Search results for: vorticity

Authors: Ning Chang, Zelong Yuan, Yunpeng Wang, Jianchun Wang

Abstract:

Large eddy simulation (LES) has been extensively used in the investigation of turbulence. LES calculates the grid-resolved large-scale motions and leaves small scales modeled by sublfilterscale (SFS) models. Among the existing SFS models, the deconvolution model has been used successfully in the LES of the engineering flows and geophysical flows. Despite the wide application of deconvolution models, the effects of subfilter scale dynamics and filter anisotropy on the accuracy of SFS modeling have not been investigated in depth. The results of LES are highly sensitive to the selection of filters and the anisotropy of the grid, which has been overlooked in previous research. In the current study, two critical aspects of LES are investigated. Firstly, we analyze the influence of sub-filter scale (SFS) dynamics on the accuracy of direct deconvolution models (DDM) at varying filter-to-grid ratios (FGR) in isotropic turbulence. An array of invertible filters are employed, encompassing Gaussian, Helmholtz I and II, Butterworth, Chebyshev I and II, Cauchy, Pao, and rapidly decaying filters. The significance of FGR becomes evident, as it acts as a pivotal factor in error control for precise SFS stress prediction. When FGR is set to 1, the DDM models cannot accurately reconstruct the SFS stress due to the insufficient resolution of SFS dynamics. Notably, prediction capabilities are enhanced at an FGR of 2, resulting in accurate SFS stress reconstruction, except for cases involving Helmholtz I and II filters. A remarkable precision close to 100% is achieved at an FGR of 4 for all DDM models. Additionally, the further exploration extends to the filter anisotropy to address its impact on the SFS dynamics and LES accuracy. By employing dynamic Smagorinsky model (DSM), dynamic mixed model (DMM), and direct deconvolution model (DDM) with the anisotropic filter, aspect ratios (AR) ranging from 1 to 16 in LES filters are evaluated. The findings highlight the DDM's proficiency in accurately predicting SFS stresses under highly anisotropic filtering conditions. High correlation coefficients exceeding 90% are observed in the a priori study for the DDM's reconstructed SFS stresses, surpassing those of the DSM and DMM models. However, these correlations tend to decrease as lter anisotropy increases. In the a posteriori studies, the DDM model consistently outperforms the DSM and DMM models across various turbulence statistics, encompassing velocity spectra, probability density functions related to vorticity, SFS energy flux, velocity increments, strain-rate tensors, and SFS stress. It is observed that as filter anisotropy intensify, the results of DSM and DMM become worse, while the DDM continues to deliver satisfactory results across all filter-anisotropy scenarios. The findings emphasize the DDM framework's potential as a valuable tool for advancing the development of sophisticated SFS models for LES of turbulence.

Keywords: deconvolution model, large eddy simulation, subfilter scale modeling, turbulence

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Authors: Frederick Ferguson, Dehua Feng, Yang Gao

Abstract:

No doubt, current CFD tools have a great many technical limitations, and active research is being done to overcome these limitations. Current areas of limitations include vortex-dominated flows, separated flows, and turbulent flows. In general, turbulent flows are unsteady solutions to the fluid dynamic equations, and instances of these solutions can be computed directly from the equations. One of the approaches commonly implemented is known as the ‘direct numerical simulation’, DNS. This approach requires a spatial grid that is fine enough to capture the smallest length scale of the turbulent fluid motion. This approach is called the ‘Kolmogorov scale’ model. It is of interest to note that the Kolmogorov scale model must be captured throughout the domain of interest and at a correspondingly small-time step. In typical problems of industrial interest, the ratio of the length scale of the domain to the Kolmogorov length scale is so great that the required grid set becomes prohibitively large. As a result, the available computational resources are usually inadequate for DNS related tasks. At this time in its development, DNS is not applicable to industrial problems. In this research, an attempt is made to develop a numerical technique that is capable of delivering DNS quality solutions at the scale required by the industry. To date, this technique has delivered preliminary results for both steady and unsteady, viscous and inviscid, compressible and incompressible, and for both high and low Reynolds number flow fields that are very accurate. Herein, it is proposed that the Integro-Differential Scheme (IDS) be applied to a set of vortex-shockwave interaction problems with the goal of investigating the nonstationary physics within the resulting interaction regions. In the proposed paper, the IDS formulation and its numerical error capability will be described. Further, the IDS will be used to solve the inviscid and viscous Burgers equation, with the goal of analyzing their solutions over a considerable length of time, thus demonstrating the unsteady capabilities of the IDS. Finally, the IDS will be used to solve a set of fluid dynamic problems related to flow that involves highly vortex interactions. Plans are to solve the following problems: the travelling wave and vortex problems over considerable lengths of time, the normal shockwave–vortex interaction problem for low supersonic conditions and the reflected oblique shock–vortex interaction problem. The IDS solutions obtained in each of these solutions will be explored further in efforts to determine the distributed density gradients and vorticity, as well as the Q-criterion. Parametric studies will be conducted to determine the effects of the Mach number on the intensity of vortex-shockwave interactions.

Keywords: vortex dominated flows, shockwave interactions, high Reynolds number, integro-differential scheme

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Authors: Alastair Hales, Xi Jiang, Siming Zhang

Abstract:

Numerical methods are used to generate vortices in a domain. Through considered design, two counter-rotating vortices may interact and effectively drive one another downstream. This phenomenon is comparable to the vortex interaction that occurs in a region immediately downstream from two counter-oscillating piezoelectric (PE) fan blades. PE fans are small blades clamped at one end and driven to oscillate at their first natural frequency by an extremely low powered actuator. In operation, the high oscillation amplitude and frequency generate sufficient blade tip speed through the surrounding air to create downstream air flow. PE fans are considered an ideal solution for low power hot spot cooling in a range of small electronic devices, but a single blade does not typically induce enough air flow to be considered a direct alternative to conventional air movers, such as axial fans. The development of face-to-face PE fan arrays containing multiple blades oscillating in counter-phase to one another is essential for expanding the range of potential PE fan applications regarding the cooling of power electronics. Even in an unoptimised state, these arrays are capable of moving air volumes comparable to axial fans with less than 50% of the power demand. Replicating the airflow generated by face-to-face PE fan arrays without including the actual blades in the model reduces the process’s computational demands and enhances the rate of innovation and development in the field. Vortices are generated at a defined inlet using a time-dependent velocity profile function, which pulsates the inlet air velocity magnitude. This induces vortex generation in the considered domain, and these vortices are shown to separate and propagate downstream in a regular manner. The generation and propagation of a single vortex are compared to an equivalent vortex generated from a PE fan blade in a previous experimental investigation. Vortex separation is found to be accurately replicated in the present numerical model. Additionally, the downstream trajectory of the vortices’ centres vary by just 10.5%, and size and strength of the vortices differ by a maximum of 10.6%. Through non-dimensionalisation, the numerical method is shown to be valid for PE fan blades with differing parameters to the specific case investigated. The thorough validation methods presented verify that the numerical model may be used to replicate vortex formation from an oscillating PE fans blade. An investigation is carried out to evaluate the effects of varying the distance between two PE fan blade, pitch. At small pitch, the vorticity in the domain is maximised, along with turbulence in the near vicinity of the inlet zones. It is proposed that face-to-face PE fan arrays, oscillating in counter-phase, should have a minimal pitch to optimally cool nearby heat sources. On the other hand, downstream airflow is maximised at a larger pitch, where the vortices can fully form and effectively drive one another downstream. As such, this should be implemented when bulk airflow generation is the desired result.

Keywords: piezoelectric fans, low energy cooling, vortex formation, computational fluid dynamics

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Authors: Timur S. Zaripov, Artur K. Gilfanov, Sergei S. Sazhin, Steven M. Begg, Morgan R. Heikal

Abstract:

The calculation of the concentration of inertial droplets in complex flows is encountered in the modelling of numerous engineering and environmental phenomena; for example, fuel droplets in internal combustion engines and airborne pollutant particles. The results of recent research, focused on the development of methods for calculating concentration and their implementation in the commercial CFD code, ANSYS Fluent, is presented here. The study is motivated by the investigation of the mixture preparation processes in internal combustion engines with direct injection of fuel sprays. Two methods are used in our analysis; the Fully Lagrangian method (also known as the Osiptsov method) and the Eulerian approach. The Osiptsov method predicts droplet concentrations along path lines by solving the equations for the components of the Jacobian of the Eulerian-Lagrangian transformation. This method significantly decreases the computational requirements as it does not require counting of large numbers of tracked droplets as in the case of the conventional Lagrangian approach. In the Eulerian approach the average droplet velocity is expressed as a function of the carrier phase velocity as an expansion over the droplet response time and transport equation can be solved in the Eulerian form. The advantage of the method is that droplet velocity can be found without solving additional partial differential equations for the droplet velocity field. The predictions from the two approaches were compared in the analysis of the problem of a dilute gas-droplet flow around an infinitely long, circular cylinder. The concentrations of inertial droplets, with Stokes numbers of 0.05, 0.1, 0.2, in steady-state and transient laminar flow conditions, were determined at various Reynolds numbers. In the steady-state case, flows with Reynolds numbers of 1, 10, and 100 were investigated. It has been shown that the results predicted using both methods are almost identical at small Reynolds and Stokes numbers. For larger values of these numbers (Stokes — 0.1, 0.2; Reynolds — 10, 100) the Eulerian approach predicted a wider spread in concentration in the perturbations caused by the cylinder that can be attributed to the averaged droplet velocity field. The transient droplet flow case was investigated for a Reynolds number of 200. Both methods predicted a high droplet concentration in the zones of high strain rate and low concentrations in zones of high vorticity. The maxima of droplet concentration predicted by the Osiptsov method was up to two orders of magnitude greater than that predicted by the Eulerian method; a significant variation for an approach widely used in engineering applications. Based on the results of these comparisons, the Osiptsov method has resulted in a more precise description of the local properties of the inertial droplet flow. The method has been applied to the analysis of the results of experimental observations of a liquid gasoline spray at representative fuel injection pressure conditions. The preliminary results show good qualitative agreement between the predictions of the model and experimental data.

Keywords: internal combustion engines, Eulerian approach, fully Lagrangian approach, gasoline fuel sprays, droplets and particle concentrations

Procedia PDF Downloads 229