Xiang Yang

Pennsylvania State University | Penn State · Department of Mechanical Engineering

We conduct direct numerical simulations and study the evolution of a pair of counter-rotating vortices in a stratified and turbulent environment beyond the first vortex linking (which is due to the Crow instability). The initial position of the two vortices is perpendicular to the direction of thermal stratification. We vary the Froude number, the...

The mean velocity follows a logarithmic scaling in the surface layer when normalized by the friction velocity, i.e. a velocity scale derived from the wall-shear stress. The same logarithmic scaling exists for the mean temperature when one normalizes the temperature with the friction temperature, i.e. a scale derived from the wall heat flux. This te...

This survey investigates wall modeling in large eddy simulations (LES) using data-driven machine learning (ML) techniques. To this end, we implement three ML wall models in an open-source code and compare their performances with the equilibrium wall model in LES of half-channel flow at eleven friction Reynolds numbers between $180$ and $10^{10}$. T...

A stratified wake has multiple flow regimes, and exhibits different behaviors in these regimes due to the competing physical effects of momentum and buoyancy. This work aims at automated classification of the weakly and the strongly stratified turbulence regimes based on information available in a full Reynolds stress model. First, we generate a di...

Design for cooling effectiveness in internal flow systems relies on accurate models for dynamic losses and heat transfer. In these systems (e.g., gas turbine blades, intercoolers, heat exchangers), thousands of individual passages of varying configuration and roughness morphology can be present. In recent years, additive manufacturing (AM) has furt...

Estimates of grid-point and time-step requirements exist for many canonical flows but not for stratified wakes. The purpose of this work is to fill in this gap. We apply the basic meshing principles and estimate the grid-point and time-step requirements for RANS and LES of stratified wake flows at high Reynolds numbers, as arise in many geophysical...

Buoyant wakes are widely encountered in ocean environment and undersea vehicle flows. These are typically characterized by high Reynolds (Re) and Froude (Fr) numbers, so turbulence resolving CFD models of such flows, i.e., Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), require significant computational resources. Therefore, Reyn...

The goal of this work is to investigate the feasibility of constructing data-driven dynamical system models of roughness-induced secondary flows in thermally stratified turbulent boundary layers. Considering the case of a surface roughness distribution which is homogeneous and heterogeneous in the streamwise and spanwise directions, respectively, w...

Conventional empirical turbulence modeling is progressive: one begins by modeling simple flows and progressively works towards more complex ones. The outcome is a series of nested models, with the next, more complex model accounting for some additional physics relative to the previous, less complex model. The above, however, is not the philosophy o...

The mixing-layer analogy is due to Raupach, Finnigan & Brunet ( Boundary-Layer Meteorol. , vol. 25, 1996, pp. 351–382). In the analogy, the flow in the roughness sublayer of a homogeneous deep vegetation canopy boundary layer is analogous to a plane mixing layer rather than a surface layer. Evidence for the analogy includes the inflected velocity p...

Computational fluid dynamics using the Reynolds-averaged Navier-Stokes (RANS) remains the most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are one of the biggest sources of errors and uncertainties in the model predictions. This work aims to quantify mode...

Metal additive manufacturing has enabled geometrically complex internal cooling channels for turbine and heat exchanger applications, but the process gives rise to large-scale roughness whose size is comparable to the channel height (which is 500 $\mathrm {\mu }$ m). These super-rough channels pose previously unseen challenges for experimental meas...

Swells are common in sea areas, but how swells affect the operation of an offshore wind farm is poorly understood. To fill in this knowledge gap, large-eddy simulations of turbine arrays above swells are performed. Specifically, downwind, upwind, and lateral swells with three different wave ages are considered. The results show that downwind and up...

Computational fluid dynamics using the Reynolds-averaged Navier–Stokes (RANS) remains the most cost-effective approach to study wake flows and power losses in wind farms. The underlying assumptions associated with turbulence closures are one of the biggest sources of errors and uncertainties in the model predictions. This work aims to quantify mode...

When manufacturing a turbine engine, the combustor annulus and the turbine annulus are created as separate parts and assembled. This leads to an inter-platform gap between the two components, which must be supplied with leakage air to prevent ingestion of the extremely hot combustion gases into the interior of the engine. The combustor and the turb...

We exploit Monin–Obukhov similarity theory and Townsend’s attached-eddy hypothesis and arrive at a logarithmic-linear law for the streamwise velocity variance in the surface layer of stably stratified boundary layers. To test the logarithmic-linear law, we conduct large-eddy simulations (LES) of stably stratified turbulent boundary layers at variou...

A practical application of universal wall scalings is near-wall turbulence modeling. In this paper, we exploit the semilocal scaling [Patel, Boersma, and Pecnik, Phys. Rev. Fluids, 2, 084604 (2017)] and derive an eddy conductivity closure for wall-modeled large-eddy simulation of high-speed flows. We show that while the semilocal scaling does not c...

Enhanced fluctuations, steep gradients, and intensified heat transfer are characteristics of wall-bounded turbulence at transcritical conditions. Although such conditions are prevalent in numerous technical applications, the structure of the thermal boundary layer under realistic density gradients and heating conditions remains poorly understood. S...

Flow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using DNS and LES, the ability of sublayer-resolved RANS to predict the bulk flow phenomena of these systems is relatively unexplored, especially...

Buoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space-time resolution requirements for DNS or LES. On the other hand, many of the important physical mechanisms, such a...

The wall-modeled large-eddy simulation (WMLES) computational framework generally includes a wall-model solver outside the large-eddy simulation (LES) infrastructure, with the two solvers communicating only at the matching location and the wall. Having a wall-model solver outside the LES jeopardizes the performance of WMLES: first, the wall-model so...

In analogy with the classical concept of mass-flux-based streamlines, we define Angular Momentum Transport (AMT) lines as an aerodynamic functional diagnostic tool. The AMT lines are the ones whose tangents are given by the average angular momentum flux. The mathematical and physical properties of these AMT lines are exploited to study the generati...

Buoyant shear layers are encountered in many engineering and environmental applications, and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson numbers, and this leads to significant/intractable space-time resolution requirements for DNS or LES modeling. On t...

Flow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using DNS and LES, the ability of sublayer-resolved RANS to predict the bulk flow phenomena of these systems is relatively unexplored, especially...

Reynolds-averaged Navier-Stokes (RANS) is one of the most cost-efficient approaches to simulate wind-farm-atmosphere interactions. However, the applicability of RANS-based methods is always limited by the accuracy of turbulence closure models, which introduce various uncertainties into the models. In this study, we estimate model-form uncertainties...

Calibrating a Reynolds-averaged Navier–Stokes (RANS) model against data leads to an improvement. Determining a priori if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work attempts to address this challenge via global epistemic Uncertainty Quantification (UQ). Unlike the available epistemic...

Buoyant shear layers are encountered in many engineering and environmental applications and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson numbers, and this leads to significant/intractable space-time resolution requirements for DNS or LES modeling. On th...

Townsend's attached eddy hypothesis (AEH) gives an accurate phenomenological description of the flow kinematics in the logarithmic layer, but it suffers from two major weaknesses. First, AEH does not predict the constants in its velocity scalings, and second, none of the predicted velocity scalings can be obtained from the Navier-Stokes (NS) equati...

Unphysical numerical oscillations (UNOs) arise when a non-dissipative scheme is employed to discretize fluid equations on a coarse grid. Treating UNOs often relies on upwind schemes, digital filtration, artificial viscosity, or adaptive mesh refinement, which are either too dissipative or too costly. We propose an alternative solution by refining o...

In analogy with the classical concept of mass-flux-based streamlines, we define Angular Momentum Transport (AMT) lines as an aerodynamic functional diagnostic tool. The AMT lines are the ones whose tangents are given by the average angular momentum flux. The mathematical and physical properties of these AMT lines are exploited to study the generati...

A practical application of universal wall scalings is near-wall turbulence modeling. In this paper, we exploit temperature's semi-local scaling [Patel, Boersma, and Pecnik, {Scalar statistics in variable property turbulent channel flows}, Phys. Rev. Fluids, 2017, 2(8), 084604] and derive an eddy conductivity closure for wall-modeled large-eddy simu...

Reynolds-averaged Navier-Stokes (RANS) is one of the most cost-efficient approaches to simulate wind-farm-atmosphere interactions. However, the applicability of RANS-based methods is always limited by the accuracy of turbulence closure models, which introduce various uncertainties into the models. In this study, we estimate model-form uncertainties...

Turbulent signals are intermittent with large instantaneous fluctuations. Such large fluctuations lead to small Kolmogorov scales that are hard to resolve in numerical simulations [P. K. Yeung, K. R. Sreenivasan, and S. B. Pope, Effects of finite spatial and temporal resolution in direct numerical simulations of incompressible isotropic turbulence,...

The self-similar Richardson cascade admits two logically possible scenarios of small-scale turbulence at high Reynolds numbers. In the first scenario, eddies' population densities vary as a function of eddies' scales. As a result, one or a few eddy types dominate at small scales, and small-scale turbulence lacks diversity. In the second scenario, e...

Lacking labeled examples of working numerical strategies, adapting an iterative solver to accommodate a numerical issue, e.g., density discontinuities in the pressure Poisson equation, is non-trivial and usually involves a lot of trial and error. Here, we resort to evolutionary neural network. A evolutionary neural network observes the outcome of a...

Impact of viscous sublayer scale roughness elements on large scale flows have not been fully understood and require high resolution 3D flow measurements to unravel. However, existing approaches fail to provide sufficient resolution for such measurements to fully resolve the sublayer. In this study, we use digital Fresnel reflection holography to ca...

We develop an augmented discontinuous Galerkin method for wall-modeled large-eddy simulations. This method is motivated by the enrichment method that has been formulated for finite-element method, by statistically augmenting the variational solution of the near-wall element with a simple wall function to model the effects of the unresolved momentum...

Calibrating a Reynolds-averaged Navier-Stokes (RANS) model against data leads to an improvement. Determining {\it a priori} if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work attempts to address this challenge via global epistemic Uncertainty Quantification (UQ). Unlike the available epis...

Accurate parameterization of wind farms’ equivalent roughness heights is critical to meso-scale climate simulations as well as power predictions of wind turbines. A notable inadequacy of the existing models is that the results sensitively depend on sx/sy, where sx and sy are the dimensionless streamwise and spanwise spacing of the turbines. To unde...

This paper reports wall-modeled large-eddy simulation (WMLES) results of low-speed turbulent flows in a plane channel, in ribbed ducts, and around a film cooling jet. We compare our WMLESs to Pirozzoli et al.’s direct numerical simulations (DNSs) of low-speed plane channel flow (Pirozzoli, S., Bernardini, M., and Orlandi, P., “Passive Scalars in Tu...

In this commentary, we revisit Raupach’s flow-sheltering paradigm that asserts reduced wall-shear stress behind a surface roughness element (MR Raupach in Boundary-Layer Meteorol, 60(4):375–395, 1992). Direct numerical simulations of a turbulent boundary layer over a wall-mounted rectangular roughness are conducted we consider roughness with three...

This paper reports wall-modeled large-eddy simulation (WMLES) results of low-speed turbulent flows in plane channel, in ribbed ducts, and around a film cooling jet. We compare our WMLESs to Pirozzoli's direct numerical simulations (DNSs) of low-speed plane channel flow [Pirozzoli, Bernardini, and Orlandi, J. Fluid Mech., 2016, 788, 614-639], our ow...

Control surfaces of hypersonic vehicle in the presence of shock wave/boundary layer interaction (SWBLI) undergo time-dependent aerothermal loading. Exposure to such extreme environment makes them vulnerable to structural fatigue and premature failure. Present study focuses on assessing this fluid-thermal-structural interaction (FTSI) on a cone-slic...

We report LES and RANS results of the flow in a return channel. Given the same inflow, the LESs and RANS lead to qualitatively similar but quantitatively different results up to the trailing edge of the deswirl vane and qualitatively different results from the trailing edge to the exit of the return channel. The RANS leads to strong vortical struct...

In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specifically, with a theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Rey...

The logarithmic law of the wall loses part of its predictive power in flows with system rotation. Previous work on the topic of mean flow scaling has mostly focused on flows with streamwise, spanwise, or wall-normal system rotation. The main objective of this work is to establish the mean flow scaling for wall-bounded flows with small but arbitrari...

We revisit the grid-point requirement estimates in Choi and Moin [“Grid-point requirements for large eddy simulation: Chapman’s estimates revisited,” Phys. Fluids 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary...

The grid point requirements of Chapman [AIAA J., 17, 1293, (1979)] and Choi and Moin [Phys. Fluid, 24, 011702 (2012)] are refined. We show that the grid requirement for DNS is $N\sim Re_{L_x}^{2.05}$ rather than $N\sim Re_{L_x}^{2.64}$ as suggested by Choi and Moin, where $L_x$ is the length of the plate. In addition, we estimate the time step requ...

We employ novel digital Fresnel reflection holography to capture the 3D flows within the viscous sublayer of a smooth-wall turbulent channel flow at Reτ=400. The measurements reveal unsteady and diverse flow patterns in the sublayer including nearly uniform high and low speed flows and strong small-scale (on the order of viscous wall units) spanwis...

Spanwise heterogeneous roughness, more specifically, spanwise-adjacent strips of relatively high and low roughness, is known to cause large-scale secondary flows in the vertical domain in neutral turbulent boundary layers. In this work, we study the response of secondary vortices to thermal stratification with focus on the stably stratified case. W...

We study the behaviors of pressure fluctuations in high Reynolds number wall-bounded flows. Pressure fluctuations are small-scale quantities compared to velocity fluctuations in a wall-bounded flow (Tsuji, Marusic, & Johansson, Int. J. Heat Fluid Flow, vol. 61, 2016, pp. 2–11.): at a given wall-normal distance y, the premultiplied velocity spectrum...

In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specially, with the theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Reyn...

Since the early work of Johnston [Johnston, Halleent, and Lezius, J. Fluid Mech. 56, 533 (1972)], the mean flow scaling in a spanwise rotating channel has received much attention. While it is known that the mean velocity near the pressure, turbulent side follows a linear scaling U=2Ωy+C at high rotation speeds, the functional dependence of C on the...

We present a derivation that begins with the Navier--Stokes equation and ends with a prediction of multiple statistically stable states identical to those observed in a spanwise rotating plane Couette flow. This derivation is able to explain the presence of multiple states in fully developed turbulence and the selection of one state over the other...

Much of our theoretical understanding of statistically stable and unstable flows is from the classical Monin–Obukhov similarity theory: the theory predicts the scaling of the mean flow well, but its prediction of the turbulent fluctuation is far from satisfactory. This study builds on Monin–Obukhov similarity theory and Townsend’s attached-eddy hyp...

According to Townsend’s attached eddy hypothesis (AEH), a boundary layer flow is comprised of wall-attached eddies, but to extract the part of the flow whose statistical behaviours are well described by the AEH is not at all straightforward. The objective of this work is to extract the part of the flow that can be described by the AEH, and study th...

Resolvent-based estimation of space–time flow statistics - Volume 883 - Aaron Towne, Adrián Lozano-Durán, Xiang Yang

Flow over aligned and staggered cube arrays is a classic model problem for rough-wall turbulent boundary layers. Earlier studies of this model problem mainly looked at rough surfaces with a moderate coverage density, i.e. $\unicode[STIX]{x1D706}_{p}>O(3\,\%)$ , where $\unicode[STIX]{x1D706}_{p}$ is the surface coverage density and is defined to be...

While data-based approaches were found to be useful for subgrid scale (SGS) modeling in Reynolds-averaged Navier-Stokes (RANS) simulations, there have not been many attempts at using machine learning techniques for wall modeling in large-eddy simulations (LESs). Large-eddy simulation differs from RANS simulation in many aspects. For one thing, LES...

Probability density functions (PDFs) give well-rounded statistical descriptions of stochastic quantities and therefore are fundamental to turbulence. Wall-bounded turbulent flows are of particular interest given their prevalence in a vast array of applications, but for these flows the scaling of velocity probability distribution is still far from b...

The one-dimensional (1D) Jensen model is probably the most often used model for engineering analysis of wind turbine wakes. Identifying a more realistic shape function for the near and far wakes behind a wind turbine and incorporating the identified shape function into a wake model can significantly improve the accuracy of wake modelling. The conve...

We develop a method to estimate space-time flow statistics from a limited set of known data. While previous work has focused on modeling spatial or temporal statistics independently, space-time statistics carry fundamental information about the physics and coherent motions of the flow and provide a starting point for low-order modeling and flow con...

At high Reynolds numbers, the logarithmic range in wall-bounded flows spans many scales. An important conceptual modeling framework of the logarithmic range is Townsend's attached eddy hypothesis [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1976)], where high Reynolds number wall-bounded flows are modeled as assemb...

In a turbulent flow, small- and large-scale fluid motions are coupled. In this work, we investigate the small-scale response to large-scale fluctuations in turbulent flows and discuss the implications on large eddy simulation (LES) wall modelling. The interscale interaction in wall-bounded flows was previously parameterized in the predictive inner–...

We show that the mean wall-shear stresses in wall-modeled large-eddy simulations (WMLES) of high-speed flows can be off by up to (Formula presented.) with respect to a DNS benchmark when using the van-Driest-based damping function, i.e., the conventional damping function. Errors in the WMLES-predicted wall-shear stresses are often attributed to the...

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing...

The kinematics of a fully developed passive scalar is modelled using the hierarchical random additive process (HRAP) formalism. Here, 'a fully developed passive scalar' refers to a scalar field whose instantaneous fluctuations are statistically stationary, and the 'HRAP formalism' is a recently proposed interpretation of the Townsend attached eddy...

At transcritical conditions, the transition of a fluid from a liquidlike state to a gaslike state occurs continuously, which is associated with significant changes in fluid properties. Therefore, boiling in its conventional sense does not exist and the phase transition at transcritical conditions is known as “pseudoboiling.” In this work, direct nu...

High Reynolds number wall-bounded flows involve dynamically important scales that cover many orders of magnitude in time and space. Fluid motions that dominate momentum transport also cover wide ranges of scales and all of these scales must be accounted for when modeling turbulence near walls. In this review, we summarize recent developments as rel...

A convective velocity must be specified when using Taylor’s frozen eddy hypothesis to relate temporal and spatial fluctuations. Depending on the quantity of interest, using different convective velocities (i.e. time-mean velocity, global convective velocity, etc.) may lead to different conclusions. Often, using Taylor’s hypothesis, the relation bet...

Turbulent flows under transcritical conditions are present in regenerative cooling systems of rocker engines and extraction processes in chemical engineering. The turbulent flows and the corresponding heat transfer phenomena in these complex processes are still not well understood experimentally and numerically. The objective of this work is to inv...

Aerospace vehicles flying at supersonic and hypersonic speeds are subject to increased wall heating rates caused by viscous friction with the gas environment. This extra heat is commonly referred to as convective aerodynamic heating. In wall-modeled large-eddy simulations, the near-wall region of the flow is not resolved by the computational grid....

Log-layer mismatch refers to a chronic problem found in wall-modeled large-eddy simulation (WMLES) or detached-eddy simulation, where the modeled wall-shear stress deviates from the true one by approximately 15%. Many efforts have been made to resolve this mismatch. The often-used fixes, which are generally ad hoc, include modifying subgrid-scale s...

Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva \textit{et al.} (\textit{J. Fluid Mech.}, vol. 823,2017, pp. 498-510) observed that remarkably the \textit{large-scale} (energy-containing range) statistics in canonical wall bounded flows exhibit unive...