arXiv subjects

Parviz Moin

Publications and source records attributed to Parviz Moin.

At least 19 recordsLinked to original sources

arXiv2026

LES of Droplet Impingement: Application to Clean and Laser-Scanned Ice Shapes

The prediction of aircraft icing is conventionally performed using multishot simulation frameworks that fail to predict the progressive roughening of the ice surface. To understand roughness formation, we investigate droplet impingement on clean and laser-scanned rough ice shapes using a high-fidelity computational framework based on wall-modeled large-eddy simulations and Lagrangian particle tracking. This methodology is validated against experimental data for a NACA 23012 airfoil and a NACA 64A008 swept tail, accurately predicting collection efficiency and supercooled large droplet splashing. The framework is subsequently applied to laser-scanned rime ice geometries to quantify the impact of surface roughness on local impingement distributions. The results reveal that physical roughness induces a highly nonuniform collection efficiency, with droplet impingement intensely concentrated on upstream-faces of roughness elements, creating sheltered shadow zones immediately downstream. While the spanwise-averaged collection efficiency remains remarkably similar to that of an equivalent smooth body, idealized smooth surfaces completely suppress these localized impingement peaks. Ice accretion simulations demonstrate that this localized impingement creates a self-reinforcing feedback loop, actively amplifying existing roughness features over time. These findings provide a direct physical explanation for the formation of characteristic rime ice structures and highlight the critical role of local surface topology in the accretion process.

physics.flu-dyn↗

arXiv2026

Gravity Wave Interactions in the Stratocumulus-Topped Boundary Layer

This work studies the breakup propensity of the stratocumulus-topped boundary layer (STBL) interacting with gravity waves using large-eddy simulation with a uniform vertical grid of $5$ m and horizontal spacing of $30$ m. A radiative-convective equilibrium (RCE) state is constructed to enforce stationarity in the STBL, and the gravity waves are introduced via a vertical momentum forcing mimicking a packet of plane waves. A nondimensionalization involving the inversion height and mean horizontal base wind as length and velocity scales is proposed to provide a framework to analyze the forcing parameter space. The magnitude of the scaled forcing amplitude ($\mathcal{A}$) is critical in understanding various STBL breakup conditions. Classification of breakup was based on the reduction of the liquid water path for each forced STBL case. We found that breakup did not occur for $\mathcal{A}<1$ and observed modest reductions in cloud for $1<\mathcal{A}<2$, but the deck recovered to the stationary state slowly after the single-period forcing ceased. Fixing $\mathcal{A}\sim 2$ showed that forcings with longer duration and wider locality promote breakup. However, when the forcing is a linear combination of waves of two different periods, the percentage of cleared cloud dramatically increases, though recovery of RCE is still observed in some cases. $\mathcal{A}\geq2.5$ marks a critical threshold by which the STBL breaks up entirely and remains patchy. We further explore the connection between these bulk breakup results and the turbulent state by examining energy budgets and the anisotropy induced by the forcing.

physics.flu-dyn↗

arXiv2025

Predictions of flow distortions inside a serpentine diffuser from large-eddy simulations

This work examines the flow separation and the resulting pressure distortions at the exit plane of a serpentine diffuser operating at both subsonic and transonic conditions. Wallmodeled large-eddy simulations (WMLES) using the charLES flow solver are performed at three exit-plane Mach numbers, Ma_AIP ~ {0.36, 0.46, 0.54}. First, it is shown that the onset of flow separation inside a serpentine diffuser may likely experience strong, non-local history effects. A grid refinement study consisting of five grids (from 30 million to 3 billion cells) is conducted for all Mach numbers. The recently proposed dynamic tensor-coefficient Smagorinsky subgrid-scale and sensor-aided non-equilibrium wall models compare favorably with experimental measurements for the pressure recovery and azimuthal flow distortion at all Mach numbers. The pressure recovery and azimuthal flow distortion are predicted to within 0.3% and 7%, respectively, which are both within the experimental error bounds. However, the simulations underpredict the maximum azimuthal distortion in comparison to the experiments for all conditions. Statistical comparisons of the dynamic azimuthal flow distortions suggest that the present LES reasonably captures the ring-averaged mean distortions, and the statistical distributions of the distortion around the mean. Extreme events are underestimated by the present simulations, potentially highlighting that significantly longer integration times may be necessary.

physics.flu-dyn↗

arXiv2025

Large eddy simulations of conjugate heat transfer in boundary layers over laser-scanned ice roughness

Accurate modeling of ice accretion is important for safe and efficient design of aircraft and wind turbine systems. Heat transfer predictions obtained from fluid flow solvers are used as input in ice accretion codes. In glaze ice conditions, freezing rates and resulting ice shapes are highly sensitive to input values of the heat transfer coefficient. Hence, accurate prediction of heat transfer on iced airfoils is crucial for correctly predicting the ice accretion process. In this study, we perform conjugate heat transfer (CHT) simulations using wall-modeled large-eddy simulation (WMLES) over surfaces characterized by ice roughness. The results show that WMLES with CHT accurately captures surface temperature distributions and heat fluxes across a range of roughness geometries. For cases considered, large roughness-to-boundary-layer thickness ratios disrupt outer-layer similarity, leading to substantial errors in estimating equivalent sandgrain roughness when applying traditional empirical models based on surface statistics. The simulations further show that local heat fluxes vary significantly across roughness elements due to low thermal conductivity of the solid; in particular, roughness crests exhibit reduced fluxes in contrast to slopes and valleys. Notably, as roughness height increases, wall heat flux at the crest diminishes, even leading to heat flux reversal in some cases, where thermal energy is transferred from fluid to solid. These effects are not captured in isothermal wall simulations, which overestimate the Stanton number, especially at roughness peaks. By enabling calculation of Stanton number using heat flux distributions, not directly available in experiments, the present simulations augment experimental results and highlight the importance of including solid conduction effects for accurately modeling heat transfer over rough, low-conductivity surfaces such as ice.

physics.flu-dyn↗

arXiv2024

Non-equilibrium wall model for large eddy simulations of complex flows exhibiting turbulent smooth body separation

In this work, a non-equilibrium wall model is proposed for the prediction of turbulent flows experiencing adverse pressure gradients, including separated flow regimes. The mean-flow nonequilibrium is identified by comparing two characteristic velocities: the friction velocity (u_tau) and the viscous-pressure gradient velocity (up). In regions where the pressure gradient velocity is comparable to the friction velocity (up \sim u_tau, the near-wall turbulent closure is modified to include the effect of the pressure-gradient and convective terms. The performance of this wall model is evaluated in two canonical flows experiencing smooth body separation: the NASA-Boeing speed bump and the Bachalo-Johnson bump. Improvements in the predictive capabilities of the proposed model for the conventional equilibrium wall model are theorized and then demonstrated through numerical experiments. In particular, the proposed wall model can capture the onset of boundary layer separation observed in experiments or DNS calculations at resolutions where the equilibrium wall model fails to separate.

physics.flu-dyn↗

arXiv2024

Studies of Transonic Aircraft Flows and Prediction of Initial Buffet Onset Using Large-Eddy Simulations

This article utilizes the Large-Eddy Simulation (LES) paradigm with a physics-based turbulence modeling approach, including a dynamic subgrid-scale model and an equilibrium wall model, to examine the flow over the NASA transonic Common Research Model (CRM), a flow configuration that has been the focus of several AIAA Drag PredictionWorkshops (DPWs). The current work explores sensitivities to laminar-to-turbulent transition, wind tunnel mounting system, grid resolution, and grid topology and suggests current best practices in the context of large-eddy simulations of transonic aircraft flows. It is found that promoting the flow transition to turbulence via an array of cylindrical trip dots, including the sting mounting system in the simulations, and leveraging stranded boundary layer grids all tend to improve the quality of the LES solutions. Non-monotonic grid convergence in the LES calculations is observed to be strongly sensitive to grid topology, and stranded meshes rectify this issue relative to their hexagonal close-packed (HCP) counterparts. The details of the boundary layer profiles both at the leading edge of the wing and within the shock-induced separation bubble are studied, with thicknesses and integral measures reported, providing details about the boundary layer characteristics to turbulence modelers not typically available from complex aircraft flows. Finally, an assessment of the initial buffet prediction capabilities of LES is made in the context of a simpler NACA 0012 flow, with computational predictions showing reasonable agreement with available experimental data for the angle of attack at initial buffet onset and shock oscillation frequency associated with sustained buffet.

physics.flu-dyn↗

arXiv2024

Are the dynamics of wall turbulence in minimal channels and larger domain channels equivalent? A graph-theoretic approach

This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at $Re_\tau \approx 180$, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately $2.83$ times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately $2.21$ times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately $2.17$ slower in the MFU than the FC.

physics.flu-dyn↗

arXiv2023

Reynolds number dependence of length scales governing turbulent flow separation with application to wall-modeled large-eddy simulations

This article proposes a Reynolds number scaling of the required grid points to perform wall-modeled LES of turbulent flows encountering separation off a solid surface. Based on comparisons between the various time scales in a non-equilibrium (due to the action of an external pressure gradient) turbulent boundary layer, a simple definition of the near-wall ``under-equilibrium" and ``out-of-equilibrium" scales is put forward (where ``under-equilibrium" refers to scales governed by a quasi-balance between the viscous and the pressure gradient terms). It is shown that the former length scale varies with Reynolds number as lp Re^(-2/3). The same scaling is obtained from a simplified Green's function solution of the Poisson equation in the vicinity of the separation point. A-priori analysis demonstrates that the resolution required to reasonably predict the wall-shear stress (for example, errors lower than approximately 10-15% in the entire domain) in several nonequilibrium flows is at least O(10) lp irrespective of the Reynolds number and the Clauser parameter. Further, a series of a-posteriori validation studies are performed to determine the accuracy of this scaling including the flow over the Boeing speed bump, Song-Eaton diffuser, Notre-Dame Ramp, and the backward-facing step. The results suggest that for these flows, scaling the computational grids () such that / lp is independent of the Reynolds number results in accurate predictions of flow separation at the same ``nominal" grid resolution across different Reynolds numbers. Finally, it is suggested that in the vicinity of the separation and reattachment points, the grid-point requirements for wall-modeled large eddy simulations may scale as Re^4/3, which is more restrictive than the previously proposed flat-plate boundary layer-based estimates (Re1) of Choi and Moin (Phys. Fluids, 2012) and Yang and Griffin (Phys. Fluids, 2021).

physics.flu-dyn↗

arXiv2023

An extension of Thwaites method for turbulent boundary layers

Thwaites (1949) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of a flow parameter, $m = \theta^2/\nu \frac{dU_e}{ds}$, thus reducing the von Karman momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. However, for turbulent flows, a similar approximation for turbulent boundary layers subjected to pressure gradients does not yet exist. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed. It is shown that the method provides good estimates of the momentum thickness, when compared to available high-fidelity simulation data, for multiple boundary layers including both favorable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model which is shown to be in agreement with prior empirical observations (Alber, \textit{$9^{th}$ Aerospace Sciences Meeting, 1971}). The sensitivity of the separation location with respect to upstream perturbations is also analyzed through this model for the NASA/Boeing speed bump and the transonic Bachalo-Johnson bump

physics.flu-dyn↗

arXiv2023

Large-eddy simulations of the NACA23012 airfoil with laser-scanned ice shapes

In this study, five ice shapes generated at NASA Glenn's Icing Research Tunnel (IRT) are simulated at multiple angles of attack (Broeren et al., J. of Aircraft, 2018). These geometries target different icing environments, both early-time and longer-duration glaze and rime ice exposure events, including a geometry that results from using a thermal ice-protection system. Using the laser-scanned geometries, detailed representations of the three-dimensional ice geometries are resolved on the grid and simulated using wall-modeled LES. Integrated loads (lift, drag, and moment coefficients) and pressure distributions are compared against experimental measurements in both clean and iced conditions for several angles of attack in both pre-and post-stall regions. The relevant comparisons to the experimental results show that qualitative and acceptable quantitative agreement with the data is observed across all geometries. Glaze ice formations exhibit larger and highly nonuniform ice features, such as `horns', in contrast to rime ice formations characterized by smaller, uniformly distributed roughness elements. In wall-modeled LES, it was observed that larger roughness scales in the glaze ice that trigger transition can be accurately resolved. Therefore, it is possible for WMLES to accurately capture the aerodynamics of glaze ice shapes without the need for additional modeling. In contrast, rime ice geometries required additional resolution to accurately represent the aerodynamic loads. This study demonstrates the effectiveness of the wall-modeled LES technique in simulating the complex aerodynamic effects of iced airfoils, providing valuable insights for aircraft design in icing environments and highlighting the importance of accurately representing ice geometries and roughness scales in simulations.

physics.flu-dyn↗

arXiv2023

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation [Griffin, Fu, & Moin, PNAS, 118:34, 2021] and an algebraic temperature-velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows, and boundary layers (48 cases with edge Mach numbers in the range of 0.77--11 and semi-local friction Reynolds numbers in the range of 170--5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range of 0.7--4 and friction Reynolds numbers in the range of 320--1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two and has a similar computational cost and implementation complexity as the commonly used ODE model.

physics.flu-dyn↗

arXiv2023

Stable, entropy-consistent, and localized artificial-diffusivity method for capturing discontinuities

In this work, a localized artificial-viscosity/diffusivity method is proposed for accurately capturing discontinuities in compressible flows. There have been numerous efforts to improve the artificial diffusivity formulation in the last two decades, through appropriate localization of the artificial bulk viscosity for capturing shocks. However, for capturing contact discontinuities, either a density or internal energy variable is used as a detector. An issue with this sensor is that it not only detects contact discontinuities, but also falsely detects the regions of shocks and vortical motions. Using this detector to add artificial mass/thermal diffusivity for capturing contact discontinuities is hence unnecessarily dissipative. To overcome this issue, we propose a sensor similar to the Ducros sensor (for shocks) to detect contact discontinuities, and further localize artificial mass/thermal diffusivity for capturing contact discontinuities. The proposed method contains coefficients that are less sensitive to the choice of the flow problem. This is achieved by improved localization of the artificial diffusivity in the present method. A discretely consistent dissipative flux formulation is presented and is coupled with a robust low-dissipative scheme, which eliminates the need for filtering the solution variables. The proposed method also does not require filtering for the discontinuity detector/sensor functions, which is typically done to smear out the artificial fluid properties and obtain stable solutions. Hence, the challenges associated with extending the filtering procedure for unstructured grids is eliminated, thereby, making the proposed method easily applicable for unstructured grids. Finally, a straightforward extension of the proposed method to two-phase flows is also presented.

physics.flu-dyn↗

arXiv2023

Wall modeled large-eddy simulations of flow over the Sandia Axisymmetric Transonic Bump

Wall-modeled large-eddy simulations (WMLES) are conducted for the flow over the Sandia Axisymmetric Transonic Bump (ATB) at bump chord Reynolds number, Re = 1x10^6 and Mach number, Ma = 0.875. Utilizing various subgrid-scale and wall models, comparisons are made between the simulations and experiments for quantities of engineering interest, such as the skin friction coefficient (Cf) and wall pressure coefficient (Cp) data. Favorable agreements between the simulations and the experiments are achieved, with the simulations predicting the shock location, size, and strength of the separation bubble with reasonable accuracy. In particular, it was established that the realism of the incoming turbulent boundary layer onto the bump is very important for the correct and robust prediction of the skin friction in the upstream region of the bump. Furthermore, a resolution limitation on the predictive capability of the equilibrium wall model in the favorable pressure gradient region is established. Finally, preliminary results utilizing a pressure-gradient inclusive modification to the equilibrium wall model predicts the skin friction within the separation bubble at affordable resolutions

physics.flu-dyn↗

arXiv2022

Prediction of aerothermal characteristics of a generic hypersonic inlet flow

The accurate prediction of aerothermal surface loading is of paramount importance for the design of high speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by three-dimensional intersecting shock-wave/turbulent boundary-layer interaction at Mach 8.3. High Reynolds numbers ($Re_L \approx 11.6 \times 10^6$ based on free-stream conditions) and the presence of cold walls ($T_w/T_o \approx 0.27$) leading to large near-wall temperature gradients necessitate the use of wall-modeled large-eddy simulation (WMLES) in order to make calculations computationally tractable. The comparison of the WMLES results with experimental measurements shows good agreement in the time-averaged surface heat flux and wall pressure distributions, and the WMLES predictions show reduced errors with respect to the experimental measurements than prior RANS calculations. The favorable comparisons are obtained using an LES wall model based on equilibrium boundary layer approximations despite the presence of numerous non-equilibrium conditions including three dimensionality, shock-boundary layer interactions, and flow separation. Lastly, it is also demonstrated that the use of semi-local eddy viscosity scaling (in lieu of the commonly used van Driest scaling) in the LES wall model is necessary to accurately predict the surface pressure loading and heat fluxes.

physics.flu-dyn↗

arXiv2022

A kinetic energy--and entropy-preserving scheme for compressible two-phase flows

Accurate numerical modeling of compressible flows, particularly in the turbulent regime, requires a method that is non-dissipative and stable at high Reynolds ($Re$) numbers. For a compressible flow, it is known that discrete conservation of kinetic energy is not a sufficient condition for numerical stability, unlike in incompressible flows. In this study, we adopt the recently developed conservative diffuse-interface method (Jain, Mani $\&$ Moin, $\textit{J. Comput. Phys.}$, 2020) along with the five-equation model for the simulation of compressible two-phase flows. This method discretely conserves the mass of each phase, momentum, and total energy of the system. We here propose discrete consistency conditions between the numerical fluxes, such that any set of numerical fluxes that satisfy these conditions would not spuriously contribute to the kinetic energy and entropy of the system. We also present a set of numerical fluxes\textemdash which satisfies these consistency conditions\textemdash that results in an exact conservation of kinetic energy and approximate conservation of entropy in the absence of pressure work, viscosity, thermal diffusion effects, and time-discretization errors. Since the model consistently reduces to the single-phase Navier-Stokes system when the properties of the two phases are identical, the proposed consistency conditions and numerical fluxes are also applicable for a broader class of single-phase flows. To this end, we present coarse-grid numerical simulations of compressible single-phase and two-phase turbulent flows at infinite $Re$, to illustrate the stability of the proposed method in canonical test cases, such as an isotropic turbulence and Taylor-Green vortex flows. A higher-resolution simulation of a droplet-laden compressible decaying isotropic turbulence is also presented, and the effect of the presence of droplets on the flow is analyzed.

physics.flu-dyn↗

arXiv2022

Non-Boussinesq subgrid-scale model with dynamic tensorial coefficients

A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical simulation (DNS) data has shown that this assumption is invalid locally as subgrid-scale stresses are poorly correlated with the large-scale strain rates [Bardina et al., AIAA 1980; Meneveau and Liu, Ann. Rev. Fluid Mech. 2002]. In the present work, a new, non-Boussinesq subgrid-scale model is presented where the model coefficients are computed dynamically. Some previous non-Boussinesq models have observed issues in providing adequate dissipation of turbulent kinetic energy [e.g.: Bardina et al., AIAA 1980; Clark et al. J. Fluid Mech., 1979; Stolz and Adams, Phys. of Fluids, 1999]; however, the present model is shown to provide sufficient dissipation using dynamic coefficients. Modeled subgrid-scale Reynolds stresses satisfy the consistency requirements of the governing equations for LES, vanish in laminar flow and at solid boundaries, and have the correct asymptotic behavior in the near-wall region of a turbulent boundary layer. The new model, referred to as the dynamic tensor-coefficient Smagorinsky model (DTCSM), has been tested in simulations of canonical flows: decaying and forced homogeneous isotropic turbulence (HIT), and wall-modeled turbulent channel flow at high Reynolds numbers; the results show favorable agreement with DNS data. In order to assess the performance of DTCSM in more complex flows, wall-modeled simulations of high Reynolds number flow over a Gaussian bump exhibiting smooth-body flow separation are performed. Predictions of surface pressure and skin friction, compared against DNS and experimental data, show improved accuracy from DTCSM in comparison to the existing static coefficient (Vreman) and dynamic Smagorinsky model.

physics.flu-dyn↗

arXiv2021

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook (2007), Subramaniam et al., (2018), and Adler and Lele (2019), in which artificial diffusion terms are added to the conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., (2010) and Tiwari et al., (2013), in which the diffusion and sharpening terms (together called regularization terms) are added to the conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., (2020), in which the regularization terms are added to the conservation equations. The primary objective of this work is to compare these three methods in terms of their ability to maintain: constant interface thickness; the conservation property; and accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer-Meshkov instability of a copper-aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. This is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

physics.comp-ph↗

arXiv2021

Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

physics.flu-dyn↗