Session X12: Boundary Layers: Turbulent II and Laminar

Numerical comparison of scalar transport over permeable and non-permeable rippled beds using κ-ε RANS models

Sediment boundaries influence the velocity field and transport of scalar quantities in the wave bottom boundary layer through their roughness scales, sediment mobility, and permeability. The occurrence of bedforms in the sediment layer, such as ripples, also introduces a form drag associated with pressure gradients generated by the ripple geometry that significantly affect momentum transfer in the region. The complex interaction of these elements affects the temporal and spatial distribution of momentum fluxes and the transport of substances near the sediment-water interface, yet their individual contributions is difficult to assess. To this end, the effect of bedform geometry was isolated by modelling the rippled coastal bottom boundary as non-permeable and fixed. A model that couples the κ-ε Reynolds–Averaged Navier–Stokes equations with an advection–diffusion solver was applied using the OpenFOAM environment. The model was used to carry out simulations of oscillatory flow with constant scalar sources at various location along the rippled bed to assess the local effects of a boundary-induced pressure gradient on passive scalar mixing. The simulations were replicated using the two-phase model SedFOAM with a Johnson-Jackson particle pressure model to introduce the effects of permeability and sediment mobility. The introduction of a permeable mobile boundary was found to significantly alter the velocity field over the rippled bed, evidenced by increased boundary layer thicknesses and phase differences as high as 45° at ripple flanks. This, combined with sediment mobility and suspension near the scalar sources, led to spatial and temporal differences as high as 30% in both scalar concentration and fluxes. These differences are thus attributed to the sediment mobility and permeability allowed by the two-phase model.

  

Grain Shape Effects on Fluid-Sediment-Structure Interaction Under Oscillatory Flow

The goal of this investigation is to accurately quantify the effects of grain shape and angularity on fluid-sediment-structure interaction under the presence of oscillating fluid motion. Solid objects were subjected to oscillating fluid forcing in a full-scale boundary layer apparatus consisting of a rippled sediment tray oscillating in a still fluid. The variable group included calcareous sediments exhibiting coral, shells and other marine fragments with a variety of shapes and angular features, while the control group consisted of homogenous silica sands with generally smooth and spherical shapes. For the test runs presented here, hydrodynamics were scaled with the object’s Shields parameter, which corresponds to the shear stress acting on the object normalized by its immerse weight, resulting in significantly less mobility and burial on the variable group for streamlined cases. For non-streamlined cases, uniform and symmetric scour patterns were found for the control group as a result of the object pivoting in place. Unstable cases (non-streamlined orientations with object located at ripple crests or flanks) resulted in directional dependencies, with the variable group showing more resistance to coherent motions dominating the near-boundary hydrodynamics. These findings suggest that the irregular nature of the variable group sediments not only increases intergranular friction, but also friction forces between the sediment and the object, thereby hindering its mobilization and burial.   

Full-scale scalar fluxes near the sediment water interface: spatial, temporal, and source location dependencies

Several biological, chemical, and ecological processes occur at the sediment-water interface of the coastal ocean. Near-boundary hydrodynamics are dominated by oscillating flows, while the porous boundary is characterized by different roughness scales including sediments (O[mm]) and bedforms (O[cm-m]). To better understand the exchange dynamics in this region, full-scale laboratory experiments were performed with an oscillating sediment tray to acquire high-resolution velocity and concentration fields using PIV and PLIF. Rhodamine 6G dye was used as the scalar and injected at three different locations along the sediment ripple: crest (CrC), flank (FlC), and trough (TrC). Phase-averaged plume concentrations remained inside the boundary layer, with no accumulation over time. The spread of dye reached 0.5, 1.3, and 0.25 of the boundary layer thickness for CrC, FlC, and TrC, respectively. Phase-averaged concentration fluxes were higher for FlC and much lower for TrC. Fluxes for TrC remain very close to the bed in a layer of roughly 10mm, following the ripple shape. The same was true for CrC during phases with u   

Methane dispersion in a zero-pressure-gradient boundary layer flow at large Reynolds number

The dispersion of methane gas released from a vertical pipe in a zero-pressure gradient boundary layer flow at large Reynolds number is investigated. A gaseous mixture of 5% methane and 95% nitrogen by volume is injected into the boundary layer in a jet in crossflow arrangement where the jet exit is h_s/δ ≈ 0.6 above the floor of the test section, where h_s is the source height and δ is the boundary layer thickness. Three jet-to-crossflow velocity ratios and three source configurations are investigated. The source configurations consist of a straight vertical pipe and two concentric pipes with aspect ratio AR (outer diameter/inner diameter) = 10.67 and 21.33. The source diameter (inner diameter) is fixed in all three configurations. Methane concentration downstream of the source is acquired using an Aeris Technologies MIRA Ultra LDS. The downstream evolution of the methane jet is characterized and the underlying mechanisms controlling the scalar dispersion are investigated.    

Scale dependency of pressure distribution, lift, and vortex shedding of a hydrofoil

Full-scale control surfaces and propulsors are subject to cavitation erosion patterns that are not always related to expectations at model scales. Turbulent flow at the trailing edge of the surface results in uneven pressure distribution in the near wake area of the hydrofoil. The behavior of turbulent flow in the boundary layer regarding transition and separation as a function of Reynolds number must be properly captured to understand pressure distribution and resultant forces, such as lift and drag, to aid in full-scale experiment design selection. A series of large-eddy simulations using the curvilinear immersed boundary method are undertaken at a range of Reynolds numbers, angles of attack, and cavitation numbers. Two trailing-edge bevel angles of the hydrofoil are considered due to the geometry-dependence of the near wake. Turbulent flow at the trailing edge results in uneven pressure distribution in the near wake area of the hydrofoil. The lift forces and pressure distribution around the hydrofoil are used to choose design parameters for the model and full-scale hydrofoils to be experimentally tested. Understanding the boundary layer and near wake dynamics that produce unsteady pressure distributions of the surface at a range of Reynolds numbers is one of the first steps in assessing the scale dependency of cavitation erosion.   

Mixing into a turbulent boundary layer with freestream turbulence

We experimentally explore the ability of freestream turbulence (FST) above a turbulent boundary layer (TBL) to facilitate the transport of a passive scalar into the TBL. Previous studies have demonstrated that increasing turbulence intensity facilitates mixing of a passive scalar in a flow. Moreover, studies focussed on how FST influences a TBL have demonstrated that increasing the intensity of the FST generally increases the wall friction velocity and the boundary layer thickness. In contrast to the growth of the boundary layer thickness, a TBL in the presence of FST sees its coherent shear layers (demarcating, for instance, uniform momentum zones) pushed closer to the wall. The question that arises is: does the manipulation of shear layers help or hinder the mixing? An experiment was conducted where a passive scalar was introduced at a fixed height (outside the TBL) in an open channel flow, and then an active grid was used to vary the FST. It is demonstrated that indeed the FST facilitates the mixing of fluid from outside the TBL into the TBL, but perhaps not for the most intuitive reasons. The scalar appears to pass straight through the velocity/shear based interfaces. The talk will explain the mechanics of what is happening.   

Incorporating intrinsic compressibility effects in velocity transformations for wall-bounded turbulent flows

A transformation that relates a compressible wall-bounded turbulent flow with non-uniform fluid properties to an equivalent incompressible flow with uniform fluid properties is derived and validated. The transformation accounts for both variable-property and intrinsic compressibility effects, the latter being the key improvement over the current state-of-the-art. The importance of intrinsic compressibility effects contradicts the renowned Morkovin's hypothesis. The proposed transformation is then used for drag and heat transfer prediction in compressible flows. This requires the precise knowledge of the entire velocity and temperature profiles. Current methods typically assume a single velocity scaling law to inverse transform the incompressible reference profile, neglecting the different scaling characteristics of the inner and outer layers. We use distinct velocity transformations for these two regions. In the inner layer, we utilize our proposed scaling law, while the outer layer profile is inverse-transformed with the well-known Van Driest transformation. The result is an analytical expression for the mean shear valid in the entire boundary layer, which combined with a temperature-velocity relationship, provides predictions of mean velocity and temperature profiles at unprecedented accuracy. Using these profiles, drag and heat transfer is evaluated with an accuracy of +/-4% and +/-8%, respectively, for a wide range of compressible turbulent boundary layers up to Mach numbers of 14.   

Three-dimensional stress measurement of a laminar flow in a rectangular channel using integrated photoelasticity

The purpose of this study is to measure the shear rate distribution of a laminar flow in a rectangular by using integrated photoelasticity. We measured a mixed solution of photoelastic material, cellulose nanoctystal (CNC), to elucidate whether there are any phenomena peculiar to CNC mixed solution that differ from integrated photoelasticity in the solid case. In addition, we examine the stress-optic law for CNC mixed solution using a high-speed polarization camera to measure the retardation and orientation angles of polarized lights. We compare the measured retardation and theoretical secondary-principal-stress-difference distribution based on the analytical solution in steady laminar flow. Results show that retardation, which was not caused by stress, appeared in the CNC mixed solution. We compared the secondary principal stress difference distribution with the retardation distribution offsetting the effect of the retardation specific to the CNC mixed solution. The result showed that the spatial intensity distributions of both agreed well. We conducted additional verification for various flow rates.   

The boundary layer structure of laminar plug-to-Poiseuille transitions mediated by a porous medium

We derive the canonical boundary layer structure for 2D plug flow transitioning to Poiseuille flow in two parallel channels connected via a porous medium, using the method of matched asymptotic expansions and validated through numerical simulations. Plug flow enters through two long thin parallel 2D channels separated by a porous membrane wall, which we model using steady Navier-Stokes and Darcy flow equations, respectively. We investigate the flow behaviour in the boundary layer regions for all (laminar) Reynolds number regimes, providing insight into the laminar transition from plug to Poiseuille flow. We explore in detail the complex nested boundary layer structure that emerges in the high Reynolds number limit. We present generalised results for arbitrary Reynolds number and channel length, and systematically derive coupling conditions to match into the outer flow lubrication regions away from the channel inlets. Finally, we validate our asymptotic analysis with full numerical simulations using COMSOL Multiphysics.

Our asymptotic analysis is key to gaining a mechanistic understanding of the transitional behaviour and coupling of flow across a porous interface, and is applicable in a wide range of industrial applications including filtration and separation problems, tissue engineering and biofilm erosion.   

Addressing The Blasius Paradox In the Flow Around A Flat Plate With A Numerical Experiment

The Blasius paradox in the laminar flow around a flat plate is the fact that the transverse component of velocity reaches a final positive value. As a consequence, the boundary layer thickness increases indefinitely. This paradox is due to the fact that the flat plate is semi infinite in the original solution to this flow problem. However, we are interested in the solution to this flow problem with a flat plate of finite length. In this case, it is impossible to verify the Blasius' solution for the transverse component of the velocity. This issue has been discussed by some researchers in the last thirty years. However, there is no consensus so far. In this work, we address this problem by performing a numerical experiment in the flow around a flat plate. We choose appropriate size of the flow domain, in order to ensure undisturbed flow conditions upstream of the leading edge of the flat plate and far away from the flat plate plate in the transverse direction of the flow. The full Navier Stokes equations are solved in the flow domain with Galerkin finite elements. Appropriate boundary conditions are formulated in the flow domain where the flat plate (with finite length) is placed. The result of this research is that the transverse component of the velocity is negative only close to the lfat plate and gradually tends to zero. In addition, the transverse velocity component is negative close to the trailing edge of the flat plate. As a consequence, the boundary layer thicknes becomes flat. In other words, the Blasius paradox disappears if we study this flow with a flat plate of finite length. The results of this work are independent of the magnitude of the Reynods (Re) number. Results are presented in the range 0.1 ≤ Re ≤ 1·10⁶.    

Compressible laminar boundary layers over isotropic porous substrates

A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes of high porosity, the momentum and enthalpy balance equations are derived by volume averaging, and the properties of the substrate are assumed to vary smoothly across a thin interfacial layer. The solid matrix is rigid and in thermal equilibrium with the fluid phase. For the first time, the self-similar solution proposed by Tsiberkin (2017, 2018) for streamwise-growing permeability is extended to include a Forchheimer term, compressibility, and heat conduction effects. The velocity and temperature profiles show an inflection point in the interfacial layer, where the velocity decreases exponentially to zero because of the Darcy-Forchheimer drag. The static temperature recovers a quasi-adiabatic value at the interface regardless of the boundary condition imposed at the bottom of the porous substrate, and a sharp reduction of the velocity gradient is observed. The effect of the grain diameter, volume porosity, and the Mach number are discussed.   

The Steady Flow Around A Rotating Sphere With Variable Viscosity

A new model of the steady flow around a rotating sphere at large Reynolds numbers is obtained and analysed which has been further augmented with a temperature dependent viscosity. As the sphere rotates, Boundary Layers are formed at the poles and are convected along the sphere surface towards the equator where a collision takes place resulting in a toroidal vortex around the equator. Using Boundary Layer approximations, the full Navier-Stokes problem is reduced to solving simpler, albeit still non-linear, PDE systems in distinct regions around the sphere including the equatorial flow. This area of the flow possesses interesting physical behaviours such as Boundary Layer Separation and Reattachment that forms a Radial Jet causing the toroidal vortex. The current models of the equatorial flow are compared to numerical simulations of the full Navier-Stokes problem, but by incorporating additional azimuthal terms due to the similarity of the equatorial geometry of the sphere with the cylinder, results are greatly improved. The full flow is then compiled and is integrated with a temperature dependent viscosity where results qualitatively agree with similar studies.