Quasi-periodic forces and conditionally averaged characteristics of unsteady cavitation flow around a hydrofoil

Large-eddy simulations are performed to investigate the cavitating flow around two dimensional hydrofoil section with angle of attack of 9° and high Reynolds number of 1.3×106. We use the Schnerr-Sauer model for accurate phase transitions modelling. Instantaneous velocity fields are compared successfully with PIV data using the methodology of conditional averaging to take into account only the liquid phase characteristics as in PIV. The presence of two frequencies in a spectrum corresponding to the full and partial cavity detachments is analysed.

Systematic Validation Study of an Unsteady Cavitating Flow over a Hydrofoil Using Conditional Averaging: LES and PIV

We present results of Large-eddy simulations (LES) modeling of steady sheet and unsteady cloud cavitation on a two-dimensional hydrofoil which are validated against Particle image velocimetry (PIV) data. The study is performed for the angle of attack of 9∘ and high Reynolds numbers ReC of the order of 106 providing a strong adverse pressure gradient along the surface. We employ the Schnerr–Sauer and Kunz cavitation models together with the adaptive mesh refinement in critical flow regions where intensive phase transitions occur. Comparison of the LES and visualization results confirms that the flow dynamics is adequately reproduced in the calculations. To correctly match averaged velocity distributions, we propose a new methodology based on conditional averaging of instantaneous velocity fields measured by PIV which only provides information on the liquid phase. This approach leads to an excellent overall agreement between the conditionally averaged fields of the mean velocity and turbulence intensity obtained experimentally and numerically. The benefits of second-order discretization schemes are highlighted as opposed to the lower-order TVD scheme.

Correlation between Large-Scale Streamwise Velocity Features and the Height of Coherent Vortices in a Turbulent Boundary Layer

The preferential organisation of coherent vortices in a turbulent boundary layer in relation to local large-scale streamwise velocity features was investigated. Coherent vortices were identified in the wake region using the Triple Decomposition Method (originally proposed by Kolář) from 2D particle image velocimetry (PIV) data of a canonical turbulent boundary layer. Two different approaches, based on conditional averaging and quantitative statistical analysis, were used to analyze the data. The large-scale streamwise velocity field was first conditionally averaged on the height of the detected coherent vortices and a change in the sign of the average large scale streamwise fluctuating velocity was seen depending on the height of the vortex core. A correlation coefficient was then defined to quantify this relationship between the height of coherent vortices and local large-scale streamwise fluctuating velocity. Both of these results indicated a strong negative correlation in the wake region of the boundary layer between vortex height and large-scale velocity. The relationship between vortex height and full large-scale velocity isocontours was also studied and a conceptual model based on the findings of the study was proposed. The results served to relate the hairpin vortex model of Adrian et al. to the scale interaction results reported by Mathis et al., and Chung and McKeon.

Processing Accuracy of Instantaneous Values of a Stochastic Signal in an Inertial Measurement System

The article presents an analysis of the dynamic error occurring when processing a stochastic signal in an inertial measurement system. The problem was illustrated using both a calculation and a laboratory example. The technique of conditional averaging of signals was used in the experiment. The possibility to minimize the root mean square value of the error as well as the need for a time correction of measurement values in an inertial measurement system was demonstrated.

A Two-Fluid Conditional Averaging Paradigm for the Theory and Modeling of Turbulent Premixed Combustion

This paper extends a recent theoretical study that was previously presented in the form of a brief communication (Zimont, C&F, 192, 2018, 221-223), in which we proposed a simple splitting method for the derivation of two-fluid conditionally averaged equations of turbulent premixed combustion in the flamelet regime, formulated more conveniently for applications involving unclosed equations without surface-averaged unknowns. This two-fluid conditional averaging paradigm avoids the challenge in the Favre averaging paradigm of modeling the countergradient scalar transport phenomenon and the unusually large velocity fluctuations in a turbulent premixed flame. It is a more suitable conceptual framework that is likely to be more convenient in the long run than the traditional Favre averaging method. In this article, we further develop this paradigm and pay particular attention to the problem of modeling turbulent premixed combustion in the context of a two-fluid approach. We formulate and analyze the unclosed differential equations in terms of the conditions of the Reynolds stresses τij,u, τij,b and the mean chemical source ρW¯, which are the only modeling unknowns required in our alternative conditionally averaged equations. These equations are necessary for the development of model differential equations for the Reynolds stresses and the chemical source in the advanced modeling and simulation of turbulent premixed combustion. We propose a simpler approach to modeling the conditional Reynolds stresses based on the use of the two-fluid conditional equations of the standard “k-ε” turbulence model, which we formulate using the splitting method. The main problem arising here is the appearance in these equations of unknown terms describing the exchange of the turbulent energy k and dissipation rate ε in the unburned and burned gases. We propose an approximate way to avoid this problem. We formulate a simple algebraic expression for the mean chemical source that follows from our previous theoretical analysis of the transient turbulent premixed flame in the intermediate asymptotic stage, in which small-scale wrinkles in the instantaneous flame surface reach statistical equilibrium, while the large-scale wrinkles remain in statistical nonequilibrium.

Effects of Outlier Flow Field on the Characteristics of In-Cylinder Coherent Structures Identified by Proper Orthogonal Decomposition-Based Conditional Averaging and Quadruple Proper Orthogonal Decomposition

Proper orthogonal decomposition (POD) offers an approach to quantify cycle-to-cycle variation (CCV) of the flow field inside the internal combustion engine cylinder. POD decomposes instantaneous flow fields (also called snapshots) into a series of orthonormal flow patterns (called POD modes) and the corresponding mode coefficients. The POD modes are rank-ordered by decreasing kinetic energy content, and the low-order, high-energy modes are interpreted as constituting the large-scale coherent flow structure that varies from engine cycle to engine cycle. Various POD-based analysis techniques have thus been proposed to characterize engine flow field CCV using these low-order modes. The validity of such POD-based analyses rests, as a matter of course, on the reliability of the underlying POD results (modes and coefficients). Yet a POD mode can be disproportionately skewed by a single outlier snapshot within a large data set, and an algorithm exists to define and identify such outliers. In this paper, the effects of a candidate outlier snapshot on the results of POD-based conditional averaging and quadruple POD analyses are examined for two sets of crank angle-resolved flow fields on the midtumble plane of an optical engine cylinder recorded by high-speed particle image velocimetry (PIV). The results with and without the candidate outlier are compared and contrasted. In the case of POD-based conditional averaging, the presence of the outlier scrambles the composition of snapshot subsets that define large-scale flow pattern variations, and thus substantially alters the coherent flow structures that are identified; for quadruple POD, the shape of coherent structures and the number of modes to define them are not significantly affected by the outlier.

Cascades of temperature and entropy fluctuations in compressible turbulence

Cascades of temperature and entropy fluctuations are studied by numerical simulations of stationary three-dimensional compressible turbulence with a heat source. The fluctuation spectra of velocity, compressible velocity component, density and pressure exhibit the $-5/3$ scaling in an inertial range. The strong acoustic equilibrium relation between spectra of the compressible velocity component and pressure is observed. The $-5/3$ scaling behaviour is also identified for the fluctuation spectra of temperature and entropy, with the Obukhov–Corrsin constants close to that of a passive scalar spectrum. It is shown by Kovasznay decomposition that the dynamics of the temperature field is dominated by the entropic mode. The average subgrid-scale (SGS) fluxes of temperature and entropy normalized by the total dissipation rates are close to 1 in the inertial range. The cascade of temperature is dominated by the compressible mode of the velocity field, indicating that the theory of a passive scalar in incompressible turbulence is not suitable to describe the inter-scale transfer of temperature in compressible turbulence. In contrast, the cascade of entropy is dominated by the solenoidal mode of the velocity field. The different behaviours of cascades of temperature and entropy are partly explained by the geometrical properties of SGS fluxes. Moreover, the different effects of local compressibility on the SGS fluxes of temperature and entropy are investigated by conditional averaging with respect to the filtered dilatation, demonstrating that the effect of compressibility on the cascade of temperature is much stronger than on the cascade of entropy.

Passive scalar dispersion in the near wake of a multi-scale array of rectangular cylinders

The near wakes of flows past single- and multi-scale arrays of bars are studied by means of planar laser induced fluorescence (PLIF) and particle image velocimetry (PIV). The aim of this research is to better understand dispersion of passive scalar downstream of the multi-scale turbulence generator. In particular, the focus is on plausible manifestations of the space-scale unfolding (SSU) mechanism, which is often considered in the literature as the reason for the enhancement of the turbulent scalar flux in flows past fractal grids (i.e. specific multi-scale turbulence generators). The analysis of qualitative and quantitative PLIF results, as well as the simultaneously acquired PIV results, confirms the appearance of a physical scenario resembling the SSU mechanism. Unlike the anticipation of the literature, however, this scenario applies to some extent also to the flow past the single-scale obstacle. Application of a triple decomposition technique (which splits the acquired fields into their means, a number of coherent fluctuations and their stochastic parts) and a conditional-averaging technique reveals that the SSU mechanism is active in the vicinity of an intersection point between two adjacent wakes and is driven almost exclusively by coherent fluctuations associated with the larger of the intersecting wakes. This suggests that the SSU mechanism is related to the coherent fluctuations embedded in the flow rather than to the fine-scale turbulence and its underlying integral length scale, as proposed in previous works.