Optimal Velocity Field Research Articles

Multiplicity in an optimised kinematic dynamo

Multiplicity in optimal kinematic dynamos exists for certain types of symmetry classes and boundary conditions, at least near the lowest dynamo onset . Here we investigate the NNT type dynamo generated by steady flows with impermeable boundary conditions in a cube, where the letter N or T stands for pseudo-vacuum or superconducting boundary conditions along x, y, z directions, respectively. We find the top two of the three branches in the neighbourhood of have their growth rates crossed over at . Within each branch, the spatial structure of the optimal velocity field gradually shifts with respect to . At about above , the original optimal branch has developed distinct combinations of dominant Fourier modes. In contrast, the first suboptimal branch shows the least change in structure. We then follow the evolution of selected optimised solutions when varies until it becomes unstable. Specific modes in the flow that can destabilise the dynamo are identified. Within the range surveyed, we find that there can be one to two dynamo windows. All three branches generate a steady dynamo near , but the first suboptimal branch can generate an oscillatory dynamo at about eight times , and for both suboptimal branches, the growth rate reaches saturation approximately at . We find the two suboptimal branches create a more robust dynamo action supercritically.

Hot spot temperature optimization of customized region in multi-region integrated system based on variational method

Multi-region integrated heat transfer process involving heat conduction and convection is commonly adopted in practical production. Optimization equations from variational method are effective for design of velocity fields in heat convection process. However, equations for optimization of hot spot temperature are not yet been proposed, which is the core issue in cooling problems, especially for microelectronic devices. Moreover, convection of flow region in multi-region system is concerned in previous researches, yet heat conduction of the solid region is usually ignored, which thus fails to obtain the optimal results. In this study, optimization equations which aim at minimizing the hot spot temperature in a multi-region integrated heat transfer system is developed. An objective function to characterize the highest temperature (Tmax) is proposed, based on which the optimization equations of target regions and constraint regions are derived using variational method for minimization of Tmax in target region. A numerical case with multiple heat sources is used to verify the effectiveness of the proposed optimization equations. The results show that the optimal velocity field from the optimization equations remarkably reduces the hot spot temperature of the target regions. When setting all the heat sources as the target regions, Tmax obtained from the optimization equations is 22.6 K lower than that before optimization, and the temperature difference of the heat sources (ΔT) is reduced by 98%. Compared to the optimization equations in the previous study, the developed equations reduce Tmax and ΔT by 1.6 K and 85%, respectively. When choosing one of the heat sources as the target region, Tmax of this heat source after optimization is reduced by 3.6–5.1 K compared with that with all heat sources as target region. The optimization equations aiming at minimizing the proposed objective function exhibit excellent performance in reducing hot spot temperature in multi-region integrated heat transfer process, and the optimal velocity fields from optimization equations can effectively guide the design of enhanced heat transfer system.

A variational approach for picking optimal surfaces from semblance-like panels

We propose and examine a variational method for determining optimal velocity fields from semblance-like volumes using continuation. The proposed approach finds a minimal-cost surface through a volume, which often corresponds to a velocity field within a semblance scan. This allows picked velocity fields to incorporate information from gathers that are spatially near the midpoint in question. The minimization process amounts to solving a nonlinear elliptic partial differential equation, which is accomplished by changing the elliptic problem to a parabolic one and solving it iteratively until it converges to a critical point which minimizes the cost functional. The continuation approach operates by using a variational framework to iteratively minimize the cost of a velocity surface through successively less-smoothed semblance scans. The method works because a global minimum for the velocity cost functional can only exist when the semblance scan varies smoothly in space and convexly in the parameter being scanned. Using a discretization of the functional with a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm, we illustrate how the continuation approach is able to avoid local minima that would typically capture the iterative solution of an optimal velocity field determined without continuation by applying the method to seismic processing of a field data set from the Viking Graben. We then use a field data set from the Gulf of Mexico to show how the final velocity model determined by the method using continuation is largely independent of the starting velocity model, producing something resembling a global minimum. Finally, we demonstrate the versatility of the variational picking approach by using it to automatically interpret a seismic horizon from the Heidrun Field.

Investigating and Simulating the Electrostatic Field of Four Types of Collectors in Electrostatic Dust Filters

Electrostatic dust purifiers are widely used in many industries such as thermal power plants, cement plants, waste incineration and glass production. Optimization of the electrode and collector is important for higher efficiency (to achieve high efficiency) in electrostatic dust filtration. This study examines the electrostatic properties of four types of collector plates: flat, curved, spike, and spike with groove. The electric field strength, the charge density, the velocity of movement, and the collection efficiency are analysed for each type of collector. The inflow of air is perpendicular to the collector plate instead of parallel in traditional models, which improves the efficiency. The velocity of dust towards the collector plate depends on the electrostatic force and the velocity field around the collector. The Deutsch model is used to determine the performance among receiver plate types. The results show that the spike plate achieves the best collection efficiency because of the optimal static electric field and velocity field around it.

Diffeomorphic Particle Image Velocimetry

The existing particle image velocimetry (PIV) do not consider the curvature effect of the non-straight particle trajectory, because it seems to be impossible to obtain the curvature information from a pair of particle images. As a result, the computed vector underestimates the real velocity due to the straight-line approximation, that further causes a systematic error for the PIV instrument. In this work, the particle curved trajectory between two recordings is firstly explained with the streamline segment of a steady flow (diffeomorphic transformation) instead of a single vector, and this idea is termed as diffeomorphic PIV. Specifically, a deformation field is introduced to describe the particle displacement, i.e., we try to find the optimal velocity field, of which the corresponding deformation vector field agrees with the particle displacement. Because the variation of the deformation function can be approximated with the variation of the velocity function, the diffeomorphic PIV can be implemented as iterative PIV. That says, the diffeomorphic PIV warps the images with deformation vector field instead of the velocity, and keeps the rest as same as iterative PIVs. Two diffeomorphic deformation schemes -- forward diffeomorphic deformation interrogation (FDDI) and central diffeomorphic deformation interrogation (CDDI) -- are proposed. Tested on synthetic images, the FDDI achieves significant accuracy improvement across different one-pass displacement estimators (cross-correlation, optical flow, deep learning flow). Besides, the results on three real PIV image pairs demonstrate the non-negligible curvature effect for CDI-based PIV, and our FDDI provides larger velocity estimation (more accurate) in the fast curvy streamline areas. The accuracy improvement of the combination of FDDI and accurate dense estimator means that our diffeomorphic PIV paves a new way for complex flow measurement.

Globally optimized cross-correlation for particle image velocimetry

We propose a global optimization method to automatically search for the correlation peak instead of computing the entire cross-correlation map throughout an interrogation window (IW) using a fast Fourier transform (FFT)-based method. The proposed method, named globally optimized cross-correlation for particle image velocimetry (GOCCPIV), minimizes an objective function consisting of a residual term for cross-correlation and a penalty term for smoothness to solve the optimal velocity field. A very small IW is adopted in GOCCPIV to obtain a dense velocity field with a high spatial resolution. The proposed method is quantitatively validated on synthetic particle image pairs with different flow patterns and is compared with the mainstream FFT-based cross-correlation method (FFTCCPIV) and physical-based optical flow (OpticalFlow). We consider the influences of the IW size, particle concentration, particle image diameter, large displacements and image noise on the velocity measurements. Error analysis indicates that GOCCPIV outperforms FFTCCPIV in resolving small-scale vortices and reducing the measurement error. Finally, the proposed method is applied to a real PIV experiment with an impinging jet. The results indicate that GOCCPIV is more suitable than FFTCCPIV for resolving high-velocity-gradient regions.

Optimal Heat Transfer and Optimal Exit Times

A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls. Starting from a positive initial temperature distribution in the interior, the goal is to flux the heat through the walls as efficiently as possible. Here we consider a distinct but closely related problem, that of the integrated mean exit time of Brownian particles starting inside the domain. Since flows favorable to rapid heat exchange should lower exit times, we minimize a norm of the exit time. This is a time-independent optimization problem that we solve analytically in some limits, and numerically otherwise. We find an (at least locally) optimal velocity field that cools the domain on a mechanical time scale, in the sense that the integrated mean exit time is independent on molecular diffusivity in the limit of large-energy flows.

Active optimization design theory and method for heat transfer unit and its application on shape design of cylinder in convective heat transfer

When heat transfer enhancing technology is applied to design heat transfer unit, the improvement of heat transfer will usually accompanied with a dramatically increase of flow resistance. The main objective of present paper is to propose an optimization design theory and develop a corresponding approach to design heat transfer unit, in which the heat transfer and flow resistance will be considered simultaneously. As an example, this paper shows how to obtain a high performance tube in convective heat transfer by optimizing the shape profile using the theory and approach. A 2-D model is used in a direct problem solver, which is solved by finite element software and provides the numerical results in the optimization. Power consumption of flow field Pf is used to measure the flow resistance while generalized thermal resistance Rh is used to measure the thermal resistance. Meanwhile, genetic algorithm (GA) and simplified conjugate-gradient method (SCGM) are applied in this study to optimize the objective function composed by these two aspects. Based on the results of numerical calculation, the optimal velocity field with 61.93% decrease in Pf and 17.13% increase in Rh is obtained. Subsequently, the performances at different inlet velocities Vi are investigated. It is found that the shape profile obtained at Vi=0.1m/s always has a better performance than the circular one, even if it is not the ideal shape. Finally, the further optimizations based on different Vi and objective functions are discussed. The results prove that the proposed optimization method is effective in designing the shape of tube.

Novel optimization approach to mixing process intensification

An approach was presented to intensify the mixing process. Firstly, a novel concept, the dissipation of mass transfer ability (DMA) associated with convective mass transfer, was defined via an analogy to the heat-work conversion. Accordingly, the focus on mass transfer enhancement can be shifted to seek the extremum of the DMA of the system. To this end, an optimization principle was proposed. A mathematical model was then developed to formulate the optimization into a variational problem. Subsequently, the intensification of the mixing process for a gas mixture in a micro-tube was provided to demonstrate the proposed principle. In the demonstration example, an optimized velocity field was obtained in which the mixing ability was improved, i.e., the mixing process should be intensified by adjusting the velocity field in related equipment. Therefore, a specific procedure was provided to produce a mixer with geometric irregularities associated with an ideal velocity.

Temporally diffeomorphic cardiac motion estimation from three-dimensional echocardiography by minimization of intensity consistency error.

Quantitative analysis of cardiac motion is important for evaluation of heart function. Three dimensional (3D) echocardiography is among the most frequently used imaging modalities for motion estimation because it is convenient, real-time, low-cost, and nonionizing. However, motion estimation from 3D echocardiographic sequences is still a challenging problem due to low image quality and image corruption by noise and artifacts. The authors have developed a temporally diffeomorphic motion estimation approach in which the velocity field instead of the displacement field was optimized. The optimal velocity field optimizes a novel similarity function, which we call the intensity consistency error, defined as multiple consecutive frames evolving to each time point. The optimization problem is solved by using the steepest descent method. Experiments with simulated datasets, images of anex vivo rabbit phantom, images of in vivo open-chest pig hearts, and healthy human images were used to validate the authors' method. Simulated and real cardiac sequences tests showed that results in the authors' method are more accurate than other competing temporal diffeomorphic methods. Tests with sonomicrometry showed that the tracked crystal positions have good agreement with ground truth and the authors' method has higher accuracy than the temporal diffeomorphic free-form deformation (TDFFD) method. Validation with an open-access human cardiac dataset showed that the authors' method has smaller feature tracking errors than both TDFFD and frame-to-frame methods. The authors proposed a diffeomorphic motion estimation method with temporal smoothness by constraining the velocity field to have maximum local intensity consistency within multiple consecutive frames. The estimated motion using the authors' method has good temporal consistency and is more accurate than other temporally diffeomorphic motion estimation methods.

不確定荷重に対する骨組構造のロバスト形状最適化

This paper presents a robust shape optimization of frame structures with unknown loadings. The concept of minimizing the maximum compliance called principal compliance is applied to a shape optimization problem of a frame structure. The principal compliance minimization problem is transformed to the equivalent maximization problem of the fundamental eigenvalue of the stiffness tensor, and then formulated as a distributed parameter shape optimization problem. The derived shape gradient function is applied to the H^1 gradient method for frames to determine the optimal shape variation, or the optimal velocity field. With this method, the optimal free-form with smooth curvature distribution of a frame structure can be determined without any shape parameterization. The calculated results show the effectiveness of the proposed method for the robust shape optimization problem of a frame structure with unknown loadings.

Optimization of the Magnetic Dynamo

In stars and planets, magnetic fields are believed to originate from the motion of electrically conducting fluids in their interior, through a process known as the dynamo mechanism. In this Letter, an optimization procedure is used to simultaneously address two fundamental questions of dynamo theory: "Which velocity field leads to the most magnetic energy growth?" and "How large does the velocity need to be relative to magnetic diffusion?" In general, this requires optimization over the full space of continuous solenoidal velocity fields possible within the geometry. Here the case of a periodic box is considered. Measuring the strength of the flow with the root-mean-square amplitude, an optimal velocity field is shown to exist, but without limitation on the strain rate, optimization is prone to divergence. Measuring the flow in terms of its associated dissipation leads to the identification of a single optimal at the critical magnetic Reynolds number necessary for a dynamo. This magnetic Reynolds number is found to be only 15% higher than that necessary for transient growth of the magnetic field.

Optimization of flue gas turbulent heat transfer with condensation in a tube

Conservation equations for sensible and latent entransy are established for flue gas turbulent heat transfer with condensation in a tube, and the entransy dissipation expression is deduced. The field synergy equation is obtained on the basis of the extremum entransy dissipation principle for flue gas turbulent heat transfer with condensation. The optimal velocity field is numerically obtained by solving the field synergy equation. The results show that the optimal velocity field contains multiple longitudinal vortices near the tube surface. These improve the synergy not only between the velocity and temperature fields but also between the velocity and vapor concentration fields. Therefore, the turbulent heat and mass transfers are significantly enhanced.

Performance improvement for chemical absorption of CO2 by global field synergy optimization

Chemical absorption of CO2 is deemed as an effectively controllable way to accomplish large reduction of greenhouse gas emission. A two dimensional (2-D) model for two-phase flows is established for chemical absorption of CO2 in the packed column. A good agreement has been reached between the simulated temperature and fluid flow profiles and experimental results. The field synergy equations are deduced to optimize the fluid flow, mass transfer, heat transfer and chemical reaction by an established Lagrange function. The synergy angle is an index to express the synergy degree among the physical phenomena. The global field synergy optimized velocity field, temperature distribution and gas concentration variation trend are obtained, contributing to improvement of 9% CO2 removal efficiency. Meanwhile, the entropy generation rate was well applied to quantify the overall improvement from the perspective of exergy. The results indicated that the entropy generation rate induced by mass transfer and reaction composes the most part of the irreversibility. The exergy loss is reduced by 12.8% after global field synergy optimization mainly for the two resistances reduction. The results showed that the field synergy optimization could be an intensification method for CO2 capture, whose improvement effect could be assessed by entropy generation analysis.

Optimization of flue gas convective heat transfer with condensation in a rectangular channel

Conservation equations of sensible entarnsy and latent entransy are established for flue gas convective heat transfer with condensation in a rectangular channel and the entransy dissipation expression is deduced. The field synergy equation is obtained on the basis of the extremum entransy dissipation principle for flue gas convective heat transfer with condensation. The optimal velocity field is numerically obtained by solving the field synergy equation. The results show that the optimal velocity field has multiple longitudinal vortices, which improve the synergy not only between the veloctiy and temperature fields but also between the velocity and vapor concentration fields. Therefore, the convective heat and mass transfers are significantly enhanced. Flow with multiple longitudinal vortices close to the optimal velocity field can be generated by discrete double-inclined ribs set in the rectangular channel. The numerical results show that the total heat transfer rate in the discrete double-inclined rib channel increases by 29.02% and the condensing heat transfer rate increases by 27.46% for Re = 600 compared with the plain channel.

The extremum principle of mass entransy dissipation and its application to decontamination ventilation designs in space station cabins

In terms of the analogy between mass and heat transfer phenomena, a new physical quantity, i.e. mass entransy, is introduced to represent the ability of an object for transferring mass to outside. Meanwhile, the mass entransy dissipation occurs during mass transfer processes as an alternative to measure the mass transfer irreversibility. Then the concepts of mass entransy and its dissipation are used to develop the extremum principle of mass entransy dissipation and the corresponding method for convective mass transfer optimization, based on which an Euler’s equation has been deduced as the optimization equation for the fluid flow to obtain the best convective mass transfer performance with some specific constraints. As an example, the ventilation process for removing gaseous pollutants in a space station cabin with a uniform air supply system has been optimized to reduce the energy consumption of the ventilation system and decrease the contaminant concentration in the cabin. By solving the optimization equation, an optimal air velocity distribution with the best decontamination performance for a given viscous dissipation is firstly obtained. With the guide of this optimal velocity field, a suitable concentrated air supply system with appropriate air inlet position and width has been designed to replace the uniform air supply system, which leads to the averaged and the maximum contaminant concentrations in the cabin been decreased by 75% and 60%, respectively, and the contaminant concentration near the contaminant source surface been decreased by 50%, while the viscous dissipation been reduced by 30% simultaneously.

Inverse Optimal Velocity Field Control of an Outdoor Blimp Robot – Blimp Surveillance Systems for Rescue –

A surveillance system is required to gather the suffering information in the stricken area safely and quickly after natural disasters. An autonomous blimp is the best option for this purpose. Inverse optimal velocity field control is proposed for the blimp to keep a desired trajectory. The desired trajectory based on velocity field is designed, and inverse optimal tracking control is applied to be robust to input uncertainties. The transient performance to the desired trajectory is very important to fly smoothly along the contour, because the blimp is affected by wind easily. The inverse optimal control is expected to improve the robustness to uncertainties of various dynamic parameters. Some experiments are performed to confirm the usefulness of the proposed method by using an outdoor blimp whose length is 12.2m.

Field synergy equation for turbulent heat transfer and its application

A field synergy equation with a set of specified constraints for turbulent heat transfer developed based on the extremum entransy dissipation principle can be used to increase the field synergy between the time-averaged velocity and time-averaged temperature gradient fields over the entire fluid flow domain to optimize the heat transfer in turbulent flow. The solution of the field synergy equation gives the optimal flow field having the best field synergy for a given decrement of the mean kinetic energy, which maximizes the heat transfer. As an example, the field synergy analysis for turbulent heat transfer between parallel plates is presented. The analysis shows that a velocity field with small eddies near the boundary effectively enhances the heat transfer in turbulent flow especially when the eddy height which are perpendicular to the primary flow direction, are about half of the turbulent flow transition layer thickness. With the guide of this optimal velocity field, appropriate internal fins can be attached to the parallel plates to produce a velocity field close to the optimal one, so as to increase the field synergy and optimize the turbulent heat transfer.

Field synergy optimization and enhanced heat transfer by multi-longitudinal vortexes flow in tube

The field synergy equation for steady laminar convection heat transfer was derived by conditional variation calculus based on the least dissipation of heat transport potential capacity. The optimum velocity field with the best heat transfer performance and least flow resistance increase can be obtained by solving the synergy equation. The numerical simulation of laminar convection heat transfer in a straight circular tube shows that the multi-longitudinal vortex flow in the tube is the flow pattern that enhances the heat transfer enormously. Based on this result, a novel enhanced heat transfer tube, the discrete double-inclined ribs tube (DDIR-tube), is developed. The flow field of the DDIR-tube is similar to the optimal velocity field. The experimental results show that the DDIR-tube has better comprehensive heat transfer performance than the current heat transfer enhancement tubes. The present work indicates that new heat transfer enhancement techniques could be developed according to the optimum velocity field.

Mass, Heat and Salt Balances in the Eastern Barents Sea Obtained by Inversion of Hydrographic Section Data

Standard hydrological section data, collected in the eastern Barents Sea in September 1997, have been analyzed using a variational data assimilation technique. This method allows us to obtain temperature, salinity and velocity fields that are consistent with observations and dynamically balanced within the framework of a steady-state model describing large-scale nearly geostrophic circulation. Error bars of the optimized fields are computed by explicit inversion of the Hessian matrix. The optimized velocity field is in agreement with independent velocity observations derived from surface drifter trajectories in the southwestern part of the Barents Sea. Optimized fields provide the following estimates of integral characteristics of the circulation in the region: i) the North Cape current transport is 2.12 ± 0.25 Sv; ii) the Karskie Vorota Strait throughflow is 0.7 ± 0.06 Sv; iii) heat flux with Atlantic water is 4.7 ± 0.16⋅1011 W; iv) salt import from the Atlantic Ocean is 7.41 ± 0.46⋅103 kg/s. The imbalance of the heat budget in the eastern part of the Barents Sea indicates the presence of statistically insignificant surface heat fluxes which are less than 1 W/m2.