Session E08: Boundary Layers: Turbulent Boundary Layers I

Direct numerical simulation of the turbulent boundary layer over a bump with relaminarization

The turbulent boundary layer over the two-dimensional Gaussian-shaped Boeing bump is computed by direct numerical simulation of the incompressible Navier–Stokes equations. At the inflow, the momentum thickness Reynolds number is approximately 1000 and the boundary layer thickness is 1/8 of the bump height. Results show that the strong favorable pressure gradient (FPG) on the upstream side of the bump causes the boundary layer to enter a partial relaminarization process, with the near-wall turbulence being significantly weakened and becoming intermittent. At the bump peak, where the FPG switches to an adverse pressure gradient (APG), the near-wall turbulence is suddenly enhanced through a partial retransition process which energizes the internal layer, making it more resilient to the strong APG. In the strong FPG and APG regions over the bump, the inner and outer layers become largely independent of each other. The near-wall region responds to the pressure gradients and determines the skin friction, whereas the outer layer behaves similarly to a free shear layer subject to pressure gradients and mean streamline curvature effects.   

Direct numerical simulation of the turbulent boundary layer over the Gaussian-shaped Boeing bump at ReL=2M

The turbulent boundary layer over a two-dimensional Gaussian-shaped Boeing bump is computed by direct numerical simulation of the incompressible Navier–Stokes equations. At the inflow, the momentum thickness Reynolds number is approximately 1900 and the boundary layer thickness is 1/9 of the bump height. Preliminary results from this on-going simulation suggest that, at this Reynolds number, the flow does not experience significant re-laminarization and the resulting flow experiences a large separation soon after the bump peak where the pressure gradient switches from favorable to adverse. While it is unlikely that fully converged statistics will be obtained for the separated flow and recovery region in time for this presentation,  the attached flow regions and early separated flow region converge much faster and the focus of the talk will be on these regions. An early assessment of the effect of simulation domain width will also be discussed.    

Wall-modeled large eddy simulations of a turbulent boundary layer over a bump at ReL = 1 and 2 million

A turbulent boundary layer involving favorable and adverse pressure gradients and flow separation is encountered in a fluid flow over an aircraft wing at a high angle of attack. For such flows, Reynolds averaged Navier-Stokes (RANS) models are found to be inadequate, and on the other hand performing scale-resolving simulations such as wall-resolved large eddy simulations (WRLES) involves large computational overhead that makes it intractable for large Reynolds numbers. For such industrial flows, the use of hybrid RANS-LES simulations such as IDDES is growing. However, the fidelity of IDDES for such flows is not yet established and we take a step in that direction.

In this talk, we present IDDES results for a turbulent boundary layer flow over Boeing/Gaussian bump at Re_L = 1 and 2 million. The flow involves favorable and adverse pressure gradient regions which eventually leads to flow separation at higher Reynolds numbers. This flow is a challenging problem for existing RANS models as they fail to account for pressure gradient effects or predict flow separation region correctly. We investigate the evolution of velocity and stress profiles along with streamwise directions estimated by IDDES for the two different Reynolds number cases and compare it to RANS and DNS predictions.   

Characteristics of the vortical fissures in turbulent wall-bounded flows

The inertial domain of the turbulent wall-bounded flows are composed of large regions of uniform momentum zones (UMZs) segregated by countable slender fissures of elevated vorticity (i.e., vortical fissures). Because they account for spatially abrupt increments in streamwise velocity, it is readily surmised that the volume-weighted momentum transport across the vortical fissures (VFs) is large. Thus it is rational to suspect that their dynamical influences are significant to sustaining the inertial layer structure. While the statistical distribution of the vortical fissures has been studied extensively, their physical characteristics remain largely unknown due to their ever decreasing size, which scales with $1/\sqrt{\delta^+}$, where $\delta^+$ is the Reynolds number. The current study employs particle image velocimetry (PIV) data acquired at the Flow Physics Facility (FPF) with a boundary layer thickness of $~1m$ to study the properties of the VFs at high Reynolds numbers. The VFs are identified and extracted directly from instantaneous velocity profiles using a vorticity threshold method, which is analytically derived based on the self-similar dynamical structure of turbulent wall flows as determined via analysis of the mean streamwise momentum equation by Wei et al. (2005).   

Self Similarity in 2D Resolvent Analysis for Developing Turbulent Boundary Layer Flows

Two-dimensional resolvent analysis is applied to turbulent boundary layer flows, incorporating both the wall normal and streamwise variation of the flow, resulting in resolvent modes that evolve in the streamwise direction. Energetically relevant modes are identified from the resolvent operator, as a function of the mean flow field, spanwise wavenumber, and temporal frequency. For zero pressure gradient turbulent boundary layer flows, the self-similar scalings in different wall normal regions of the flow are well-known. Using the known mean flow scaling, as well as the analytic form of the resolvent operator, appropriate scaling is identified for the spanwise wavenumber and temporal frequency that results in a self similar resolvent operator. The resolvent modes, like the mean flow, are shown to evolve downstream in a self similar fashion. The global resolvent analysis is then used to investigate the effects of an external pressure gradient on the identified resolvent modes and their streamwise development.    

The influence of turbulence on surface heat transfer in boundary layers using a moment of temperature integral equation

Transition to turbulence dramatically increases the skin friction and heat transfer coefficients of boundary layer flows. The angular momentum integral (AMI) equation has previously shown that the skin friction coefficient is equal to the sum of the laminar skin friction (a function of Reynolds number only) and other terms representing skin friction enhancement by turbulent stresses ($-\overline{u^\prime v^\prime}$), freestream pressure gradients, and other physical effects. In this presentation, we extend this analysis to include heat transfer. A moment of temperature integral (MTI) equation is introduced to quantify the Stanton number as the sum of the laminar Stanton number (a function of Reynolds and Prandtl numbers) and other terms representing turbulent heat fluxes ($\overline{v^\prime T^\prime}$), streamwise growth, and other flow effects. The MTI equation is evaluated using direct numerical simulation results for transitional and turbulent boundary layers. The enhanced Stanton number in turbulent boundary layers is quantitatively tied to the integral of the turbulent heat flux across the boundary layer. The rapid increase in turbulent heat flux during transition creates a Stanton number peak that is partially mitigated by a reversal of the wall-normal mean velocity.   

Experimental Investigation of the Response of the Turbulent Boundary Layer to Synthetic Outer Layer Large-Scale Structure using PIV

It has been established that the dynamics of large-scale structures (LSS) in the outer region of turbulent boundary layers (TBL) and the near-wall small-scale turbulence are correlated. In previous experiments using a single hot-wire; it was shown that a synthetic LSS introduced by a plasma-based actuator in the outer region of TBL had a strong modulating effect on the near-wall turbulence. Results showed that for streamwise locations close to the actuator, an actuation frequency comparable to the burst/sweep frequency of the near-wall structure created the strongest modulation effect. Farther downstream, an actuation frequency related to the streamwise wavelength of the naturally occurring LSS resulted in the strongest modulation effect.  In the study reported here, an improved plasma-based active flow control device was placed in a similar region of the TBL to introduce a periodic synthetic LSS. Planar PIV was used to measure the time-resolved two-dimensional velocity field downstream of the actuator at various streamwise locations. Using PIV, the streamwise evolution of the synthetic LSS and its modulating effect on the near-wall turbulence are described in more detail. The results are discussed and compared with previous hot-wire measurements.   

Assessment of non-Boussinesq effects in a separated turbulent boundary layer with an emphasis on non-locality

In this work, we consider a canonical separated boundary layer flow at Re_θ= 350, where a separation bubble is induced in a fully turbulent boundary layer over a flat plate. Using the macroscopic forcing method (MFM), the leading-order anisotropic eddy viscosity is quantified, and its key anisotropic directions are identified to narrow down to 5 components. A posteriori analysis demonstrates significant improvement in RANS prediction of mean flow when this leading-order eddy viscosity operator is used instead of isotropic models based on the Boussinesq approximation. However, non-negligible errors still remain due to the non-local effects which are not captured by the leading-order eddy viscosity model. We present a preliminary attempt to address the need for non-locality using a simple non-local Boussinesq model.   

Turbulent fluid-structure-acoustic interaction of an elastic plate in turbulent channel flow for different plate boundary conditions

We perform a one-way coupled fluid-structure-acoustic interaction of an elastic plate in a turbulent channel flow using Direct Numerical Simulation (DNS) for different plate and flow parameters. The boundary condition's effect on the plate's response is studied at two friction Reynolds numbers, 180 and 400. Most previous works that studied the boundary condition's effect were performed in the frequency domain and compute only statistical quantities such as the plate's displacement cross-spectral density (CSD) using a model wall-pressure CSD. On the other hand, our calculations are performed in the time domain and yield the plate displacement's actual time-history using the DNS wall-pressure fluctuations. To simulate the turbulent flow, we solve the incompressible Navier-Stokes equations using finite volume DNS. To simulate the plate's response, we solve the linear elasticity equations using the continuous Galerkin finite element method. To simulate the far-field sound radiation, we solve the acoustic wave equation using the half-space Green's function. Furthermore, to examine how the fluid sources contribute to the structural vibration as a function of frequency and boundary condition, we use the framework of Anantharamu and Mahesh (2021) to post-process our DNS data.   

Influence of inflow tripping intensity on stimulating a fully developed state in open channel flow experiments

Open channel flow is fully developed when there is no streamwise variation of flow variables and boundary layer thickness is equal to flow depth. Planar particle image velocimetry is used to study the variation of flow characteristics with different tripping intensities, keeping Reynolds number, flow depth and upstream development length constant. Trip intensity is gradually increased from zero up to a critical value at which a fully developed state is achieved, beyond which distribution of flow variables deviates from the fully developed state.

In previous studies, fully developed flow is ensured based on validation of log-law and velocity defect law. These criteria are not adequate since they only demonstrate a well-behaved boundary layer which is possible for a properly normalized developing flow. Due to uncertainty in evaluating free stream velocity, in this study the boundary layer thickness is estimated using the wall-normal distribution of Reynolds stresses and fully developed flow is achieved at the highest trip intensity that ensures boundary layer thickness equals flow depth, while retaining properties of a well-behaved boundary layer. Quadrant analysis shows a difference in boundary layer characteristics of the developing and developed flow due to the free surface.