6 results
Finite-element analysis case retrieval based on an ontology semantic tree
- Xuesong Xu, Zhenbo Cheng, Gang Xiao, Yuanming Zhang, Haoxin Zhang, Hangcheng Meng
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The widespread use of finite-element analysis (FEA) in industry has led to a large accumulation of cases. Leveraging past FEA cases can improve accuracy and efficiency in analyzing new complex tasks. However, current engineering case retrieval methods struggle to measure semantic similarity between FEA cases. Therefore, this article proposed a method for measuring the similarity of FEA cases based on ontology semantic trees. FEA tasks are used as indexes for FEA cases, and an FEA case ontology is constructed. By using named entity recognition technology, pivotal entities are extracted from FEA tasks, enabling the instantiation of the FEA case ontology and the creation of a structured representation for FEA cases. Then, a multitree algorithm is used to calculate the semantic similarity of FEA cases. Finally, the correctness of this method was confirmed through an FEA case retrieval experiment on a pressure vessel. The experimental results clearly showed that the approach outlined in this article aligns more closely with expert ratings, providing strong validation for its effectiveness.
Spatial–temporal transformation for primary and secondary instabilities in weakly non-parallel shear flows
- Jiakuan Xu, Jianxin Liu, Zhongyu Zhang, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 959 / 25 March 2023
- Published online by Cambridge University Press:
- 17 March 2023, A21
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When studying instability of weakly non-parallel flows, it is often desirable to convert temporal growth rates of unstable modes, which can readily be computed, to physically more relevant spatial growth rates. This has been performed using the well-known Gaster's transformation for primary instability and Herbert's transformation for the secondary instability of a saturated primary mode. The issue of temporal–spatial transformation is revisited in the present paper to clarify/rectify the ambiguity/misunderstanding that appears to exist in the literature. A temporal mode and its spatial counterpart may be related by sharing either the real frequency or wavenumber, and the respective transformations between their growth rates are obtained by a simpler consistent derivation than the original one. These transformations, which consist of first- and second-order versions, are valid under conditions less restrictive than those for Gaster's and Herbert's transformations, and reduce to the latter under additional conditions, which are not always satisfied in practice. The transformations are applied to inviscid Rayleigh instability of a mixing layer and a jet, secondary instability of a streaky flow as well as general detuned secondary instability (including subharmonic and fundamental resonances) of primary Mack modes in a supersonic boundary layer. Comparison of the transformed growth rates with the directly calculated spatial growth rates shows that the transformations derived in this paper outperform Gaster's and Herbert's transformations consistently. The first-order transformation is accurate when the growth rates are small or moderate, while the second-order transformations are sufficiently accurate across the entire instability bands, and thus stand as a useful tool for obtaining spatial instability characteristics via temporal stability analysis.
Elevated low-frequency free-stream vortical disturbances eliminate boundary-layer separation
- Dongdong Xu, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 920 / 10 August 2021
- Published online by Cambridge University Press:
- 08 June 2021, A14
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A steady two-dimensional boundary layer subject to an adverse streamwise pressure gradient usually separates. In this paper, we investigate how free-stream vortical disturbances (FSVD) of moderate level prevent the separation in such a boundary layer over a plate or concave wall. The focus is on physically realisable FSVD with sufficiently long wavelength (low frequency) as they have the most significant impact on the boundary layer. The FSVD intensity $\epsilon$ is taken to be small but nevertheless strong enough that the streaks or Görtler vortices generated in the boundary layer are fully nonlinear and can alter the mean-flow profile by an order-one amount. The excitation and evolution of streaks and Görtler vortices are governed by the nonlinear unsteady boundary-region equations supplemented by appropriate initial (upstream) and boundary (far-field) conditions, which describe appropriately the action of FSVD on the boundary layer. The flow variables are decomposed into two parts: the steady spanwise-averaged and the unsteady or spanwise-varying components. These two parts are coupled and are computed simultaneously. Numerical results show that the separation is eliminated when the FSVD level exceeds a critical intensity $\epsilon _c$. It is inferred that the strong nonlinear mean-flow distortion associated with the nonlinear streaks or Görtler vortices prevents the separation. The critical FSVD intensity $\epsilon _c$ depends on the streamwise curvature, the pressure gradient and the frequency of FSVD. The value of $\epsilon _c$ decreases significantly with the Görtler number, indicating that concave curvature inhibits separation. A higher $\epsilon _c$ is required to prevent the separation in the case of stronger adverse pressure gradient. Interestingly, unsteady FSVD with low frequencies are found to be more effective than steady ones in suppressing the separation.
Görtler vortices and streaks in boundary layer subject to pressure gradient: excitation by free stream vortical disturbances, nonlinear evolution and secondary instability
- Dongdong Xu, Jianxin Liu, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 900 / 10 October 2020
- Published online by Cambridge University Press:
- 06 August 2020, A15
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This paper investigates streaks and Görtler vortices in a boundary layer over a flat or concave wall in a contracting or expanding stream, which provides a favourable or adverse pressure gradient, respectively. We consider first the excitation of streaks and Görtler vortices by free stream vortical disturbances (FSVD), and their nonlinear evolution. The focus is on FSVD with sufficiently long wavelength, to which the boundary layer is most receptive. The formulation is directed at the general case where the Görtler number $G_{\Lambda }$ (based on the spanwise length scale $\Lambda$ of FSVD) is of order one, and the FSVD is strong enough that the induced vortices acquire an $O(1)$ streamwise velocity in the region where the boundary layer thickness becomes comparable with $\Lambda,$ and the vortices are governed by the nonlinear boundary region equations (NBRE). An important effect of a pressure gradient is that the oncoming FSVD are distorted by the non-uniform inviscid flow outside the boundary layer through convection and stretching. This process is accounted for by using the rapid distortion theory. The impact of the distorting FSVD is analysed to provide the appropriate initial and boundary conditions, which form, along with the NBRE, the appropriate initial boundary value problem describing the excitation and nonlinear evolution of the vortices. Numerical results show that an adverse/favourable pressure gradient cause the Görtler vortices to saturate earlier/later, but at a lower/higher amplitude than that in the case of zero-pressure-gradient. On the other hand, for the same pressure gradient and at low levels of FSVD, the vortices saturate earlier and at a higher amplitude as $G_{\Lambda }$ increases. Raising FSVD intensity reduces the effects of the pressure gradient and curvature. At a high FSVD level of 14 %, the curvature has no impact on the vortices, while the pressure gradient only influences the saturation intensity. The unsteadiness of FSVD is found to reduce the boundary layer response significantly at FSVD levels, but that effect weakens as the turbulence level increases. A secondary instability analysis of the vortices is performed for moderate adverse and favourable pressure gradients. Three families of unstable modes have been identified, which may become dominant depending on the frequency and streamwise location. In the presence of an adverse pressure gradient, the secondary instability occurs earlier, but the unstable modes appear in a smaller band of frequency, and have smaller growth rates. The opposite is true for a favourable pressure gradient. The present theoretical framework, which accounts for the influence of the curvature, turbulence level and pressure gradient, allows for a detailed and integrated description of the key transition processes, and represents a useful step towards predicting the pretransitional flow and transition itself of the boundary layer over a blade in turbomachinery.
Nonlinear evolution and secondary instability of steady and unsteady Görtler vortices induced by free-stream vortical disturbances
- Dongdong Xu, Yongming Zhang, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 829 / 25 October 2017
- Published online by Cambridge University Press:
- 25 September 2017, pp. 681-730
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We study the nonlinear development and secondary instability of steady and unsteady Görtler vortices which are excited by free-stream vortical disturbances (FSVD) in a boundary layer over a concave wall. The focus is on low-frequency (long-wavelength) components of FSVD, to which the boundary layer is most receptive. For simplification, FSVD are modelled by a pair of oblique modes with opposite spanwise wavenumbers $\pm k_{3}$, and their intensity is strong enough (but still of low level) that the excitation and evolution of Görtler vortices are nonlinear. For the general case that the Görtler number $G_{\unicode[STIX]{x1D6EC}}$ (based on the spanwise wavelength $\unicode[STIX]{x1D6EC}$ of the disturbances) is $O(1)$, the formation and evolution of Görtler vortices are governed by the nonlinear unsteady boundary-region equations, supplemented by appropriate upstream and far-field boundary conditions, which characterize the impact of FSVD on the boundary layer. This initial-boundary-value problem is solved numerically. FSVD excite steady and unsteady Görtler vortices, which undergo non-modal growth, modal growth and nonlinear saturation for FSVD of moderate intensity. However, for sufficiently strong FSVD the modal stage is bypassed. Nonlinear interactions cause Görtler vortices to saturate, with the saturated amplitude being independent of FSVD intensity when $G_{\unicode[STIX]{x1D6EC}}\neq 0$. The predicted modified mean-flow profiles and structure of Görtler vortices are in excellent agreement with several steady experimental measurements. As the frequency increases, the nonlinearly generated harmonic component $(0,2)$ (which has zero frequency and wavenumber $2k_{3}$) becomes larger, and as a result the Görtler vortices appear almost steady. The secondary instability analysis indicates that Görtler vortices become inviscidly unstable in the presence of FSVD with a high enough intensity. Three types of inviscid unstable modes, referred to as sinuous (odd) modes I, II and varicose (even) modes I, are identified, and their relevance is delineated. The characteristics of dominant unstable modes, including their frequency ranges and eigenfunctions, are in good agreement with experiments. The secondary instability is intermittent when FSVD are unsteady and of low frequency. However, the intermittence diminishes as the frequency increases. The present theoretical framework, which allows for a detailed and integrated description of the key transition processes, from generation, through linear and nonlinear evolution, to the onset of secondary instability, represents a useful step towards predicting the pre-transitional flow and transition itself of the boundary layer over a blade in turbomachinery.
The behaviour of Tollmien–Schlichting waves undergoing small-scale localised distortions
- Hui Xu, Spencer J. Sherwin, Philip Hall, Xuesong Wu
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- Journal:
- Journal of Fluid Mechanics / Volume 792 / 10 April 2016
- Published online by Cambridge University Press:
- 03 March 2016, pp. 499-525
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This paper is concerned with the behaviour of Tollmien–Schlichting (TS) waves experiencing small localised distortions within an incompressible boundary layer developing over a flat plate. In particular, the distortion is produced by an isolated roughness element located at $\mathit{Re}_{x_{c}}=440\,000$. We considered the amplification of an incoming TS wave governed by the two-dimensional linearised Navier–Stokes equations, where the base flow is obtained from the two-dimensional nonlinear Navier–Stokes equations. We compare these solutions with asymptotic analyses which assume a linearised triple-deck theory for the base flow and determine the validity of this theory in terms of the height of the small-scale humps/indentations taken into account. The height of the humps/indentations is denoted by $h$, which is considered to be less than or equal to $x_{c}\mathit{Re}_{x_{c}}^{-5/8}$ (corresponding to $h/{\it\delta}_{99}<6\,\%$ for our choice of $\mathit{Re}_{x_{c}}$). The rescaled width $\hat{d}~(\equiv d/(x_{c}\mathit{Re}_{x_{c}}^{-3/8}))$ of the distortion is of order $\mathit{O}(1)$ and the width $d$ is shorter than the TS wavelength (${\it\lambda}_{TS}=11.3{\it\delta}_{99}$). We observe that, for distortions which are smaller than 0.1 of the inner deck height ($h/{\it\delta}_{99}<0.4\,\%$), the numerical simulations confirm the asymptotic theory in the vicinity of the distortion. For larger distortions which are still within the inner deck ($0.4\,\%<h/{\it\delta}_{99}<5.5\,\%$) and where the flow is still attached, the numerical solutions show that both humps and indentations are destabilising and deviate from the linear theory even in the vicinity of the distortion. We numerically determine the transmission coefficient which provides the relative amplification of the TS wave over the distortion as compared to the flat plate. We observe that for small distortions, $h/{\it\delta}_{99}<5.5\,\%$, where the width of the distortion is of the order of the boundary layer, a maximum amplification of only 2 % is achieved. This amplification can however be increased as the width of the distortion is increased or if multiple distortions are present. Increasing the height of the distortion so that the flow separates ($7.2\,\%<h/{\it\delta}_{99}<12.8\,\%$) leads to a substantial increase in the transmission coefficient of the hump up to 350 %.