Search

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]

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]

• 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]

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]

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]

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]

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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)