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The speed of sound in bubbly water is an important parameter in the wave equations governing pressure–density relations for turbulent multi-phase flow simulations. Recent molecular simulation results indicate that, for bubbles that are thermodynamically stable at finite volume conditions, the derivative of total pressure P with density ρ has a negative sign, complicating the interpretation of the speed of sound. We show that such a negative compressibility is thermodynamically consistent in a single-component two-phase model at finite volume, and identify an empirically derived equation of state to illustrate that this observation is not an artifact of small simulation length scales. To reconcile this thermodynamic relation with measurements of sound propagation, we decompose the derivative ∂P/∂ρ for bubbly water into its constituent phases to identify absorptive and transmissive contributors, both with an equation of state and using molecular simulations. We find that the speed of sound in the liquid phase remains real-valued while the bubble attenuates sound, giving a negative system compressibility. The inclusion of N2 molecules in molecular simulations illustrates that these observations are robust and hold also for mixtures. From these simulations, we also compute scattering functions for bubbly systems to identify oscillations associated with the speed of sound. Finally, the spherical harmonic modes of bubble oscillations are analyzed in the context of resonance with propagating waves. [ABSTRACT FROM AUTHOR]

The direct measurement of wall shear stress in turbulent boundary layers (TBL) is challenging, therefore, requiring it to be indirectly determined from mean profile measurements. Most popular methods assume the mean streamwise velocity to satisfy either a logarithmic law in the inner layer or a composite velocity profile with many tuned constants for the entire TBL, both of which require reliable data from the inner layer. The presence of roughness and pressure gradient brings additional complications where most existing methods either fail or require significant modification. A novel method is proposed to determine the wall shear stress in zero pressure gradient TBL from measured mean profiles, without requiring near-wall data. The method is based on the stress model of Kumar and Mahesh (Phys Rev Fluids 6:024603, 2021), who developed accurate models for mean stress and wall-normal velocity in zero pressure gradient TBL. The proposed method requires a single point measurement of mean streamwise velocity and mean shear stress in the outer layer, preferably between 20 and 50 % of the TBL, and an estimate of boundary layer thickness and shape factor. The method can handle wall roughness without modification and is shown to predict friction velocities to within 3 % over a range of Reynolds number for both smooth and rough wall zero pressure gradient TBL. In order to include the pressure gradients effects, the work of Kumar and Mahesh (Phys Rev Fluids 6:024603, 2021) is revisited to derive a novel model for both mean stress and wall-normal velocity in pressure gradient TBL, which is then used to formulate a method to obtain the wall shear stress from the profile data. Overall, the proposed method is shown to be robust and accurate for a variety of pressure gradient TBL. [ABSTRACT FROM AUTHOR]

Abstract A novel technique based on the Full Orthogonalization Arnoldi (FOA) is proposed to perform Dynamic Mode Decomposition (DMD) for a sequence of snapshots. A modification to FOA is presented for situations where the matrix A is unknown, but the set of vectors { A i − 1 v 1 } i = 1 N are known. The modified FOA is the kernel for the proposed projected DMD algorithm termed, FOA based DMD. The proposed algorithm to compute DMD modes and eigenvalues i) does not require Singular Value Decomposition (SVD) for snapshot matrices X with κ 2 (X) ≪ 1 / ϵ m , where κ 2 (X) is the 2-norm condition number of the snapshot matrix and ϵ m is the relative round-off error or machine epsilon, ii) has an optional rank truncation step motivated by round off error analysis for snapshot matrices X with κ 2 (X) ≈ 1 / ϵ m , iii) requires only one snapshot at a time, thus making it a 'streaming' method even with the optional rank truncation step, iv) consumes less memory and requires less floating point operations to obtain the projected matrix than existing projected DMD methods and v) lends itself to easy parallelism as the main computational kernel involves only vector additions, dot products and matrix vector products. The new technique is therefore well-suited for DMD of large datasets on parallel computing platforms. We show both theoretically and using numerical examples that for FOA based DMD without rank truncation, the finite precision error in the computed projection of the linear mapping is O (ϵ m κ 2 (X)). The proposed method is also compared to existing projected DMD methods for computational cost, memory consumption and relative round off error. Error indicators are presented that are useful to decide when to stop acquiring new snapshots. The proposed method is applied to several examples of numerical simulations of fluid flow. Highlights • Novel algorithm – 'FOA based DMD' based on Arnoldi proposed for large datasets. • Algorithm is parallel and streaming. • Less memory and floating point operations than existing DMD methods. • Error indicators proposed to decide when to stop acquiring new snapshots. • Finite precision error analysis of FOA based DMD and other DMD methods performed. [ABSTRACT FROM AUTHOR]

Abstract We present a method that dynamically and efficiently performs connectivity calculations between many (O (10 5)) moving, unstructured overset meshes in parallel. In order to connect overset meshes, elements exterior to the solution domain must be removed from the simulation. In regions with many overlapping meshes, elements must be selectively removed to reduce redundancy while maintaining a solution over the entire domain. Around masked regions interpolation partner pairing is required between meshes to provide boundary conditions. For general unstructured meshes, these steps involve challenging computational geometry calculations which must be efficient and automatic. For many moving meshes each step must be massively parallelized and scalable to large numbers of computational cores. To establish communication patterns a parallelized master/slave algorithm is used which minimizes global communication and storage. To remove elements a parallel 'Forest Fire' flood-fill algorithm is used to set a masking variable. For interpolation partner pairing, and other necessary searches, k-dimensional tree data structures (k-d trees) are extensively used. Often in a calculation, the connectivity between overset meshes remains largely the same between time steps. The temporal coherence of the various objects in the connectivity calculation is directly used to only update necessary information with time, resulting in substantial cost savings. Details of the different algorithms are presented. Resulting connectivity and timings are shown for complex geometries. Parallel scaling is demonstrated for 100,000 spherical particles within a channel up to 492,000 processors. Highlights • Dynamic, parallel method for connectivity between unstructured overset grids. • Approaches for mesh cutting, interpolation partner pairing and parallel communication. • Scaling shown for 100,000 particles in a channel up to 492,000 processors. [ABSTRACT FROM AUTHOR]

A polar coordinate system introduces a singularity at the pole, r = 0 , where terms with a factor 1 / r can be ill-defined. While there are several approaches to eliminate this pole singularity in finite difference methods, finite volume methods largely bypass this issue by not storing or computing data at the pole. However, all methods face a very restrictive time step when using an explicit time advancement scheme in the azimuthal direction, where cell sizes are of the order O ( Δ r ( r Δ θ ) ) . We use a conservative finite volume approach of merging cells on a structured O-mesh to remove this time step limit imposed by the CFL condition. The cell-merging procedure is implemented as a corrector step and incurs no changes to the underlying data structure for a structured grid. This short note describes the procedure and presents the validation and application of the algorithm to various problems. The algorithm is shown to be inexpensive and scalable. In addition, the cell-merging procedure is easily coupled with a line implicit scheme in the radial direction. [ABSTRACT FROM AUTHOR]

LES of sheet to cloud cavitation over a wedge is performed at Reynolds number R e = 200 , 000 (based on the wedge height and free stream velocity) and cavitation number σ = 2.1 . The attached sheet cavity grows upto a critical length, after which it breaks into a cloud cavity which is highly three–dimensional and vortical in nature. The mean and RMS void fraction profiles obtained inside the cavity are compared to experiment and good agreement is observed. The frequency of the shedding process is obtained from point spectra at several locations and the obtained frequency is found to agree with the experiment. It is observed that the mean pressure at the wedge apex does not fall below vapor pressure; however cavitation occurs there due to the unsteady pressure falling below vapor pressure. The maximum mean void fraction occurs in the sheet cavity and is about 0.5, while the cloud region has even lesser amount of void fraction. The velocity fluctuations immediately downstream of the cavity show comparable streamwise and spanwise values, while the spanwise values are smaller in comparison inside the cavity region. The probability density function of void fraction examined at several locations inside the cavity show that the mean value obtained from time averaged data is very different from the most probable value of void fraction, indicating the considerable unsteadiness of the flow. The pressure waves produced upon cloud collapse are found to display both cyclic behavior and small scale transient behavior downstream of the wedge. The LES results agree better with experiment than unsteady RANS in predicting this highly unsteady flow. [ABSTRACT FROM AUTHOR]

Numerical simulations using the Reynolds Averaged Navier-Stokes (RANS) methodology have been widely used to study fluid problems in a variety of fields including ship research. Although computationally cheap, RANS fails to predict the fluid behavior accurately in complex flow problems where the underlying physics is dominated by unsteady complex physical phenomena. This paper discusses the use of large eddy simulation (LES) to study such complex flow physics. The predictive capability of LES is demonstrated in three complex flow problems: crashback, cavitation, and hydro-acoustics, which are of particular interest to the ship community. LES results are shown to be in good agreement with experiments for the mean and root mean square values of flow quantities in all these cases. [ABSTRACT FROM AUTHOR]

A seriesof manganese(II) complexes containing aryl-substitutedN-heterocyclic carbene (NHC) ligands have been synthesized and characterized.Chloride complexes of Mn(II) containing the NHC ligands 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene(IPr) and 1,3-dimesitylimidazol-2-ylidene (IMes) were prepared instraightforward fashion by direct carbene addition to MnCl2(THF)1.6. These complexes exist as chloride-bridged dimersin solution of formula [Mn2Cl2(μ-Cl)2(NHC)2]. The monomeric complex [MnCl2(IMes)2] has also been prepared and structurally characterized,although NMR studies are consistent with facile dissociation of oneof the IMes ligands in solution. [Mn2Cl2(μ-Cl)2(IPr)2] serves as a precursor to dimeric alkyland aryl compounds of Mn(II) including [Mn2R2(μ-Cl)2(NHC)2] (R = Bn, o-tolyl, and Ph) and the bridging methyl complex [Mn2Me2(μ-Me)2(IPr)2]. Stoichiometricreactions of these hydrocarbyl species with bromocyclohexane demonstratethat they are not chemically competent in C–C coupling reactionsinvolving alkyl electrophiles. [ABSTRACT FROM AUTHOR]

A dynamic end cap methodology is proposed to account for spurious contributions to the far-field sound within the context of the Ffowcs-Williams and Hawkings (FW-H) acoustic analogy. The quadrupole source terms are correlated over multiple planes to obtain a convection velocity which is then used to determine a corrective convective flux at the FW-H porous surface. The proposed approach is first demonstrated for a convecting potential vortex. It is then evaluated by computing the sound emitted by flow over circular cylinders at Reynolds number of 150, 10000, and 89000, respectively. The low Re cylinder is used to validate against direct numerical simulation (DNS) and demonstrate insensitivity to end plane location and spacing, the effect of dynamic convection velocity and to compare to commonly used end cap corrections. The Re 10000 cylinder is used to validate at turbulent Reynolds numbers against other simulations. Finally the Re 89000 simulations are used to compare to experiment. The proposed approach demonstrates better performance than other commonly used approaches with the added benefit of computational efficiency and the ability to query independent volumes. [ABSTRACT FROM AUTHOR]

It is common for jets of fluid to interact with crossflow. This article reviews our understanding of the physical behavior of this important class of flow in the incompressible and compressible regimes. Experiments have significantly increased in sophistication over the past few decades, and recent experiments provide data on turbulence quantities and scalar mixing. Quantitative data at high speeds are less common, and visualization still forms an important component in estimating penetration and mixing. Simulations have progressed from the Reynolds-averaged methodology to large-eddy and hybrid methodologies. There is a general consensus on the qualitative structure of the flow at low speeds; however, the flow structure at low-velocity ratios (jet speed/crossflow speed) might be fundamentally different from the common notion of shear-layer vortices, counter-rotating vortex pairs, wakes, and horseshoe vortices. Fluid in the near field is strongly accelerated, which affects the jet trajectory, entrainment, and mixing behavior. At low speeds, mixing depends more on Reynolds number than the jet trajectory or spatial extent does. Turbulence kinetic energy budgets are discussed that reveal the considerable nonequilibrium nature of the flow and the consequent challenges posed to time-averaged prediction methodologies. The parameter space at high speeds is fairly large, and even experimentally derived correlations for trajectories show significant scatter. Coherent motions in high-speed jets are seen to entrain large amounts of crossflow fluid but do not mix effectively in the near field. [ABSTRACT FROM AUTHOR]

The dynamic Lagrangian averaging approach for the dynamic Smagorinsky model for large eddy simulation is extended to an unstructured grid framework and applied to complex flows. The Lagrangian time scale is dynamically computed from the solution and does not need any adjustable parameter. The time scale used in the standard Lagrangian model contains an adjustable parameter θ. The dynamic time scale is computed based on a 'surrogate-correlation' of the Germano-identity error (GIE). Also, a simple material derivative relation is used to approximate GIE at different events along a pathline instead of Lagrangian tracking or multi-linear interpolation. Previously, the time scale for homogeneous flows was computed by averaging along directions of homogeneity. The present work proposes modifications for inhomogeneous flows. This development allows the Lagrangian averaged dynamic model to be applied to inhomogeneous flows without any adjustable parameter. The proposed model is applied to LES of turbulent channel flow on unstructured zonal grids at various Reynolds numbers. Improvement is observed when compared to other averaging procedures for the dynamic Smagorinsky model, especially at coarse resolutions. The model is also applied to flow over a cylinder at two Reynolds numbers and good agreement with previous computations and experiments is obtained. Noticeable improvement is obtained using the proposed model over the standard Lagrangian model. The improvement is attributed to a physically consistent Lagrangian time scale. The model also shows good performance when applied to flow past a marine propeller in an off-design condition; it regularizes the eddy viscosity and adjusts locally to the dominant flow features. [ABSTRACT FROM AUTHOR]

We revisit the Germano-identity error in the dynamic modeling procedure in the sense that the current modeling procedure to obtain the dynamic coefficient may not truly minimize the error in the mean and global sense. A “corrector step” to the conventional dynamic Smagorinsky model is proposed to obtain a corrected eddy viscosity which further reduces the error. The change in resolved velocity due to the coefficient variation as well as nonlocal nature of the filter and flow unsteadiness is accounted for by a simplified suboptimal control formalism without resorting to the adjoint equations. The objective function chosen is the Germano-identity error integrated over the entire computational volume and pathline. In order to determine corrected eddy viscosity, the Fréchet derivative of the objective function is directly evaluated by a finite-differencing formula in an efficient predictor-corrector-type framework. The proposed model is applied to decaying isotropic turbulence and turbulent channel flow at various Reynolds numbers and resolutions to obtain noticeable reduction in the Germano-identity error and significantly improved flow statistics. From channel flow large-eddy simulation, it is shown that conventional dynamic model underestimates subgrid scale eddy viscosity when the resolution gets coarse, and this underestimation is responsible for increased anisotropy of predicted Reynolds stress. The proposed model raises both the overall and near-wall subgrid scale eddy viscosity to reduce exaggerated Reynolds stress anisotropy and yield significantly improved flow statistics. [ABSTRACT FROM AUTHOR]

Abstract: Direct numerical simulation (DNS) is used to study chemically reacting, laminar vortex rings. A novel, all-Mach number algorithm developed by Doom et al. [J. Doom, Y. Hou, K. Mahesh, J. Comput. Phys. 226 (2007) 1136–1151] is used. The chemical mechanism is a nine species, nineteen reaction mechanism for H2/air combustion proposed by Mueller et al. [M.A. Mueller, T.J. Kim, R.A. Yetter, F.L. Dryer, Int. J. Chem. Kinet. 31 (1999) 113–125]. Diluted H2 at ambient temperature (300 K) is injected into hot air. The simulations study the effect of fuel/air ratios, oxidizer temperature, Lewis number and stroke ratio (ratio of piston stroke length to diameter). Results show that auto-ignition occurs in fuel lean, high temperature regions with low scalar dissipation at a ‘most reactive’ mixture fraction, (Mastorakos et al. [E. Mastorakos, T.A. Baritaud, T.J. Poinsot, Combust. Flame 109 (1997) 198–223]). Subsequent evolution of the flame is not predicted by ; a most reactive temperature is defined and shown to predict both the initial auto-ignition as well as subsequent evolution. For stroke ratios less than the formation number, ignition in general occurs behind the vortex ring and propagates into the core. At higher oxidizer temperatures, ignition is almost instantaneous and occurs along the entire interface between fuel and oxidizer. For stroke ratios greater than the formation number, ignition initially occurs behind the leading vortex ring, then occurs along the length of the trailing column and propagates toward the ring. Lewis number is seen to affect both the initial ignition as well as subsequent flame evolution significantly. Non-uniform Lewis number simulations provide faster ignition and burnout time but a lower maximum temperature. The fuel rich reacting vortex ring provides the highest maximum temperature and the higher oxidizer temperature provides the fastest ignition time. The fuel lean reacting vortex ring has little effect on the flow and behaves similar to a non-reacting vortex ring. [Copyright &y& Elsevier]

Abstract: Purely dissipative eddy-viscosity subgrid models have proven very successful in large-eddy simulations (LES) at moderate resolution. Simulations at coarse resolutions where the underlying assumption of small-scale universality is not valid, warrant more advanced models. However, non-eddy viscosity models are often unstable due to the lack of sufficient dissipation. This paper proposes a simple modeling approach which incorporates the dissipative nature of existing eddy viscosity models into more physically appealing non-eddy viscosity SGS models. The key idea is to impose the SGS dissipation of the eddy viscosity model as a constraint on the non-eddy viscosity model when determining the coefficients in the non-eddy viscosity model. We propose a new subgrid scale model (RSEM), which is based on estimation of the unresolved velocity field. RSEM is developed in physical space and does not require the use of finer grids to estimate the subgrid velocity field. The model coefficient is determined such that total SGS dissipation matches that from a target SGS model in the mean or least-squares sense. The dynamic Smagorinsky model is used to provide the target dissipation. Results are shown for LES of decaying isotropic turbulence and turbulent channel flow. For isotropic turbulence, RSEM displays some level of backward dissipation, while yielding as good results as the dynamic Smagorinsky model. For channel flow, the results from RSEM are better than those from the dynamic Smagorinsky model for both statistics and instantaneous flow structures. [Copyright &y& Elsevier]

Direct numerical simulations of flow past cactus-shaped cylinders are performed at Reynolds numbers of 20, 100, and 300. The results are contrasted to those from smooth cylinders at the same Reynolds numbers. The cavities in the cactus-shaped cylinders are seen to reduce the forces acting on them. At Reynolds number of 20, the drag is reduced by 22% due to reduction in the viscous forces. At Reynolds number of 100, the unsteady pressure forces increase, while the unsteady viscous forces acting on the cactus-shaped cylinder decrease. The overall reduction in drag force is about 18%. At Reynolds number of 300, onset of three dimensionality is observed together with significant decrease in pressure and viscous forces. Both the mean and fluctuating forces are found to decrease considerably. The Strouhal number is also found to decrease by about 10%. These reductions in force magnitudes and observed wake instabilities are attributed to the presence of large-scale, quiescent, recirculating flow within the cactus cavities. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops a dynamic error analysis procedure for the numerical errors arising from spatial discretization in large-eddy simulation. The analysis is based on EDQNM closure theory, and is applied to the LES of decaying isotropic turbulence. First, the effects of finite-differencing truncation error, aliasing error and the dynamic Smagorinsky model are independently considered. The time-evolution of kinetic energy and spectra predicted by the analysis are compared to actual LES using the Navier–Stokes equations, and good agreement is obtained. The analysis is then extended to simultaneously consider all sources of error in a second-order discretely energy conserving, central-difference LES solver. Good agreement between the analysis and actual LES is obtained. The analysis is used to compare the contribution of the subgrid model to that of numerical errors, and it is shown that the contribution of the subgrid scale model is much higher than the numerical errors. The proposed one-dimensional EDQNM-LES model shows potential as a more general tool for the analysis of numerical error, and SGS model in simulations of turbulent flow. [Copyright &y& Elsevier]

A two-dimensional model problem is used to study the evolution of the cross section of a transverse jet and the counter-rotating vortex pair (CVP). The solution to the model problem shows deformation of the jet similar to that observed in a transverse jet, and also yields a CVP. These phenomena are explained in terms of the acceleration the jet experiences in the direction of the cross-flow, and the pressure field around the jet. The initial stages of the jet’s evolution are at constant acceleration while the later stages are at constant velocity. The effects of Reynolds number and velocity ratio on the evolution of the jet are used to explain the dependence of CVP formation on velocity ratio, as observed by Smith and Mungal [J. Fluid Mech. 357, 83 (1998)]. [ABSTRACT FROM AUTHOR]

Abstract: A non-dissipative, robust, implicit algorithm is proposed for direct numerical and large-eddy simulation of compressible turbulent flows. The algorithm addresses the problems caused by low Mach numbers and under-resolved high Reynolds numbers. It colocates variables in space to allow easy extension to unstructured grids, and discretely conserves mass, momentum and total energy. The Navier–Stokes equations are non-dimensionalized using an incompressible scaling for pressure, and the energy equation is used to obtain an expression for the velocity divergence. A pressure-correction approach is used to solve the resulting equations, such that the discrete divergence is constrained by the energy equation. As a result, the discrete equations analytically reduce to the incompressible equations at very low Mach number, i.e., the algorithm overcomes the acoustic time-scale limit without preconditioning or solution of an implicit system of equations. The algorithm discretely conserves kinetic energy in the incompressible inviscid limit, and is robust for inviscid compressible turbulence on the convective time-scale. These properties make it well-suited for DNS/LES of compressible turbulent flows. Results are shown for acoustic propagation, the incompressible Taylor problem, periodic shock tube problem, and isotropic turbulence. [Copyright &y& Elsevier]

Reynolds-averaged Navier-Stokes (RANS) methods often cannot predict shock/turbulence interaction correctly. This may be because RANS models do not account for the unsteady motion of the shock wave that is inherent in these interactions. Previous work proposed a shock-unsteadiness correction that significantly improves prediction of turbulent kinetic energy amplification across a normal shock in homogeneous isotropic turbulence. We generalize the modification to shock-wave/turbulent boundary-layer interactions and implement it in the k-∈, k-ω, and Spalart-Allmaras models. In compression-corner flows, the correction decreases the turbulent kinetic energy amplification across the shock compared to the standard k-∈ and k-ω models. This results in improved prediction of the separation shock location, delayed reattachment, and slower recovery of the boundary layer on the ramp. For the Spalart-Allmaras model, the modification amplifies eddy viscosity across the shock, moving the separation location closer to the experiment. [ABSTRACT FROM AUTHOR]

Direct numerical simulation is used to study the effect of entrainment near the inflow nozzle on spatially evolving round jets. Inflow entrainment is obtained by providing a buffer region upstream of the inflow nozzle. Simulations are performed at Reynolds numbers of 300 (laminar) and 2400 (turbulent), respectively. Simulations without the inflow buffer are contrasted to those with the buffer region. The potential core is seen to close earlier in the presence of inflow entrainment. As a result, near-field turbulent intensities and pressure fluctuations on the jet centerline are noticeably affected. It is suggested that inflow entrainment results in an effective co-flow, whose effect on the volumetric flow rate near the inflow nozzle is appreciable for both laminar and turbulent jets. When plotted in similarity variables, the far-field solutions with and without inflow entrainment agree well with each other, and experiment. The results suggest the importance of allowing for inflow entrainment in simulations of turbulent jets, particularly for studies where near-field behavior is important. [ABSTRACT FROM AUTHOR]

The RANS (Reynolds averaged Navier-Stokes) equations can yield significant error when applied to practical flows involving shock waves. We use the interaction of homogeneous isotropic turbulence with a normal shock to suggest improvements in the k - e model applied to shock/ turbulence interaction. Mahesh et al. [J. Fluid Mech. 334, 353 (1997)] and Lee et al. [J. Fluid Mech. 340, 22 (1997)] present direct numerical simulation (DNS) and linear analysis of the flow of isotropic turbulence through a normal shock, where it is found that mean compression, shock unsteadiness, pressure-velocity correlation, and up-stream entropy fluctuations play an important role in the interaction. Current RANS models based on the eddy viscosity assumption yield very high amplification of the turbulent kinetic energy, k, across the shock. Suppressing the eddy viscosity in a shock improves the model predictions, but is inadequate to match theoretical results at high Mach numbers. We modify the k equation to include a term due to shock unsteadiness, and model it using linear analysis. The dissipation rate equation is similarly altered based on linear analysis results. These modifications improve the model predictions considerably, and the new model is found to match the linear theory and DNS data well. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 106 and 4.5 × 109 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L−1. Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models' differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models' thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. We also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state. [ABSTRACT FROM AUTHOR]

We present a numerical study of inception in the shear layer of a backward-facing step under the same conditions as experiments (Agarwal et al., 2018). The velocity field is shown to be in good agreement with experiments. Since inception is a stochastic process that generates small amounts of vapor for short periods of time, the effects of these small regions of vapor on the liquid density and dynamics can be neglected. Vapor is therefore treated as a passive scalar in an incompressible liquid and modeled using the same vapor transport equation as that in a fully compressible homogeneous mixture model. The model is validated against the compressible homogeneous mixture approach at incipient conditions. Both velocity and scalar fields are advanced using the implicit Crank–Nicolson scheme. However, the scalar field is solved in an inner loop at a smaller time step than the velocity field. Statistics are computed for both pressure and vapor volume fraction, and the likelihood of inception is determined. The locations of the preferred sites for cavitation are compared to experimental results and good agreement is achieved. The effects of finite rate evaporation and condensation are revealed by the probability density functions of pressure and volume fraction. The flow topology is investigated and inception is found to occur in the core of the stretched tubular vortical structures with a rotation rate four times higher than the stretching rate. These cavitating tubular structures are elongated two to three times more in their most extensive principal direction than in their intermediate principal direction, and are most likely aligned with the streamwise direction. Decreasing the cavitation number from 0.55 to 0.45 is found to drop the minimum pressure inside the vortices from − 1500 Pa to − 550 0 Pa and increase the cavitation event rates by around O (1). • We present a numerical study of inception in the shear layer of a backstep. • The locations of the preferred sites for cavitation agree with experimental results. • Inception occurs in the cores of the stretched tubular vortical structures. • Incipient structures have a rotation rate four times higher than the stretching rate. • Reducing the cavitation number increases the cavitation event rates by around O(1). [ABSTRACT FROM AUTHOR]

• Fully GPU accelerated unstructured overset method to simulate flows over moving bodies. • Novel overset assembly method inspired by real-time ray tracing algorithms. • Accurate and cost effective artificial compressibility pressure regularization shown. • Primal-dual reconstruction introduced for accurate calculations on general meshes. • Speedups of 15-50x found compared to benchmark overset solver for high cell loadings. Hardware acceleration consists of offloading computational work to devices such as graphics processing units (GPUs) to produce overall speed-up. Algorithms and numerical methods must be constructed to suit the available hardware in order to effectively produce speed-up. In this work a numerical method is presented which can effectively use hardware acceleration to simulate incompressible turbulent fluid flow. The method is an unstructured overset method where unstructured meshes are attached to individual bodies and connected throughout the flow domain to produce a single domain solution through an overset assembly process. The unstructured overset method shown in Horne and Mahesh [1] and Horne and Mahesh [2] was found capable of scaling to O(105) computational cores for O(105) moving bodies in turbulent flow fields while producing accurate flow results. This highly scalable method is modified and extended to effectively utilize on-node hardware acceleration. Overset assembly algorithms which use hardware acceleration are presented based on successful accelerated algorithms in real-time ray tracing and computational geometry. Timing results for core overset assembly operations are presented showing a maximum O(100x) speedup when using hardware acceleration. A novel method for turbulent fluid flow is presented which utilizes over-decomposition of the flow domain to produce task-parallelism allowing asynchronous calculation of the different steps of the method while also providing overlap between data transfer and computation. A mixed precision solver is utilized which provides a balance between optimal performance and numerical accuracy. A cost effective and accurate artificial compressibility pressure regularization is used which has minimal memory complexity and minimizes computational cost while maintaining accuracy. A primal-dual Laplacian operator is introduced which produces accurate results on skewed meshes. Results for canonical flow cases with overset meshes are shown illustrating the method's accuracy and numerical properties. Substantial speed-up is demonstrated for the numerical method reaching upwards of 50 times as fast as the non-accelerated method for high cell loadings. [ABSTRACT FROM AUTHOR]

A numerical approach based on preconditioning and dual-time stepping (DTS) is proposed to simulate cavitating flows at low Mach numbers. The methodology is based on a fully-compressible homogeneous mixture model and finite rate mass transfer as discussed in Gnanaskandan and Mahesh (2015). The method has shown promising results for capturing the large-scale cavitation in developed cavitation regimes (e.g. Bhatt and Mahesh, 2020; Gnanaskandan and Mahesh, 2016a). Small-scale vapor regions in the incipient cavitation, cavitation inception and wetted conditions are sensitive to free-stream nuclei content (e.g. Hsiao and Chahine, 2005; Bhatt and Mahesh, 2019, 2020). In these regimes, lower values of free-stream nuclei are necessary than what is typically prescribed in homogeneous mixture models that use a fully-compressible formulation. While important for the physical modeling, lower values of free-stream nuclei lead to acoustic stiffness. The goal of the present work is to present a numerical approach to enable such low free-stream nuclei calculations in an accurate manner and in a reasonable amount of time. The key aspects of the numerical approach are: (i) preconditioning applied to the cavitating flow equations in a fully-compressible (density-based) solver, (ii) modifications based on the all-speed Roe-type scheme to the characteristic-based filtering, and (iii) implementation in parallel and on unstructured grids that allow the simulation of complex problems. The numerical formulation of the time-derivative preconditioning matrix, the DTS framework, and modification to the shock-capturing are discussed. A proper conditioning of the preconditioned system of equations is obtained. The methodology is demonstrated for the unsteady flow over a cylinder under wetted and cavitation inception conditions, and LES of flow over a propeller under wetted conditions. Overall, a significant saving in total run-time as compared to the original solver is obtained, without compromising accuracy. [ABSTRACT FROM AUTHOR]

Reviews the direct numerical simulation (DNS) of turbulent flows. Background of the study of DNS; Issues involved in the DNS of turbulence; Examples of novel numerical experiments on turbulence.

Proposes a simple inviscid model to predict the onset of breakdown in an asymmetric vortex. Problems about compressible and incompressible vortices considered; Assumption of breakdown if pressure exceeds the axial momentum flux; Derivation of a formula for the critical swirl number in all three problems.

Homogeneous rapid distortion theory is used to study the response of shear flows and axisymmetric turbulence to rapid one-dimensional compression. In the shear flow problem, both normal and oblique compressions are considered. The response of these anisotropic flows to compression is found to be quite different from that of isotropic turbulence. Upon normal compression, the amplification of the streamwise component of kinetic energy and the total kinetic energy in shear flows is higher than that in isotropic turbulence. Also, normal compression decreases the magnitude of the Reynolds shear stress by amplifying the pressure-strain correlation in the shear stress equation. Obliquity of compression (defined as the angle between the directions of shear and compression) is seen to significantly affect the evolution of the Reynolds stresses. For a range of oblique angles from -60° to 60°, the amplification of streamwise kinetic energy and total kinetic energy decrease with increasing magnitude of the oblique angle. Also, the tendency of the shear stress to decrease in magnitde is diminished upon increasing the oblique angle; for large oblique angles the shear stress amplifies. Upon compression along the axis of axisymmetry, the amplification of the streamwise component of kinetic energy is higher for contracted turbulence than for isotropic turbulence, while the amplification of the total kinetic energy is lower. The above results are interpreted in a more general framework. It is shown that the amplification of the streamwise component of kinetic energy is determined by the initial E[SUB11](κ [SUB1]) (x[SUB1] is the direction of compression). Flows with u[SUB1] at lower κ[SUB1] have a lower effect of pressure during compression and hence, higher amplification of &u[SUB1SUP2]sline;. The amplification of the total kinetic energy is determined by the initial fraction of energy along the direction of compression (&u[SUB1SUP2]sline;/q[SUP2]) and the... [ABSTRACT FROM AUTHOR]

The paper performs simulation of a rectangular plate excited by turbulent channel flow at friction Reynolds numbers of 180 and 400. The fluid–structure interaction is assumed to be one-way coupled, i.e, the fluid affects the solid and not vice versa. We solve the incompressible Navier–Stokes equations using finite volume direct numerical simulation in the fluid domain. In the solid domain, we solve the dynamic linear elasticity equations using a time-domain finite element method. The obtained plate averaged displacement spectra collapse in the low frequency region in outer scaling. However, the high frequency spectral levels do not collapse in inner units. This spectral behavior is reasoned using theoretical arguments. The resonant vibration is stronger at the third natural frequency than at the first natural frequency. We explain this behavior by comparing the fluid and solid length scales. We further study the sources of plate excitation using a novel formulation. This formulation expresses the average displacement spectrum of the plate as an integrated contribution from the fluid sources within the channel. Analysis of the sources reveals that at the plate natural frequencies, the contribution of the fluid sources to the plate excitation peaks in the buffer layer. The corresponding wall-normal width is found to be ≈ 0. 75 δ. The integrated contribution of the overlap and outer regions together to the plate response is comparable to that from the buffer region for R e τ = 180 and exceeds the buffer region contribution for R e τ = 400. We analyze the decorrelated features of the sources using spectral Proper Orthogonal Decomposition (POD) of the net displacement source. We enforce the orthogonality of the modes in an inner product with a symmetric positive definite kernel. The dominant spectral POD mode contributes to the entire plate excitation. The contribution of the remaining modes from the different wall-normal regions undergo destructive interference resulting in zero net contribution. The envelope of the dominant mode further shows that the intensity of the sources peaks in the buffer region and the wall-normal width of the sources extend well into the outer region of the channel. [ABSTRACT FROM AUTHOR]

• Partial cavitation over incipient, transitory and periodic regimes is investigated using LES. • Very good comparison to experiments is observed for vapor volume fractions, shock speed and shedding frequency. • LES flow field is used to investigate the conditions that lead to either the formation of re-entrant jet or bubbly shock wave. • The initiation of bubbly shock wave by the collapse-induced pressure wave from previously shed clouds is explained. Partial cavitation over incipient, transitory and periodic regimes is investigated using large eddy simulation (LES) in the (experimental) sharp wedge configuration of Ganesh et al. (2016). The numerical approach is based on a compressible homogeneous mixture model with finite rate mass transfer between the phases. Physical mechanisms of cavity transition observed in the experiments; i.e. re-entrant jet and bubbly shock wave, are both captured in the LES over their respective regimes. Vapor volume fraction data obtained from the LES is quantitatively compared to X-ray densitometry. In the transitory and periodic regimes, void fractions resulting from complex interactions of large regions of vapor in the sheet/cloud show very good comparison with the experiments. In addition, very good agreement with the experiments is obtained for the shedding frequency and the bubbly shock wave propagation speed. In the incipient regime, the qualitative characteristics of the flow (e.g. cavitation inside spanwise vortices in the shear layer) are captured in the simulations. Conditions favoring either the formation of the re-entrant jet or the bubbly shock wave are analyzed by contrasting the LES results between the regimes. In the transitory regime, large pressure recovery from within the cavity to outside, and the resulting high adverse pressure gradient at the cavity closure support the formation of re-entrant jet. In the periodic regime, overall low pressures lead to reduced speed of sound and increased medium compressibility, favoring the propagation of shock waves. In a re-entrant jet cycle, vapor production occurs predominantly in the shear layer, and intermittently within the cavity. In a bubbly shock cycle, vapor production is observed spanning the entire thickness of the cavity. Bubbly shock wave propagation is observed to be initiated by the impingement of the collapse-induced pressure waves from the previously shed cloud. Supersonic Mach numbers are observed in the cavity closure regions, while the regions within the grown cavity are subsonic due to the negligible flow velocities. [ABSTRACT FROM AUTHOR]

An unstructured overset method capable of performing direct numerical simulation (DNS) and large eddy simulation (LES) of many (O (10 5)) moving bodies, utilizing many computational cores (O (10 5)), in turbulent, incompressible fluid flow is presented. Unstructured meshes are attached to bodies and placed within a fixed background domain. Body meshes are allowed to arbitrarily overlap and move throughout the domain. Within each mesh a high resolution, unstructured, non-dissipative finite volume method is used to solve for the flow field. Boundary conditions for each mesh are provided by interpolation from flow solutions on overlapping meshes. When many unstructured meshes of different resolution overlap, care is required in the connection between the different flow solutions. An interpolant is created which seeks to preserve volume conservation of flow quantities between meshes regardless of overlapping mesh differences. An implicit fractional step method is used for time advancement, requiring the calculation of a predicted fluid velocity and corrector pressure field. For the predictor step, the resulting interpolation is directly introduced into the implicit equations for the predicted flow field. For the corrected pressure field, the continuity between meshes is weakly enforced using a penalty formulation. The pressure formulation is symmetric, positive-definite and non-singular resulting in a formulation which is readily solvable using traditional iterative matrix inversion techniques. An Arbitrary Euler-Lagrangian (ALE) method coupled to a 6 degrees of freedom rigid body equation system (6-DOF) is used for body motion. For rotation, a quaternion representation is used to solve Euler's equations of rigid body motion. A linear spring damper model, which uses geometry information readily available from the overset assembly process, is used for collisions. Validation of the method for canonical flow fields is presented including assessment of order of accuracy and kinetic energy conservation properties. Particle-resolved direct numerical simulation (PR-DNS) of single particles in various flow fields are presented for validation. PR-DNS results of 50,000 spherical particles freely moving within turbulent channel flow are shown as a demonstration of the method at full scale. LES results of a marine propeller under crashback conditions are shown to demonstrate the ability to simulate highly unsteady turbulent flows over complex, moving geometries. • Unstructured overset method shown for LES/DNS of many (O (10 5)) moving bodies, using many cores (O (10 5)), in turbulent flow. • Novel overset supercell reconstruction introduced which yields superior kinetic energy properties to other reconstructions. • Novel penalty formulation shown that produces efficient linear systems to enforce pressure continuity between overset meshes. • LES of propeller crashback illustrates method's ability to simulate turbulent flow over complex moving geometry. • PR-DNS of 50,000 freely moving particles in a turbulent channel demonstrates the method at full scale. [ABSTRACT FROM AUTHOR]

Large-eddy simulation (LES) is used to simulate flow over a three-dimensional elliptical hydrofoil at 12 degrees angle of attack and Reynolds numbers (R e) of 9 × 1 0 5 and 1. 4 × 1 0 6 based on root chord length and freestream velocity. The simulations are performed at the cavitation number (σ) of 2.1 and are based on the experiments of Boulon et al. (1999), who studied the tip vortex cavitation behavior under the confinement of side and bottom walls. The present simulations correspond to their case where the confinement due to the bottom wall is negligible. The computational model of Brandao and Mahesh (2022) that treats vapor as a passive scalar in an incompressible liquid is extended to account for multiple groups of bubbles of different sizes, effectively making it a polydisperse model. This allows us to investigate the effects of water quality on inception. The simulations include two different freestream nuclei distributions that are taken from the water tunnel data of Khoo et al. (2020c). It was found that inception is strongly dependent on the amounts of nuclei in the freestream. When the flow is depleted of nuclei, inception is an intermittent event confined to a location very close to the hydrofoil tip. However, when the flow is rich in nuclei, a larger portion of the tip vortex cavitates, as well as part of the suction side very close to the leading edge of the hydrofoil. Probability density functions revealed that cavitation occurs in any region experiencing a pressure field lower than vapor pressure when the flow is rich in nuclei, while extremely low values of pressure (usually kPa of tension) are required to make a flow depleted of nuclei cavitate. The topology of a flow poor in nuclei was investigated and inception was found to occur in regions dominated by irrotational straining with high stretching rates. Lagrangian statistics showed that as R e is increased, nuclei have higher likelihood of experiencing very low pressure fields. However, the amount of time they are subject to very low pressures is also shorter with increasing R e. [Display omitted] • A population balance model was developed to simulate cavitation inception conditions. • Inception characteristics are found to change depending on the water quality. • An extremely low value of pressure is required to make water poor in nuclei cavitate. • Water rich in nuclei cavitates as soon as pressure drops below vapor pressure. • R e has low impact on inception when the flow is very depleted of nuclei. [ABSTRACT FROM AUTHOR]

A novel constrained formulation for the dynamic subgrid-scale model for large eddy simulation (LES) is proposed. An externally prescribed Reynolds stress is used as the constraint and is imposed in the near-wall region of wall-bounded flows. However, unlike conventional zonal approaches, Reynolds stress is not imposed as the solution, but used as a constraint on the subgrid-scale stress so that the computed Reynolds stress closely matches the prescribed one only in the mean sense. In the absence of an ideal wall model or adequate near-wall resolution, a LES solution at coarse resolution is expected to be erroneous very near the wall while giving reasonable predictions away from the wall. The Reynolds stress constraint is limited to the region where the LES solution is expected to be erroneous. The Germano-identity error is used as an indicator of LES quality such that the Reynolds stress constraint is activated only where the Germano-identity error exceeds a certain threshold. The proposed model is applied to LES of turbulent channel flow at various Reynolds numbers and grid resolutions to obtain significant improvement over the dynamic Smagorinsky model, especially at coarse resolutions. This constrained formulation can be extended to incorporate constraints on the mean of other flow quantities. [ABSTRACT FROM AUTHOR]

Propulsor crashback is an off-design operating condition where a propulsor rotates in the reverse direction to yield negative thrust. Crashback is characterized by the interaction of the free stream with the reverse flow generated by propulsor rotation. This causes a highly unsteady vortex ring which leads to flow separation and unsteady forces and moments on the blades. Large eddy simulation (LES) is performed for marine propulsors in crashback for various configurations and advance ratios and validated against experiments. The predictive capability of LES as a tool for propulsor crashback is demonstrated on an open propulsor, open propulsor with a submarine hull, and ducted propulsor with and without stator blades. LES is in good agreement with experiments for the mean and RMS levels, and spectra of the unsteady loads on the propulsors. [ABSTRACT FROM AUTHOR]

Abstract: A spatially non-dissipative, implicit numerical method to simulate turbulent reacting flows over a range of Mach numbers, is described. The compressible Navier–Stokes equations are rescaled so that the zero Mach number equations are discretely recovered in the limit of zero Mach number. The dependent variables are co-located in space, and thermodynamic variables are staggered from velocity in time. The algorithm discretely conserves kinetic energy in the incompressible, inviscid, non-reacting limit. The chemical source terms are implicit in time to allow for stiff chemical mechanisms. The algorithm is readily extended to complex chemical mechanisms. Numerical examples using both simple and complex chemical mechanisms are presented. [Copyright &y& Elsevier]

• Robust variational level set methodology is proposed to capture equilibrium interface shapes over arbitrary rough surfaces. • Distance regularization is used instead of reinitialization. Mass conservation and no-penetration constraints are incorporated. • A harmonic mean based surface tension distribution is used that leads to accurate numerical results. • Parallel implementation validated with canonical level set test cases and analytical solutions of Gibbs free energy. • Applied to problems for the prediction of equilibrium interface shapes over grooves, posts and arbitrary surface roughness. A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the no-penetration and volume-conservation constraints. In this framework, we avoid reinitialization that is typically used in traditional level set methods. This allows for a more efficient algorithm since only one advection equation is solved, and avoids numerical error associated with the re-distancing step. A novel surface tension distribution, based on harmonic mean, is prescribed such that the zero level set has the correct liquid-solid surface tension value. This leads to a more accurate prediction of the triple contact point location. The method uses second-order central difference schemes which facilitates easy parallel implementation, and is validated by comparing to traditional level set methods for canonical problems. The application of the method in the context of Gibbs free energy minimization, to obtain liquid-air interfaces is validated against existing analytical solutions. The capability of the methodology to predict equilibrium shapes over both structured and realistic rough surfaces is demonstrated. [ABSTRACT FROM AUTHOR]

Background. Inflammation in an ESRD patient may impact responsiveness to erythropoiesis-stimulating agent (ESA) therapy. We sought to investigate the association between C-reactive protein (CRP) levels and average per-administration epoetin alfa (EPO) dose over 3 months following a CRP measurement. Methods. The study is a retrospective cohort study of hemodialysis patients ≥18 years of age receiving care at a Fresenius Medical Care-North America facility between 1 July 2000 and 30 June 2002 who had no history of peritoneal dialysis. All patients had ≥1 CRP measurement and ≥3 months of recorded information before the CRP measurement (entry period). We evaluated the association between CRP levels and average hemoglobin (Hb) and per-administration EPO dose over the 3 months following the CRP measurement. Results. We identified 1754 patients with a CRP measurement; mean age was 62.6 years (SD 14.1), 51.5% were male, 56.2% were white and the median CRP value was 2.04 mg/dL (20.4 mg/L). Patients in the upper CRP quartiles were more likely to be older, recently hospitalized; have a catheter vascular access; have lower albumin, Hb and transferrin saturation levels and greater EPO doses. In the subsequent 3 months, EPO doses but not Hb levels were significantly higher for patients in the highest CRP quartile [3.21 mg/dL (32.1 mg/L)] (P = 0.01). Conclusions. Inflammation as measured by an elevated CRP level appears to be an independent predictor of greater ESA dose requirements. Patients with the highest CRP levels required significantly higher ESA doses to achieve comparable Hb levels even after controlling for potential confounding variables. [ABSTRACT FROM AUTHOR]

Background. The Dialysis Outcomes and Practice Patterns Study (DOPPS) database was used to develop and validate a practice-related risk score (PRS) based on modifiable practices to help facilities assess potential areas for improving patient care. Methods. Relative risks (RRs) from a multivariable Cox mortality model, based on observational haemodialysis (HD) patient data from DOPPS I (1996–2001, seven countries), were used. The four practices were the percent of patients with Kt/V ≥1.2, haemoglobin ≥11 g/dl (110 g/l), albumin ≥4.0 g/dl (40g/l) and catheter use, and were significantly related to mortality when modelled together. DOPPS II data (2002–2004, 12 countries) were used to evaluate the relationship between PRS and mortality risk using Cox regression. Results. For facilities in DOPPS I and II, changes in PRS over time were significantly correlated with changes in the standardized mortality ratio (SMR). The PRS ranged from 1.0 to 2.1. Overall, the adjusted RR of death was 1.05 per 0.1 points higher PRS (P N = 119), a 0.2 decrease in PRS was associated with a 0.19 decrease in SMR (P = 0.005). On average, facilities that improved PRS practices showed significantly reduced mortality over the same time frame. Conclusions. The PRS assesses modifiable HD practices that are linked to improved patient survival. Further refinements might lead to improvements in the PRS and will address regional variations in the PRS/mortality relationship. [ABSTRACT FROM AUTHOR]