Multiscale Turbulence Research Articles

Flow induced acoustic characteristics analysis of propulsion pump by indirect acoustic variable method and FEM

The acoustic characteristics of water-jet propulsion pumps present significant challenges, primarily due to the interaction between flow and high-speed rotating impellers wall. Notably, such complicated turbulence induced acoustic sources by brings great difficulty to identify and control. This paper firstly analyzes the flow characteristics of the propulsion pump by using the scalable Hybrid RANS-LES model. Subsequently, an indirect acoustics variable method based on Lamb vector divergence is proposed to characterize acoustic sources caused by multiscale turbulence. The effectiveness and advantages of indirect acoustics variable method are evaluated through comparison with the acoustic finite element method and experimental results. The proposed indirect acoustics variable method demonstrates the ability to accurately quantify the contribution of turbulent flow to acoustic sources. Furthermore, the intensity of acoustic sources in different flow regions can be obtained through volume integrals, which can serve as optimization parameters in the initial hydraulic design of propulsion pumps. This study provides a novel approach for predicting turbulent noise and offers guidance for the design of low-noise propulsion systems.

Impurity convection reversal caused by edge localized turbulence for generating a stationary edge radiative layer in the HL-2A tokamak

Abstract Effect of impurity on edge turbulence was investigated on the HL-2A tokamak by using Neon supersonic molecular beam injection (SMBI). For the first time, a stationary radiative layer accompanied by edge localized turbulence lasting more than 100ms is observed at the edge region ρ=0.7-0.9. This duration is much longer than the SMBI pulse length (1.2ms), indicating that the impurity diffusion is on the whole cancelled out by the impurity convection without spreading of the localized turbulence during this period. This implies that the impurity convection is reversed from positive to negative impurity density gradient region. This reversal could be explained by the parallel impurity compression mechanism. The observed turbulence is a broadband electrostatic turbulence (25-70 kHz) propagating in the electron diamagnetic drift direction with normalized poloidal wavenumber of 0.1≤ kθρs≤0.4. It has been found that the excitation of the edge localized turbulence strongly depends on the local collisionality. This feature is qualitatively predicted by the spectral multiscale gyrokinetic turbulence simulation, which suggests that the turbulence could be a dissipative trapped electron mode (DTEM). This experiment demonstrates that mutual interaction between externally injected impurity ions and edge turbulence can generate a stationary edge radiative layer and avoid impurity core accumulation. These results could provide a potential approach for the formation of a stable impurity radiative layer by impurity injection in tokamaks.

Overview of multiscale turbulence studies covering ion-to-electron scales in magnetically confined fusion plasma

Turbulent transport in magnetically confined fusion plasma has conventionally been analyzed at the ion gyroradius scale based on the microturbulence theory. However, ion-scale turbulence analysis sometimes fails to predict the turbulent transport flux observed experimentally. Microturbulence at the electron gyroradius scale and cross-scale interactions between disparate-scale turbulences are possible mechanisms to resolve this issue. This overview discusses the recent progress in multiscale turbulence studies and presents future perspectives from recent experimental, theoretical, and numerical investigations. The following aspects are highlighted: (1) the importance of electron-scale effects in experiments, (2) the physical mechanisms of cross-scale interactions, (3) modeling electron-scale effects in quasilinear transport models, and (4) the impacts of cross-scale interactions on burning plasmas. Understanding multiscale turbulence is necessary to improve performance prediction and explore optimal operations for future burning plasmas.

A resolution-enhanced seventh-order weighted essentially non-oscillatory scheme based on non-polynomial reconstructions for solving hyperbolic conservation laws

In high-resolution numerical simulations of flows characterized by both multiscale turbulence and discontinuities, the conflict between spectral characteristics and stability becomes increasingly pronounced as the order of accuracy improves. To address this challenge, we proposed a novel seventh-order weighted essentially non-oscillatory scheme (WENO-K7). This scheme utilizes non-polynomial reconstructions by incorporating kriging interpolation and Gaussian exponential function. Then, a hyper-parameter associated with the Gaussian function is adaptively optimized to achieve higher convergence orders on sub-stencils, reducing numerical errors on global stencils. Additionally, a criterion based on monotone interpolations is devised to automatically identify problematic hyper-parameters, facilitating the transition from non-polynomial to polynomial reconstructions near discontinuities and preserving the essentially non-oscillatory property. Compared to the conventional seventh-order WENO-Z7 scheme, WENO-K7 scheme exhibits smaller computational error and reduced numerical dissipation in smooth regions while maintaining non-oscillatory and high-resolution capabilities around discontinuities. Results from various one- and two-dimensional benchmark cases demonstrate that the proposed WENO-K7 scheme outperforms the widely used WENO-Z7 scheme with only a 12% increase in computational cost. Moreover, the WENO-K7 scheme shares the same sub-stencils as the WENO-Z7 scheme, making it easily applicable to other variants of seventh-order WENO schemes and enhancing their spectral characteristics.

Weighted compact nonlinear scheme based on smooth scale separation for self-adaptive turbulence eddy simulations

Multiscale compressible turbulent flow is widely present in the aerospace field, and the co-existence of shock wave discontinuities and multi-scale turbulence in the flow field poses significant challenges for high-fidelity numerical simulation. To design high-order nonlinear scheme to improve the accuracy of complex turbulence simulation with stable shock wave capture, a weighted compact nonlinear scheme – targeted essentially non-oscillatory (WCNS-T) scheme is developed based on targeted essentially non-oscillatory scheme within the WCNS framework. Also, an improved variant of WCNS-T with smooth scale separation (denoted as WCNS-ST) is proposed from the perspective of both numerical convergence and accuracy. The numerical properties of different nonlinear weights are discussed in classical numerical problems, including spectral properties analysis, and two-dimensional Riemann problem. Then, the newly developed WCNS-ST scheme based on smooth scale separation was used to combine a unified turbulence model called Self-Adaptive Turbulence Eddy Simulation (SATES), which is applied to simulate subsonic flow past a 30P30N airfoil and supersonic base flow. The good convergence and numerical results are obtained using the newly developed WCNS-ST scheme, whereas WCNS-T shows worse convergence. In addition, adaptive dissipation control is further introduced for the WCNS-ST scheme, and the new variant (denoted as WCNS-STA) still shows good residual convergence and predicts more accurate results due to low numerical dissipation. The above results indicate that the proposed smooth scale separation and its WCNS-STA scheme have a good performance in SATES simulations of multiscale flow problems, making it more potential for complex engineering applications.

Projection-based reduced-order modelling of time-periodic problems, with application to flow past flapping hydrofoils

Simulating forced time-periodic flows in industrial applications presents significant computational challenges, partly due to the need to overcome costly transients before achieving time-periodicity. Reduced-order modelling emerges as a promising method to speed-up computations. We extend upon the work of Lotz et al. (2024) where a time-periodic space–time model is introduced. We present a time-periodic reduced-order model that directly finds the time-periodic solution without requiring extensive time integration. The reduced-order model gives a reduction in variables in both space and time. Our approach involves a POD-Galerkin reduced-order model based on a time-periodic full-order model that employs isogeometric analysis, residual-based variational multiscale turbulence modelling and weak boundary conditions. The projection-based reduced-order model inherits these features. We evaluate the reduced-order model with numerical experiments on moving hydrofoils. The motion is known a priori and we restrict ourselves to two spatial dimensions. In these experiments we vary the Strouhal and Reynolds numbers, and the motion profile respectively. Reduced-order model solutions agree well with those of the full-order model. The errors over the entire time period of thrust and lift forces are less than 0.2%. This includes complex scenarios such as the transition from drag to thrust production with increasing Strouhal number. Our time-periodic reduced-order model offers speed-ups ranging from O(102) to O(103) compared to the full-order model, depending upon the basis size. This makes it an appealing solution for prescribed time-periodic problems, with potential for additional speedup through nonlinear reduction techniques such as hyper-reduction.

Quasi-perpendicular shocks of galaxy clusters in hybrid kinetic simulations

Context. Cosmic ray acceleration in galaxy clusters is still an ongoing puzzle, with relativistic electrons forming radio relics at merger shocks and emitting synchrotron radiation. These shocks are also potential sources of ultra-high-energy cosmic rays, gamma rays, and neutrinos. Our recent work focuses on electron acceleration at low Mach number merger shocks in the hot intracluster medium which is characterized by high plasma beta. Using particle-in-cell (PIC) simulations, we previously showed that electrons are energized through the stochastic shock-drift acceleration process, which is facilitated by multi-scale turbulence, including ion-scale shock surface rippling. For the present work, we performed hybrid-kinetic simulations in a range of various quasi-perpendicular foreshock conditions, including plasma beta, magnetic obliquity, and the shock Mach number. Aims. We study the ion kinetic physics, which is responsible for the shock structure and wave turbulence, that in turn affects the particle acceleration processes. We cover the spatial and temporal scales, which allow the development of large-scale ion turbulence modes in the system. Methods. We applied a recently developed generalized fluid-particle hybrid numerical code that can combine fluid modeling for both electrons and ions with an arbitrary number of kinetic species. We limited this model to a standard hybrid simulation configuration with kinetic ions and fluid electrons. The model utilizes the exact form of the generalized Ohm’s law, allowing for an arbitrary choice of mass and energy densities, as well as the charge-to-mass ratio of the kinetic species. Results. We show that the properties of ion-driven multi-scale magnetic turbulence in merger shocks are in agreement with the ion structures observed in PIC simulations. In typical shocks with the sonic Mach number Ms = 3, the magnetic structures and shock front density ripples grow and saturate at wavelengths reaching approximately four ion Larmor radii. Only shocks with Ms ≳ 2.3 develop ripples. At very weak shocks with Ms ≲ 2.3, weak turbulence is formed downstream of the shock. We observed a moderate dependence of the strength of magnetic field fluctuations on the quasi-perpendicular magnetic field obliquity. However, as the field obliquity decreases, the shock front ripples exhibit longer wavelengths. Finally, we note that the steady-state structure of Ms = 3 shocks in high-beta plasmas shows evidence that there is little difference between 2D and 3D simulations. The turbulence near the shock front seems to be a 2D-like structure in 3D simulations.

Multi-scale aware turbulence network for underwater object recognition

Underwater imagery is subject to distortion, and the presence of turbulence in the fluid medium poses difficulties in accurately discerning objects. To tackle these challenges pertaining to feature extraction, this research paper presents a novel approach called the multi-scale aware turbulence network (MATNet) method for underwater object identification. More specifically, the paper introduces a module known as the multi-scale feature extraction pyramid network module, which incorporates dense linking strategies and position learning strategies to preprocess object contour features and texture features. This module facilitates the efficient extraction of multi-scale features, thereby enhancing the effectiveness of the identification process. Following that, the extracted features undergo refinement through comparison with positive and negative samples. Ultimately, the study introduces multi-scale object recognition techniques and establishes a multi-scale object recognition network for the precise identification of underwater objects, utilizing the enhanced multi-scale features. This process entails rectifying the distorted image and subsequently recognizing the rectified object. Extensive experiments conducted on an underwater distorted image enhancement dataset demonstrate that the proposed method surpasses state-of-the-art approaches in both qualitative and quantitative evaluations.

Flow-shear destabilization of multiscale electron turbulence

The impact of sheared E×B flow on multiscale turbulence is studied with nonlinear gyrokinetic simulations. Simulations are based on DIII-D-like, high-confinement mode (H-mode) pedestal parameters in the regime of low ion temperature gradient drive, where there is a broad spectrum of electron temperature gradient (ETG)-driven turbulence. It is found that E×B shear can have a significant effect on ETG-driven electron transport, with an unexpected transition from a turbulence stabilization regime at moderate to large shearing rates γ E to a novel turbulence destabilization regime at low levels of γ E . In the turbulence stabilization regime, the electron energy flux decreases monotonically with γ E , even when γ E is small compared to electron mode growth rates. The stabilizing effect comes dominantly from the electron, not ion, gyrokinetic equation. In the novel destabilization regime, reduction of zonal energy results from the interaction of γ E -modulated nonlinear drive in the zonal ion gyrokinetic equation, increasing the electron transport over a broad range of shearing rates. Neither of these effects have been observed in previous electron-scale simulations.

Multiscale Turbulence Characteristics of Gas–Liquid Pressure Fluctuations in an Industrial Quatro Static Mixer

Multiscale Turbulence Characteristics of Gas–Liquid Pressure Fluctuations in an Industrial Quatro Static Mixer

Experimental validation on a calibration position of a hot-wire anemometer for measuring multi-scale grid-generated turbulence

This study aims to experimentally examine conditions that should be satisfied by a calibration position of a constant-temperature hot-wire anemometer. Specifically, this study addresses an appropriate measurement point when this calibration is performed downstream of a turbulent field generated by a multi-scale turbulence grid. The hot-wire measurement in this study is based on an I-type probe with a standard 5 μm tungsten wire. The hot-wire anemometer in this study is small and can be attached to a probe support. In this study, uncertainty in the calibration curve of the hot-wire measurement is first checked. Here, Pitot tube velocimetry to obtain the calibration curves is carried out using two bell-type micro-differential pressure gauges. Then, the characteristics of the obtained velocity fluctuations and turbulence will be examined. Based on this relative velocity fluctuation RMS value, the effects of the obtained streamwise velocity fluctuation on output voltage are obtained by asymptotically expanding a calibration curve. Using these results, the intensity of the free-stream turbulence, which has a negligible effect on output voltage giving a calibration curve, is clarified.

Energy conservation uncertainly due to the use of an implicit time integration method clarified by a multiplexed TGV inviscid flow

This study attempts to elucidate the conservation errors induced by the implicit time integration method within a multiscale flow. Using the multiplexed Taylor analytical solution as the initial field, three distinct multiscale turbulence fields were formulated, each characterised by different wavenumber attributes. A two-dimensional inviscid flow field, replicated in a computational domain with a side of 2π and subject to periodic boundary conditions, was used to illuminate kinetic energy conservation errors. The implicit time integration method - specifically the second-order accurate Crank-Nicolson method - was compared with explicit methods, such as the second-order accurate Adams-Bashforth and third-order accurate Runge-Kutta methods. The study also examines the differences between the analytical Taylor solution and a random flow field, particularly in their satisfaction of the Navier-Stokes equations and wavenumber composition, while highlighting the need for preliminary analysis for random flow fields prior to validation calculations.

Multiscaled inviscid Taylor-Green vortex flow for examining energy conservation error in incompressible flows

This study investigates kinetic energy conservation errors in incompressible flows using multiplexed inviscid Taylor-Green vortices. Fourth-order precision Runge-Kutta methods, specifically five- and six-step methods, were employed and an inviscid two-dimensional periodic flow field was used as a test case. This method allows the energy conservation error to be suppressed to a very low level. Recent previous studies have dealt with turbulence generation using a multi-scale turbulence grid. In this study, the Taylor-Green vortex of the analytical solution is multiplexed to generate a flow field with a number of wavenumbers. Visualisation results of the initial field and the energy distribution over time were obtained. It was observed that the errors in the time evolution of the fluid energy were extremely small, and that the errors actually increased with time. However, the influence of the time step range was limited and the analytical and numerical solutions were in general agreement. As a result, it was confirmed that the inviscid Taylor-Green vortex is effective in examining the energy conservation error for incompressible flows.

Comparative Testing the Uncertainty of A/D Converters in A Hot-Wire Anemometer Measurement Using Grid-Generated Turbulence

This study investigates the uncertainty of the A/D converter when measuring multi-scale turbulence fluctuations using a hot-wire anemometer. The flow is generated in a low-speed wind tunnel, the turbulence is generated by a turbulence grid and the fluctuations are measured. A compact hot-wire anemometer was used and a high accuracy A/D converter was introduced for the measurements. Methods to minimise the influence of noise were also incorporated and measurements were carried out in two situations, one with and one without turbulence. The experimental results showed that measurements under a specific condition (Case 1 in this study) had the sufficienty reproducibility of turbulence fluctuations and the least effect of noise. The results showed that the high frequency characteristics of the turbulence could also be accurately measured under this condition. In conclusion, it is clear that the choice of a suitable A/D converter and the optimisation of the measurement environment are critical for turbulence measurements with a hot-wire anemometer.

Energy transport analysis of NSTX plasmas with the TGLF turbulent and NEO neoclassical transport models

This work presents a study of plasma transport at low aspect ratio on the National Spherical Torus Experiment tokamak, where the turbulent and neoclassical energy fluxes calculated by the quasilinear Trapped Gyro Landau Fluid (TGLF) model and the multi species drift-kinetic Neoclassical solver (NEO) are validated against experimental data. The turbulent energy transport of two plasma discharges, one in the L-mode confinement regime and another in the H-mode regime, is dominated by electrostatic drift-wave instabilities, while the ion heat transport has a significant neoclassical contribution. The data analysis workflow is described in detail to understand how the variations of mapping and fitting of experimental data affect the power balance solution and subsequent flux-matching plasma profile predictions with the TGYRO solver. On average, the predicted plasma profiles are consistent with experimental data. However, the solutions are sensitive to various input parameters, including boundary conditions, and the electron-ion coupling. Linear gyrokinetic stability analysis demonstrates close agreement of the real frequencies of unstable modes between TGLF and CGYRO gyrokinetic simulations, but higher growth rates are predicted by TGLF, especially for the H-mode case. Estimates of the low-k modes’ contributions to the total flux are consistent with linear stability analysis and the E × B suppression of turbulence in TGLF simulations with the SAT1 saturation model, while the SAT2 saturation model over-predicts the low-k modes’ contribution in the H-mode case. Moreover, the results with SAT1 model are consistent with power balance analysis, which indicates only neoclassical ion energy fluxes inside ρ < 0.4 in the L-mode case and ρ⩽0.7 in the H-mode case. The presence of multi-scale turbulence and ion-scale driven zonal flow mixing effects are also observed in TGLF scans of the electron turbulent heat flux over a range of temperature gradients and the electron-ion temperature ratio, which could explain the strong model sensitivity to variations of input parameters.

Stabilization of trapped electron mode through effective diffusion in electron temperature gradient turbulence

Multi-scale gyrokinetic theory and simulations of a toroidal magnetized plasma have revealed the existence of cross-scale interactions of the trapped electron mode (TEM) and the electron temperature gradient (ETG) turbulence. Reduction of the TEM instability growth rate in the ETG turbulence is clearly identified, and is well represented in the form of effective diffusion. A theoretical model based on the stochastic forcing by the ETG turbulence well describes the turbulent diffusion coefficient observed in multi-scale turbulence simulations.

Spectral transition of multiscale turbulence in the tokamak pedestal

The transition in the turbulence spectrum from ion-scale dominated regimes to multiscale transport regimes that couple ion and electron scales is studied with gyrokinetic simulations of turbulent transport. The simulations are based on DIII-D high-confinement mode (H-mode) plasma parameters in the tokamak pedestal. The transition is initiated by varying the ion temperature gradient. To our knowledge, no full multiscale simulations of pedestal-like transport have been done previously. The experimental parameters lie in a bifurcation region between the two regimes. At long wavelengths, a complex, ion-direction hybrid mode is the dominant linearly unstable drift wave, while an electron temperature gradient-driven mode is unstable at short wavelengths. In the transition from the multiscale branch to the ion-scale branch, the magnitude of the ion-scale poloidal wavenumber spectrum of the nonlinear turbulent energy flux increases and the magnitude of the high-wavenumber spectrum decreases. The decrease in the electron-scale transport is due to nonlinear mixing with ion-scale fluctuations and the ion-scale-driven zonal flows. A shift in the total energy associated with the fluctuating electrostatic potential intensity from dominantly drift kinetic energy in the multiscale regime to dominantly potential intensity in the ion-scale regime is well-correlated with the trend in the total energy flux.

Energy redistribution analysis of multi-scale turbulence in centrifugal pump

HIGHLIGHTS • Effectiveness of vice blades flow control method. • Improvement mechanism of flow control method on centrifugal pump. • Energy redistribution of multi-scale turbulence by flow control method. • Design strategy for high-performance centrifugal pump. The demand for the high-performance centrifugal pumps has grown considerably in order to address various working conditions and application scenarios. Here, a high-performance centrifugal pump capable of great hydraulic and anti-cavitation performance, and low-pressure pulsation and vibration, is realized by adding drainage vice blade to the conventional blade type. The multi-scale turbulence in centrifugal pumps is characterized by the Hybrid RANS/LES method, then the energy distributions are obtained by the proper orthogonal decomposition (POD) method. The experimental methods are employed to study the pressure pulsation and vibration characteristics. The new-type of blades can reconstruct the energy of multi-scale turbulence in centrifugal pump by concentrating the energy on low-frequency large-scale flow structures, while reducing the energy of high-frequency small-scale flow structures. A higher energy of large-scale flow structures can enhance the energy transportation and hydraulic performance in centrifugal pump. The small-scale flow structures with lower energy can suppress high-frequency excitation in flow to avoid the hydraulic resonance, which is essential to improve the dynamic characteristics of the centrifugal pumps. We propose a flow control method that can reconstruct the energy distribution of multi-scale turbulence which can greatly improve its overall performance, suggesting a broad range of promising applications.

Validation study of a Spatially-Averaged Two-Fluid Model for heat transport in gas-particle flows

We validate a multi-scale turbulence model for the thermal energy estimation in coarse-grid simulations of moderately dense gas-particle flows. The model is based on spatially-averaging the Two-Fluid Model balance equations including the thermal energy balance equation of both phases. We found, that the drift temperature is a valid measure for the heat transfer reduction due to heterogeneous particle clusters. Furthermore, we propose the dynamic estimation of the drift temperature through the application of test-filters and the solution of transport equations for the variances of the phase temperatures and the solid volume fraction. Closure models for the Reynolds stress contributions are based on single-phase Large-Eddy Simulation models, such as gradient assumptions. In this study, we consider different test-cases including Geldart type A and type B particles in moderately dense regimes with domain averaged volume fractions ranging from 0.05 to 0.25. The operating conditions include unbounded sedimentation under gravity, as well as a turbulent-sluggish fluidization. In all cases, we discuss the influence of the meso-scale particle clusters on the macro-scale temperature distributions through the individual contributions of the unresolved terms in coarse-grid simulations. Thereby, we find that the dynamic estimation of the drift temperature leads to accurate results for the influence of local heat sinks on the global temperature difference decay between the phases and that the jump-response of a fluidized bed to an elevated gas-inflow temperature is correctly captured by the proposed multi-phase turbulence model. Furthermore, the importance of the correct estimation of the hydrodynamics for a correct prediction of the thermodynamics is highlighted.

The state space and travelling-wave solutions in two-scale wall-bounded turbulence

The computation of invariant solutions and the visualisation of the associated state space have played a key role in the understanding of transition and the self-sustaining process in wall-bounded shear flows. In this study, an extension of this approach is sought for a turbulent flow which explicitly exhibits multi-scale behaviour. The minimal unit of multi-scale near-wall turbulence, which resolves two adjacent spanwise integral length scales of motion, is considered using a shear stress-driven flow model (Doohan, Willis &amp; Hwang J. Fluid Mech., vol. 913, 2021, A8). The edge state, 26 travelling waves and two periodic orbits are computed, which represent either the large- or small-scale self-sustaining processes. Given that the spanwise length scales are not widely separated here, it could be envisaged that turbulent trajectories visit these solutions in the state space. Considering the intra- and inter-scale dynamics of the flow, numerous phase portraits are examined, but the turbulent state is not found to approach any of these solutions. A detailed analysis reveals that this is due to the lack of scale interaction processes captured by the invariant solutions, including the mean–fluctuation interaction, the energy cascade in the streamwise wavenumber space and the cascade-driven energy production discovered recently. There is a single solution that resembles turbulence much more than the others, which captures two-scale energetics and a scale interaction process involving energy feeding from small to large spanwise scales through the subharmonic sinuous streak instability mode. Based on these observations, it is conjectured that the state space view of turbulent trajectories wandering between solutions would need suitable refinement to model multi-scale turbulence, when each solution does not represent multi-scale processes of turbulence. In particular, invariant solutions that are inherently multi-scale would be required.