where coherent turbulence resembles a turbulent mixing layer. The proposed LES does not resolve the near wall region. Instead, a near surface canopy stress model has been combined with a wall adapting local eddy viscosity model. The canopy stress is represented as a threedimensional time dependent momentum sink, where the total kinematic drag of the canopy is adjusted based on the measurements in a forest canopy. This LES has been employed to analyze turbulence structures in the canopy/roughness sublayer. Results indicate that turbulence is more efficient at transporting momentum and scalars in the roughness sublayer. The LES result has been compared with the turbulence profile measured over a forest canopy to predict the turbulence statistics in the inertial sublayer above the canopy. Turbulence statistics between the inertial sublayer, the canopy sublayer, and the roughwall boundary layer have been compared to characterize whether turbulence in the canopy sublayer resembles a turbulent mixing layer or a boundary layer. The canopy turbulence is found dominated by energetic eddies much larger in scale than the individual roughness elements. [Preview Abstract] 
Tuesday, November 21, 2017 1:55PM  2:08PM 
Q24.00006: Largeeddy simulation of turbulent boundarylayer flow through a roughsmooth wallsurface transition A. Sridhar, D.I. Pullin We describe results from a largeeddysimulation (LES) study of a zeropressure gradient, flatplate turbulent boundary layer that flows across a discontinuous, spanwise, roughsmooth, wallsurface transition. The virtualwall model of Saito and Pullin (PoF, 2012) is utilized to model subgridscale roughness by use of the Colebrook form of the roughness function $\Delta U^+(k_s^+)$, where $k_s^+ = k_s\,u_\tau/\nu$ and $k_s$ is the equivalent sandgrain roughness. For given $Re_\tau = \delta_0\,u_\tau/\nu$ and ratio of $k_s$ to the boundary layer thickness at the transition $k_s/\delta_0$, the variation of $C_f(x)$ through the surface transition is calculated dynamically from the LES. Results at $Re_\tau\approx 4000$ are compared with detailed measurements for roughsmooth transition obtained at the University of Melbourne. The LES is used to explore the scaling behaviour of the discontinuity in $C_f$ at the transition and also the relaxation of $C_f(x)$ to appropriate downstream, equilibrium conditions (and any dependence on $Re_\tau$ and $k_s/\delta_0$). [Preview Abstract] 
Tuesday, November 21, 2017 2:08PM  2:21PM 
Q24.00007: WallRoughness Eddy Viscosity for RANS Closures Giles Brereton, Junlin Yuan In turbulent boundary layers over rough walls, a triple decomposition of variables into mean, spatially varying, and fluctuating components, together with a doubleaveraging procedure, can be used to identify extra terms in the $x$momentum equation which describe the pressure and viscous drag forces per unit mass \textit{on account of roughness}. These terms, which are significant only in the roughness sublayer, have been measured in the DNS of Yuan \& Piomelli (2014). In this talk, we describe a model for the effects of these terms as if they make an additive contribution to the eddy viscosity within the roughness sublayer, by recasting them as a simple algebraic function of the dimensionless roughness scale $k_s^+$, for which a theoretical rationale is proposed. With this modification, $k$$\epsilon$ and $k$$\epsilon$$v^\prime v^\prime$$f$ closures for turbulent channel flow yield mean velocity profiles and friction factors which are in good agreement with measured data in roughwall duct flows over a wide range of values of $k_s^+$ and $\hbox{Re}$. [Preview Abstract] 
Tuesday, November 21, 2017 2:21PM  2:34PM 
Q24.00008: Dependence of nearwall flow on the higher moments of a multiscale rough surface Thomas Jelly, Sotirios Sarakinos, Angela Busse Fully developed turbulent channel flow past irregular multiscale surface roughness has been investigated using direct numerical simulation (DNS) at a fixed friction Reynolds number of 395. The details of a surface generation algorithm  which permits realistic rough surfaces to be synthesised with specified statistical properties for either experimental or computational studies  will be outlined and discussed. The aim of the current work is to investigate the response of the nearwall region to systematic changes of higher order surface statistics, such as skewness and kurtosis. The influence of higher order moments is examined using doubleaveraged statistics of the turbulent flow which is decomposed into mean, dispersive and stochastic components. Firstorder roughness effects are investigated by quantifying the roughness function and examining the innerscaled mean streamwise velocity profile. Secondorder roughness effects are investigated by quantifying the relative magnitude of dispersive and Reynolds stresses in the nearwall region as a function of the surface skewness and kurtosis. Finally, modifications to the nearwall turbulence structure are examined by quantifying twopoint velocity correlations for both the dispersive and stochastic components. [Preview Abstract] 
Tuesday, November 21, 2017 2:34PM  2:47PM 
Q24.00009: Irregular wall roughness in turbulent TaylorCouette flow Pieter Berghout, Xiaojue Zhu, Roberto Verzicco, Detlef Lohse, Richard Stevens Many wall bounded flows in nature, engineering and transport are affected by surface roughness. Often, this has adverse effects, e.g. drag increase leading to higher energy costs. A major difficulty is the infinite number of roughness geometries, which makes it impossible to systematically investigate all possibilities. Here we present Direct Numerical Simulations (DNS) of turbulent TaylorCouette flow. We focus on the transitionally rough regime, in which both viscous and pressure forces contribute to the total wall stress. We investigate the effect of the mean roughness height and the effective slope on the roughness function, $\Delta U^+$. Also, we present simulations of varying $Ta$ ($Re$) numbers for a constant mean roughness height ($k_{mean}^+$). Alongside, we show the behavior of the large scale structures (e.g. plume ejection, Taylor rolls) and flow structures in the vicinity of the wall. [Preview Abstract] 
Tuesday, November 21, 2017 2:47PM  3:00PM 
Q24.00010: Direct numerical simulation of open channel flow over smoothtorough and roughtosmooth step changes Amirreza Rouhi, Daniel Chung, Nicholas Hutchins Direct numerical simulations (DNSs) are reported for open channel flow over streamwisealternating patches of smooth and fully rough walls. Owing to the streamwise periodicity, the flow configuration is composed of a step change from smooth to rough, and a step change from rough to smooth. The friction Reynolds number varies from 443 over the smooth patch to 715 over the rough patch. The flow is thoroughly studied by mean and fluctuation profiles, and spectrograms. The detailed flow from DNS reveals discrepancies of up to 50\% among the various definitions of the internallayer thickness, with apparent powerlaw exponents differing by up to 60\%. The definition based on the logarithmic slope of the velocity profile, as proposed by Chamorro \textit{et al.} (\textit{BoundaryLayer Meteorol.}, vol. 130, 2009, pp. 2941), is most consistent with the physical notion of the internal layer; this is supported by the defect similarity based on this internallayer thickness, and the streamwise homogeneity of the dissipation lengthscale within this internal layer. The statistics inside this internallayer, and the growth of the internal layer itself, are minimally affected by the streamwise periodicity when the patch length is at least six times the channel height. [Preview Abstract] 
Tuesday, November 21, 2017 3:00PM  3:13PM 
Q24.00011: Investigation of secondary flows in turbulent pipe flows with threedimensional sinusoidal walls Leon Chan, Michael MacDonald, Daniel Chung, Nicholas Hutchins, Andrew Ooi The occurrence of secondary flows is systematically investigated via Direct Numerical Simulations (DNS) of turbulent flow in a rough wall pipe at friction Reynolds numbers of 540. In this study, the peaktotrough height of the roughness elements, which consist of threedimensional sinusoidal roughness, is fixed at 120 viscous units while the wavelength of the roughness elements is varied. The solidity or effective slope ($ES$) of the roughness ranges from the sparse regime ($ES = 0.18$) to the closely packed roughness/dense regime ($ES = 0.72$). The timeindependent dispersive stresses, which arise due to the stationary features of the flow, are analysed and are found to increase with increasing roughness wavelength. These dispersive stresses are related to the occurrence of secondary flows and are maximum within the roughness canopy. Above the crest of the roughness elements, the dispersive stresses reduce to zero at wallnormal heights greater than half of the roughness wavelength. This study has found that the size and wallnormal extent of the secondary flows scales with the roughness wavelength and can reach wallnormal heights of almost half of the pipe radius. [Preview Abstract] 
Tuesday, November 21, 2017 3:13PM  3:26PM 
Q24.00012: Spatial characteristics of secondary flow in a turbulent boundary layer over longitudinal surface roughness Hyeon Gyu Hwang, Jae Hwa Lee Direct numerical simulations of turbulent boundary layers (TBLs) over spanwise heterogeneous surface roughness are performed to investigate the characteristics of secondary flow. The longitudinal surface roughness, which features lateral change in bed elevation, is described by immersed boundary method. The Reynolds number based on the momentum thickness is varied in the range of\textit{ Re}$_{\theta }=$300900. As the TBLs over the roughness elements spatially develop in the streamwise direction, a secondary flow emerges in a form of counterrotating vortex pair. As the spanwise spacing between the roughness elements and roughness width vary, it is shown that the size of the secondary flow is determined by the valley width between the roughness elements. In addition, the strength of the secondary flow is mostly affected by the spanwise distance between the cores of the secondary flow. Analysis of the Reynoldsaveraged turbulent kinetic energy transport equation reveals that the energy redistribution terms in the TBLs overthe ridge type roughness play an important role to derive lowmomentum pathways with upward motion over the roughness crest, contrary to the previous observation with the striptype roughness. [Preview Abstract] 
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