Normal Velocity Field Research Articles

Adaptive restoration and reconstruction of incomplete flow fields based on unsupervised learning

Due to experimental limitations and data transmission constraints, we often encounter situations where we can only obtain incomplete flow field data. However, even with incomplete data, we can still extract valuable information about the main structural characteristics of the flow field. In this study, we propose a novel unsupervised learning reconstruction method to restore the incomplete flow field data. Our method comprises several key steps: First, based on the temporal evolution characteristics of the flow field, we employ the Autoregressive Integrated Moving Average model method to pre-reconstruct the incomplete data. Next, we introduce the Fuzzy Spatial Consistency Index (FSCI), which measures the spatial coherence among neighboring data variations. By utilizing FSCI as a guiding metric, we iteratively optimize and replace missing values using the Proper Orthogonal Decomposition method. Importantly, our reconstruction process does not rely on expensive high-fidelity data fusion or external intervention, making it highly efficient and cost-effective. We focus our research on the classic problem of flow around the hydrofoil and apply the unsupervised learning reconstruction method to restore incomplete flow fields with varying missing rates. We also investigate the impact of flow field stability, snapshot sampling frequency, and missing structure on reconstruction accuracy. Our results indicate that these factors significantly influence the reconstruction of velocity fields with a high missing rate compared with a lower missing rate. Additionally, we observe that the reconstruction performance of the streamwise velocity field is relatively inferior compared to the normal velocity field, and the reconstruction accuracy is higher for relatively stable flow fields. These findings provide valuable insights and further validate the effectiveness and applicability of the unsupervised learning reconstruction method for restoring incomplete flow fields.

Comoving mesh method for certain classes of moving boundary problems

A Lagrangian-type numerical scheme called the "comoving mesh method" or CMM is developed for numerically solving certain classes of moving boundary problems which include, for example, the classical Hele-Shaw flow problem and the well-known mean curvature flow problem. This finite element scheme exploits the idea that the normal velocity field of the moving boundary can be extended throughout the entire domain of definition of the problem using, for instance, the Laplace operator. Then, the boundary as well as the finite element mesh of the domain are easily updated at every time step by moving the nodal points along this velocity field. The feasibility of the method, highlighting its practicality, is illustrated through various numerical experiments. Also, in order to examine the accuracy of the proposed scheme, the experimental order of convergences between the numerical and manufactured solutions for these examples are also calculated.

Optimal Design of Electrode Topology of Dielectric Elastomer Actuators Based on the Parameterized Level Set Method.

Dielectric elastomer actuators (DEAs) are widely used to drive soft machines, and optimal design is required in more advanced designs of soft robots. In this research article, a computational approach is originally proposed and validated for the topology optimization of electrodes of DEAs. The nonlinear finite elements of absolute nodal coordinate formulation are applied to model the dynamic electromechanical behaviors of DEAs. The parameterized level set method is employed to optimize the electrode topology of DEAs. Then, the method of system-wise equivalent static load is employed to convert the optimization problem of dynamic responses into the static one. Based on the sensitivity analysis, the normal velocity field for optimizing the electrode topology is derived. Finally, two case studies are presented to validate the proposed optimization approach. The experimental test is also performed, and the measured results are compared with the numerical ones to further validate the proposed methodology.

Vibroacoustic response of mode localized thin functionally graded plates using physical neutral surface

This paper investigates an analytical solution to the sound radiation behavior of vibrating thin mode localized Al/Al2O3 functionally graded plates (FGM) with varying boundary conditions utilizing its physical neutral surface through analysis and simulation. For the study, simply-supported, clamped–clamped, and clamped–free FGM plates with power-law index k = 0,1,5,10 are examined. 20% of the plate’s weight is used to constraint the plate with point and distributed mass. Matlab formulation is used to compute the modal participation factors by analytically solving the governing equation. Furthermore, modal participation factors are used to compute the normal velocity and far-field sound radiation fields by solving the Rayleigh integral using the elemental radiator approach. Sound power level results are verified using ANSYS’s finite element method and good agreement is observed. The effects of boundary conditions and power law indexes on the sound radiation fields of mode localized FGM plate are correspondingly discussed. Cross-comparison of sound radiation by mode-localized FGM plate with point and distributed mass are discussed. Sound power level in terms of “A” weighted scale(dBA) illustrates that the sound power level increases with an increased power-law index. Moreover, mode localized FGM plate with distributed mass reported a lower sound power level for all power-law indexes.

A Novel Reduced-Order Model for Predicting Compressible Cavity Flows

Compressible cavity flows exist widely in aeronautical vehicles. The cost of the computational fluid dynamics to solve compressible cavity flows is high. To address this issue, in this work, a novel reduced-order model (ROM) combining proper orthogonal decomposition (POD) with the long short-term memory (LSTM) neural network named LSTM-ROM for predicting the compressible cavity flows is proposed. First, POD is used to provide a low-dimensional subspace. Then, the LSTM neural network is designed to predict the POD coefficients with time evolution. The results show that the LSTM-ROM can accurately predict the POD coefficients for a long time and capture the shock wave structures at supersonic speed. The predicted density and normal velocity field are consistent with those simulated by direct numerical simulation (DNS). The calculation time of LSTM-ROM is almost one-seventh of that of DNS. By comparing the performance of LSTM-ROM with that of dynamic mode decomposition (DMD) and multilayer perceptron (MLP), it is found that the root mean square errors of density and normal velocity field predicted by LSTM-ROM are smaller than those predicted by DMD and MLP. In addition, the LSTM-ROM can accurately and efficiently predict the flows over cavities with different inclination angles at subsonic speed. Therefore, the LSTM-ROM is an accurate and efficient method for predicting the compressible cavity flows, which lays a foundation for other complex flows.

An isogeometric boundary element approach for topology optimization using the level set method

Among the various types of structural optimization, topology has been occupying a prominent place over the last decades. It is considered the most versatile because it allows structural geometry to be determined taking into account only loading and fixing constraints. This technique is extremely useful in the design phase, which requires increasingly complex computational modeling. Modern geometric modeling techniques are increasingly focused on the use of NURBS basis functions. Consequently, it seems natural that topology optimization techniques also use this basis in order to improve computational performance. In this paper, we propose a way to integrate the isogeometric boundary techniques to topology optimization through the level set function. The proposed coupling occurs by describing the normal velocity field from the level set equation as a function of the normal shape sensitivity. This process is not well behaved in general, so some regularization technique needs to be specified. Limiting to plane linear elasticity cases, the numerical investigations proposed in this study indicate that this type of coupling allows to obtain results congruent with the current literature. Moreover, the additional computational costs are small compared to classical techniques, which makes their advantage for optimization purposes evident, particularly for boundary element method practitioners.

A sharp-interface method for the simulation of shock-induced vaporization of droplets

A sharp-interface method is developed to calculate the vaporization of droplets in high-speed flows. The levelset method is used to track the liquid-gas interface. A sharp-interface approach using an interfacial Riemann solver based ghost fluid method (RS-GFM) is developed to couple the liquid and gas flow-fields at the interface. The interfacial Riemann problem accounts for surface tension and phase change effects, which affect the jump in pressure and the normal velocity fields across the interface. The current RS-GFM also accounts for the jump in viscous stresses at the interface caused by the Marangoni effect. The resulting sharp-interface approach captures all the first-order physical effects at play in shock-induced droplet vaporization. The method is validated by comparing the current results with benchmark experimental and numerical results. Finally, 2D and 3D simulations of shock-droplet interactions are performed to quantify the shock-induced vaporization rate of the droplets, under the influence of viscosity and surface tension.

Penetration resistance and the critical cavitation velocity for an ogive-nosed rigid projectile penetrating into a semi-infinite metallic target

This paper studies penetration resistance and projectile-target separation for an ogive-nosed rigid projectile penetrating into a metallic target. A prescribed normal velocity field is introduced to determine the contact stress on the projectile nose, based on which the dynamic equation of a rigid projectile is formulated. Projectile-target separation occurs when the impact velocity of the projectile is greater than the critical cavitation velocity according to Hill's cavitation criterion. Target material is assumed incompressible in both elastic and rigid, perfectly plastic regions in order to simplify the analyses. It shows that the penetration resistance derived from the prescribed velocity field has a different form from that based on the dynamic cavity expansion model. When the impact velocity is greater than the critical cavitation velocity, the projectile-target separation point moves further to the nose tip, leading to the reduction of the contact area between the projectile nose and the target and a large increase of the inertia term (velocity square term) in penetration resistance. The predicted penetration depth and critical cavitation velocity agree reasonably with experimental and numerical results.

Velocity field level‐set method for topological shape optimization using freely distributed design variables

SummaryThe velocity field level‐set topological shape optimization method combines the implicit representation in the standard level‐set method and the capabilities of general mathematical programming algorithms in handling multiple constraints and additional design variables. The key concept is to construct the normal velocity field using basis functions and the velocity design variables at specified points (referred to as velocity knots) in the entire design domain. In this study, the velocity design variables are decoupled from the level‐set grid points. Making use of this property, we can adaptively change the arrangement of the velocity knots as the structural boundary evolves. This provides more design freedom in the optimization and allows for a significant reduction in the number of design variables. Several numerical examples in two‐ and three‐dimensional design domains are presented to demonstrate the robustness and efficiency of the proposed method. We also show that changing the number of velocity knots may implicitly exert certain control on topological complexity and length scale.

Power operator dimensional reduction to obtain the useful intensity in rectangular plates with several boundary conditions

This work investigates the acoustical intensity generated by the sound radiated from rectangular baffled plates in eight cases with distinct combinations of classical boundary conditions. The primary objective is to identify the regions of these plates that effectively contribute to the radiated sound power into the far-field, especially when the driven frequency occurs below the critical coincidence frequency. This identification is done by filtering the non-propagating waves, both using the (analytical) supersonic intensity method and the (numerical) useful intensity model. The spectral decomposition of the sound energy operator is applied, becoming possible the dimensional reduction of this operator to remove the components that do not propagate. Brief theoretical formulations, both for the plates vibration and the resulting acoustical field, are discussed. The closed form solution of the normal velocity field for the eight cases is given. Then, the supersonic intensity is estimated. On the other hand, a summary of the useful intensity technique is discussed and it is computed for the same cases. In the numerical examples, the comparison of the supersonic intensity, the useful intensity and the classical acoustic intensity is shown. The edge and corner modes are clearly identified and the useful intensity plots showed to fit well with the supersonic intensity ones.

Boundary element method applied to topology optimization using the level set method and an alternative velocity regularization

The topology optimization (TO) is a valuable tool in the early stages of structural engineering design. It enables the determination of the structural layout accounting for the required performance and utilizing less amount of material. In this study, an algorithm for TO is proposed, which is based on two computational procedures. On one hand the boundary element method (BEM), which is efficient for mechanical modelling and remeshing due to its mesh dimension reduction. On the other hand, the level set method (LSM) is an efficient approach to parameterize the design domain. Moreover, it handles complex topology changes without difficulties. The new feature presented here is showing a different formulation of the problem and explore its benefits. The idea is based on the augmented Lagrangian method in which shape sensitivity is used to drive the topology search. The shape derivative takes advantage of conformal and invertible mappings contributing for global stability. To reduce the susceptibility to local minima, a topology perturbation scheme based on local stresses is also adopted. The normal boundary velocity field may be locally singular. In this case the Peng regularization is utilized to maintain stability. These improvements make the algorithm convergent even on the presence of local instabilities. The LSM provides the structural geometry from its zero-level-set curve. Then, this curve is discretised through the BEM. The classical upwind fashion respecting strict CFL conditions is utilised for solving LSM equations. Local holes may be included at each time step, which enables topology changes based on local stress. Classical benchmark examples are used to illustrate the efficiency of the numerical procedure.

ON THE SCATTERING OF SURFACE WAVES BY UNDERWATER OBSTACLES

The paper considers a 2D linear problem on scattering of the low-amplitude surface wave in an incompressible fluid that propagates over the bottom obstacle in form of a vertical rectangular wall of the finite of infinitesimal length. The bottoms of the channel and obstacle walls are absolutely rigid. The solution is found by the method of partial domains implying the subdivision of the complex geometry of the overall domain of wave field existence into the subdomains of canonical shapes. This approach allows the formal representing of the corresponding general solutions as the series with respect to eigenfunctions satisfying part of the boundary conditions in each subdomain. The unknown coefficients present in these general solutions may be found from matching conditions that postulate continuity of pressure and normal velocity fields at the boundaries of adjacent subdomains. Applying algebraization procedure to matching conditions for the corresponding general solutions leads to generation of infinite systems of linear equations with respect to the unknown coefficients. The obtained systems possess slow convergence that is determined by the presence of velocity singularities in angular points of the obstacle. To accelerate the convergence, the method of improved reduction is applied in analyzing the infinite systems. It is based on the a priori hypotheses about the asymptotic behavior of the unknown coefficients in general solutions that is controlled by the order of field singularity in the vicinity of the corresponding angular point. The dependence of calculated energy discrepancy on the amount of considered terms in the reduced system is assessed. The method of improved reduction is shown to provide the better convergence quality at moderate number of kept terms (50 to 70), in comparison with the ordinary reduction. The use of the improved reduction also leads to some widening of the region for which the numerical error remains within acceptable limits.

Transverse heterogeneity of interfacial bonding behavior during roll bonding of Cu/Al bimetallic plates

The transverse heterogeneity of interfacial bonding behavior during roll bonding of Cu/Al bimetallic plates were studied through experimental research and numerical simulation. The experimental results showed that the bonding strength along the transverse interfacial gradually decreased from center to edge, and decrease accelerates near the edge. Combining with the results of numerical simulation, it was found that the variation of bonding strength along the transverse interfacial appeared to be the result of the synergistic effect of the normal stress, strain and velocity field of the bonding interface. The bonding strength in the intermediate zone of the interface slowly decreased because of a decrease in the equivalent strain at the interface. The normal stress decreases rapidly near the edge of the plate which results in the rapid reduction of the bonding strength. The poor synchronism of the metal flow on both sides of the interfaces might lead to wavy interfaces, which tend to form interface defects such as cracks and gaps.

Level set based shape optimization using trimmed hexahedral meshes

This paper presents a new approach for level set based shape optimization using trimmed hexahedral meshes that geometrically conform to shape and topology changes during the optimization process. The marching cubes algorithm is employed to generate trimmed hexahedral meshes at each optimization iteration by splitting a regular background hexahedral mesh with the zero-isosurface of a level set function. A simple method is proposed to handle nonconforming polyhedral elements at the interface due to the face ambiguity arising in the marching cubes algorithm. The motion of the zero-isosurface of a level set function is obtained from the solution of the Hamilton–Jacobi transport equation using a normal velocity field defined on the regular background hexahedral mesh. Numerical results show that the present approach provides a natural and effective tool to solve shape optimization problems relying on explicitly discretized meshes of the shapes throughout the optimization process.

A velocity field level set method for shape and topology optimization

SummaryIn this paper, we propose a new implementation of the level set shape and topology optimization, the velocity field level set method. Therein, the normal velocity field is constructed with specified basis functions and velocity design variables defined on a given set of points that are independent of the finite element mesh. A general mathematical programming algorithm can be employed to find the optimal normal velocities on the basis of the sensitivity analysis. As compared with conventional level set methods, mapping the variational boundary shape optimization problem into a finite‐dimensional design space and the use of a general optimizer makes it more efficient and straightforward to handle multiple constraints and additional design variables. Moreover, the level set function is updated by the Hamilton‐Jacobi equation using the normal velocity field; thus, the inherent merits of the implicit representation is retained. Therefore, this method combines the merits of both the general mathematical programming and conventional level set methods. Integrated topology optimization of structures with embedded components of designable geometries is considered to show the capability of this method to deal with general design variables. Several numerical examples in 2D or 3D design domains illustrate the robustness and efficiency of the method using different basis functions.

Dynamics of the vortex line density in superfluid counterflow turbulence

Describing superfluid turbulence at intermediate scales between the inter-vortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines $\cal{L}$. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides $\cal{L}$ and the normal and superfluid velocity fields. In this paper we offer a minimal closure using one additional anisotropy parameter $I_{l0}$. Using the example of counterflow superfluid turbulence we derive two coupled closure equations for the vortex line density and the anisotropy parameter $I_{l0}$ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.

Normal move-out correction in anisotropic and laterally heterogeneous media using simultaneous velocity variation with offset

In this paper, we present a new method of normal move-out (NMO) correction that works on a trace by trace basis technique rather than the current conventional sample by sample semblance analysis. The method corrects the pre-stack seismic data due to the NMO effect in both anisotropic and laterally heterogeneous mediums and simultaneously provides a full NMO velocity field that covers every single offset/azimuth in a common depth point (CDP). Also, we introduce a new computational method to recover the anisotropy effect from the extracted NMO velocity field. The presented method gives every single primary seismic reflector in a CDP, three different corrections; Positive correction (where the NMO velocity increases), Negative correction (where NMO velocity decreases) and zero correction (where NMO velocity doesn't change). The first two corrections (positive and negative) work only in case of anisotropy or laterally heterogeneous mediums while the last correction is applicable in case of the seismic reflector is isotropic. The method starts by picking the NMO velocity for each seismic reflector using the conventional semblance plot, then we use these picked NMO velocities as an initial input to our method and since every seismic reflector has three different possibilities, getting all the possible combinations is crucial. To get these combinations, we simply use the combination with repetition mathematical method. To control the degree of the increasing and the decreasing of the NMO velocity correction, we use two parameters called the Anisotropy range parameter(Ar) and its increment. The Ar parameter is used to modify the picked NMO velocity of the primary seismic reflector N times (by adding and subtracting a correction value) based on the number of combinations. The total number of times where initial NMO velocities are modified is based on both the Ar parameter and the number of the seismic reflectors. After all the picked NMO velocities are modified then, we use each of the modified NMO velocity traces (after the interpolation between the modified NMO velocities) to correct the corresponding seismic trace due to the NMO effect then, measure the similarity/semblance between the pilot trace (e.g. Zero offset trace but it dynamically changes) and that seismic trace under the NMO correction. This corresponding seismic trace is corrected due to the NMO effect N times and at each time we measure the semblance value. The modified NMO velocity trace that gives the highest semblance measure is selected. The process is repeated for all the other seismic traces in a CDP. We tested the method on different real and synthetic examples; Isotropic, anisotropic and laterally heterogeneous mediums synthetic examples are presented. Furthermore, we tested the method on a pre-stack CDP real example using Alaska dataset. The results show an excellent flattening to the seismic reflectors and provides a reasonably accurate normal move-out velocity field that covers every offset in a CDP.

Electric response in superfluid helium

We report an experimental investigation of the electric response of superfluid helium that arises in the presence of a second sound standing wave. It was found that the signal of the electric response is observed in a narrow range of second sound excitation power. The linear dependence of the signal amplitude has been derived at low excitation power, however, above some critical power, the amplitude of the signal is considerably decreased. It was established that the rapid change of the electric response is not associated with a turbulent regime generated by the second sound wave. A model of the appearance of the electric response as a result of the oscillation of electron bubbles in the normal fluid velocity field in the second sound wave is presented. Possible explanation for the decrease of the electric response are presented.

Acoustic propagation in two-dimensional waveguide for membrane bounded ducts

This work aims to investigate the mode-matching (MM) and low frequency approximation (LFA) solutions of a two dimensional waveguide problem with flanged junction. The relative merits of each approach are compared for the scattering of fluid-coupled wave. The boundary value problem involving higher order derivatives at boundaries becomes a non-Sturm–Liouville problem where the use of standard orthogonality relation (OR) enables the MM solution. The derivation of LFA is made which proves to be surprisingly accurate for structure-borne mode incident. In order to validate the truncated model expansion the distribution of power in duct regions is discussed and Gibbs oscillations are incorporated by reconstruction of the normal velocity field using Lanczos filter.

Level Set Based Shape Optimization of Linear Structures using Topological Derivatives

Abstract Using a level set method and topological derivatives, a topological shape optimization method that is independent of an initial design is developed for linearly elastic structures. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. The “Hamilton-Jacobi(H-J)” equation and computationally robust numerical technique of “up-wind scheme” lead the initial implicit boundary to an optimal one according to the normal velocity field while minimizing the objective function of compliance and satisfying the constraint of allowable volume. Based on the asymptotic regularization concept, the topological derivative is considered as the limit of shape derivative as the radius of hole approaches to zero. The required velocity field to update the H-J equation is determined from the descent direction of Lagrangian derived from optimality conditions. It turns out that the initial holes are not required to get the optimal result since the developed method can create holes whenever and wherever necessary using indicators obtained from the topological derivatives. It is demonstrated that the proper choice of control parameters for nucleation is crucial for efficient optimization process.