quasi-3D Method Research Articles

Ultrafast quasi-three-dimensional imaging

Understanding laser induced ultrafast processes with complex three-dimensional (3D) geometries and extreme property evolution offers a unique opportunity to explore novel physical phenomena and to overcome the manufacturing limitations. Ultrafast imaging offers exceptional spatiotemporal resolution and thus has been considered an effective tool. However, in conventional single-view imaging techniques, 3D information is projected on a two-dimensional plane, which leads to significant information loss that is detrimental to understanding the full ultrafast process. Here, we propose a quasi-3D imaging method to describe the ultrafast process and further analyze spatial asymmetries of laser induced plasma. Orthogonally polarized laser pulses are adopted to illuminate reflection-transmission views, and binarization techniques are employed to extract contours, forming the corresponding two-dimensional matrix. By rotating and multiplying the two-dimensional contour matrices obtained from the dual views, a quasi-3D image can be reconstructed. This successfully reveals dual-phase transition mechanisms and elucidates the diffraction phenomena occurring outside the plasma. Furthermore, the quasi-3D image confirms the spatial asymmetries of the picosecond plasma, which is difficult to achieve with two-dimensional images. Our findings demonstrate that quasi-3D imaging not only offers a more comprehensive understanding of plasma dynamics than previous imaging methods, but also has wide potential in revealing various complex ultrafast phenomena in related fields including strong-field physics, fluid dynamics, and cutting-edge manufacturing.

Semianalytical Model of Multiphase Halbach Array Axial Flux Permanent-Magnet Motor Considering Magnetic Saturation

This paper proposes a nonlinear semi-analytical model (SAM) of the multi-phase Halbach array axial flux permanent magnet motor (AFPMM) to speed up the computation of its magnetic field. Compared to the existing analytical models, the proposed nonlinear SAM can directly consider magnetic saturation to obtain more accurate results. To this end, the multi-phase Halbach Array AFPMM is equivalent to several 2-D models by the Quasi-3D method under the Cartesian coordinate system. Then, the nonlinear SAM is developed by using the convolution theorem and the fast Fourier factorization. The proposed nonlinear SAM is studied on a five-phase Halbach array AFPMM with different rotors, and the nonlinear finite element (FE) model and experiment verify its effectiveness. The proposed SAM is computationally efficient and accurate, and it is also applicable to other types of multi-phase Halbach array PM electrical motors in Cartesian coordinates.

Research on Aerodynamic Design of an End Wall Based on a Quasi-3D Optimization Method

To investigate the effects of different passage structures on the aerodynamic performance of the transonic fans, this paper develops a reliable and practical quasi-3D optimization method for the hub based on the experimental data of Stage 67. In the method, the hub profile of Stage 67 can be optimized without changing the geometrical data of the blades. The optimization results show that stream tube diffusion characteristics depend on the hub profile’s curvature in the boundary layer near the hub. In the front part of the hub, the end wall with a concave construction can enhance the expansion of the stream tubes near the root of the rotor blade, which helps control the diffusion flow of viscous fluid effectively to decrease the low-energy fluid’s energy degradation and radial secondary flow in the boundary layer. In the latter part of the hub, the end wall with a convex construction facilitates the shrinkage of stream tubes to decrease the secondary flow loss and separated flow loss by controlling the separation of the boundary layer efficiently. This construction of the hub profile is beneficial to promote the aerodynamic performance of a transonic fan.

Prediction of spontaneous imbibition with gravity in porous media micromodels

In this work, theoretical modelling, quasi-three-dimensional (quasi-3D) simulations and micromodel experiments are conducted to study spontaneous imbibition with gravity in porous media micromodels. By establishing the force balance governing the spontaneous imbibition process, we develop a theoretical model for predicting the imbibition length against time in a rectangular capillary. The theoretical model is then extended to the prediction of a compact displacement process in a micromodel by using an equivalent width, which is derived by analogising the micromodel to a rectangular capillary. By simulating spontaneous imbibition in a rectangular capillary with various aspect ratios ( $\varepsilon$ ), we show that the application condition of the quasi-3D method is $\varepsilon \leqslant 1/3$ . Next, we simulate spontaneous imbibition in micromodels with various geometries and flow conditions. Fingering and compact displacement are identified for varying viscosity ratios and gravitational accelerations. At low (high) viscosity ratio of wetting to non-wetting fluids, an upward (downward) gravity can promote the stability of the wetting front, favouring the transition from fingering to compact displacement. In addition, we find that the depth-oriented interface curvature dominates the capillary effect during the imbibition, and such a mechanism is considered by introducing an equivalent contact angle into the theoretical model. With the help of equivalent width and contact angle, the theoretical model is shown to provide satisfactory prediction of the compact displacement process. Finally, a micromodel experiment is presented to further verify the developed theoretical model and the quasi-3D simulation.

Analysis and comparison of the 2D/1D and quasi-3D methods with the direct transport code SHARK

The 2D/1D method has become the mainstream of the direct transport calculation considering the balance of accuracy and efficiency. However, the 2D/1D method still suffers from stability issues. Recently, a quasi-3D method has been proposed with axial Legendre expansion. Analysis and comparison of the 2D/1D and quasi-3D method is conducted in theory from the equation derivation. Besides, the C5G7 benchmark, the KUCA benchmark and the macro BEAVRS benchmark are calculated to verify the theory comparisons of these two methods with the direct transport code SHARK. All results show that the quasi-3D method has better stability and accuracy than the 2D/1D method with worse efficiency and memory cost. It provides a new option for direct transport calculation with the quasi-3D method.

Unsteady Modeling of Turbochargers for Automotive Applications by Means of a Quasi3D Approach

Abstract This work describes the development and the application of a quasi3D method for the simulation of turbochargers for automotive applications under unsteady flow conditions. The quasi3D approach is based on the solution of conservation equations for mass, momentum, and energy for unsteady flows and applied to zero-dimensional (0D) and one-dimensional (1D) elements arbitrarily oriented in the space. The compressor is divided into different regions, each one treated numerically in a different way. For the impeller region, a relative reference system has been used, and the presence of a centrifugal force field has been introduced both in the momentum and energy conservation equations. The direction of the ports at the inlet and outlet of the impeller are used to determine the design flow angles and therefore the deviation during off-design conditions. Conversely in the vaneless diffuser, the conservation of the angular momentum of the flow stream has been imposed in the tangential direction and then combined with the solution of the momentum equation in the radial direction. The model has been validated against measurements carried out on the test bench of the University of Genoa both in diabatic and adiabatic conditions.

A quasi-3D direct transport method in the direct transport code KuaFu

The 2D/1D transport method is suffered from the stability issues, which affects the application in direct whole-core transport calculation for advanced nuclear reactors. The root of stability issues in the 2D/1D method is researched. To overcome the bottleneck of the stability issues, a quasi-3D method with axial difference relationship is derived, developed and analyzed based on the 2D/1D method. The quasi-3D method is applied in a newly-developed direct transport code KuaFu. Verification of KuaFu is conducted by several benchmarks, such as the C5G7 benchmark. All numerical results show the good accuracy of the quasi-3D method in KuaFu.

Free vibration and transient analysis of advanced composite plates using a new higher-order shear and normal deformation theory

This study makes an attempt at analyzing free vibration and transient behavior of advanced composites such as FGM plates by isogeometric approach. A new hybrid-type HSDT capable of taking into account through-thickness expansion for the dynamic analysis is developed and coupled with the NURBS-based IGA method. The quasi-3D theory in which the transverse displacement is divided into the bending and shear terms employs the independent shear and normal shape functions. The Hamilton’s principle is used to derive the governing equilibrium equations for the dynamic problem. Some numerical examples available in the relevant literature are first simulated to verify the proposed quasi-3D analysis method, and their results are matched with the reference values. The accuracy and effectiveness of the present higher-order shear and normal deformation theory combined with the IGA method in obtaining solution for the free vibration and transient response are evidenced. Illustrative parametric studies are also performed to further investigate the effects of the plate geometric parameter, ingredient fraction, boundary condition and FGM constituents, all of which have significant influences on the dynamic and transient behavior.

VIV modelled using simplified cable dynamics coupled to sub-critical cylinder flow simulations in a moving reference frame

This work focuses on the study of the phenomenon of vortex-induced vibrations in overhead lines under the effect of weak winds. Full three-dimensional simulation is not feasible because of the high length to width aspect ratios of the overhead lines. Thus a quasi-3D method based on strip theory is adopted in this work. This method decouples the system of interactions between the overhead line and the wind into a series of sub-systems. The fluid flow in each sub-system is represented as a series of independent rigid oscillating cylinder flows that are only coupled through the transmission line model. To avoid the use of a moving mesh for the fluid domain, a moving reference frame approach is employed. In this approach, the coordinate axes of the flow simulation are attached to the oscillating cylinder and an acceleration term in the flow equations accounts for the cable motion. Moreover, in order to take into account the turbulent effect in the flow, turbulence models, including RANS, LES and DES, are evaluated for the present application involving flows in the sub-critical regime. Finally, numerical test cases are performed in order to validate the turbulence models and the moving reference frame approach, then cable dynamics test cases are conducted to validate the quasi-3D method.

Layerwise Theories of Laminated Composite Structures and Their Applications: A Review

It is very challenging to accurately analyze the displacement and stress fields in the laminated composite structures due to the transverse anisotropy and higher transverse flexibilities. The equivalent single-layer theory (EST) is first developed to simplify this complex 3D problem to a pure 2D problem based on a displacement assumption in the thickness direction. The EST gives good results for the global responses of the very thin laminates with minimum computation cost, but poor results for the local responses at the interfaces and can not presents the zig-zag distribution of in-plane displacements. The elasticity solutions based on the 3D displacement-based finite element method (FEM) can present the accurate displacement and stress fields, but requires huge computational cost. As a quasi 3D method, the layerwise theories (LWT) is more accurate than most of the ESTs, and its computational cost is less than that of the 3D-based displacement FEMs, so it is attracting more and more attention with the rapid development of computer technology. This paper presents an overall review for the LWTs of the laminated composite structures and their applications. In general, there are two basic schemes employed to establish a LWT according to the construction of the displacements fields in the thickness direction. In the first scheme, the laminated composite structures are described as an assembly of individual layers, and these individual layers are combined by the interlaminar relationships to keep the displacement continuity and stress equilibrium. All of the individual layers are simulated by using the EST. In the second scheme, the displacement and/or stress fields along the thickness direction are constructed by a 1D interpolation functions and the in-plane displacement and/or stress fields are discretized by the 2D finite elements. The review in this paper is organized by the this classification.

The optimal gas dynamic design system of industrial centrifugal compressors based on Universal modeling method

We present the modern stage of development of Universal Modeling Method, a complex of mathematical models and software for optimal design of centrifugal compressors - a new version of simplified mathematical model of efficiency and new software for variation calculations of multistage compressors. Based on this numerical calculation complex we have created a method for preliminary design of flow paths of stages - 2D and 3D impellers, vane and vaneless diffusers and return channels. The new, 9th version of its mathematical model features a quasi-3D calculation method of 2D and 3D impellers design, a new principle of pressure characteristic calculation, a new model of vaneless diffusers and much more. “Digital twin of a centrifugal compressor stage” and “3D compressor” software create digital descriptions of the flow part and its solid model (“digital twin”).

Inverse Design of a Centrifugal Pump on the Meridional Plane Using Ball-Spine Algorithm

In this work, an inverse design algorithm called Ball-Spine (BSA) is developed as a quasi-3D method and applied to the meridional plane of a centrifugal pump impeller in an effort to improve its performance. In this method, numerical analyses of viscous flow field in the passage between two blades are coupled with BSA to modify the corresponding hub and shroud geometries. Here, full 3D Navier-Stokes equations are solved within a thin plane of flow instead of solving inviscid, quasi-3D flow equations in the meridional plane. To demonstrate the validity of the present work, the performance of a centrifugal pump is first numerically investigated, and then compared against available experimental data. Defining a target pressure distribution on the hub and shroud surfaces of the flow passage, a new impeller geometry is then obtained in accordance with the modified pressure distribution. The results indicate a good rate of convergence and desirable stability of BSA in the design of rotating flow passages. Overall, the proposed design method resulted in the following major improvements: an increase in static pressure along the streamline, 5% of increase in the pump total head and delay in the onset of flow cavitation inside the impeller.

A Quasi‐3D Numerical Model for Grout Injection in a Parallel Fracture Based on Finite Volume Method

The purpose of the present work is to develop a quasi‐3D numerical method that can be used to study the diffusion mechanism of grout injection in a rock fracture based on the collocated structured grid of the finite volume method (FVM). Considering the characteristics of fracture in geometry that the aperture is much less than its length and width, the Hele‐Shaw model is introduced to deduce the z-derivatives of velocities u and v at walls, which is a function of the relevant average velocity and the fracture aperture. The traditional difference scheme for the diffusive term is partly substituted with the derived analytical expressions; hence a three‐dimensional problem of grout flow in the parallel fracture can be transformed into a two‐dimensional one that concerns fracture aperture. The new model is validated by the analytical solution and experimental data on three cases of grouting in the parallel‐plate fracture. Compared with the results from ANSYS‐Fluent software, the present model shows better agreement with the analytical solution for the distribution of pressure and velocity. Furthermore, the new model needs less grid unit, spends less time, but achieves greater accuracy. The complexity of the grout flow field in the rock fracture is reduced; thus the computational efficiency can be improved significantly.

A New Effective-Conducting-Path-Driven Subthreshold Behavior Model for Junctionless Dual-Material Omega-Gate Nano-MOSFETs

In this paper, a generalized analytical subthreshold behavior model for junctionless omega-gate (JLΩG) MOSFETs combining dual-material gate (DMG) is built. Through the effective conducting path effects (ECPEs), we propose a new concept of off-center ratio (δ) dominating the effective scaling length to derive our model based on the effective conducting central potential (Φ eff,C ), obtained by quasi-3D potential method. It provides a more accurate expression of scaling equation for JLΩGFETs and leads to an improved subthreshold behavior prediction. Accounting for these renewed potential and current models, we utilize dual materials to achieve better immunity to short channel effects. The proposed modeling can be extensively applied to other multiple-gate (MG) nano-transistors as well.

Size dependent bending analysis of two directional functionally graded microbeams via a quasi-3D theory and finite element method

Abstract This paper presents the flexural behaviour of two directional functionally graded (2D-FG) microbeams subjected to uniformly distributed load with various boundary conditions. A four-unknown shear and normal deformation theory or quasi-3D one is employed based on the modified couple stress theory, Ritz method and finite element formulation. The material properties are assumed to vary through the thickness and longitudinal axis and follow the power-law distribution. Firstly, the static deformations of conventional FG microbeams are investigated to verify the developed finite element code. For the convergence studies, a simply supported FG microbeam is considered by employing various number of elements in the problem domain, aspect ratios, material length scale parameters and gradient indexes. The verification of the developed code is established and then extensive studies are performed for various boundary conditions. Secondly, since there is no reported data regarding to the analysis of 2D-FG microbeams, verification studies are performed for 2D-FG beams with different aspect ratios and gradient indexes. The effects of the normal and shear deformations as well as and material length scale parameters on the flexural behaviour of the 2D-FG microbeams are investigated. Finally, some new results for deflections of conventional FG and 2D-FG microbeams for various boundary conditions are introduced for the first time and can be used as reference for future studies.

A Novel Quasi-3D Method for Cascade Flow Considering Axial Velocity Density Ratio

Abstract A novel quasi-3D Computational Fluid Dynamics (CFD) method of mid-span flow simulation for compressor cascades is proposed. Two dimension (2D) Reynolds-Averaged Navier-Stokes (RANS) method is shown facing challenge in predicting mid-span flow with a unity Axial Velocity Density Ratio (AVDR). Three dimension (3D) RANS solution also shows distinct discrepancies if the AVDR is not predicted correctly. In this paper, 2D and 3D CFD results discrepancies are analyzed and a novel quasi-3D CFD method is proposed. The new quasi-3D model is derived by reducing 3D RANS Finite Volume Method (FVM) discretization over a one-spanwise-layer structured mesh cell. The sidewall effect is considered by two parts. The first part is explicit interface fluxes of mass, momentum and energy as well as turbulence. The second part is a cell boundary scaling factor representing sidewall boundary layer contraction. The performance of the novel quasi-3D method is validated on mid-span pressure distribution, pressure loss and shock prediction of two typical cascades. The results show good agreement with the experiment data on cascade SJ301-20 and cascade AC6-10 at all test condition. The proposed quasi-3D method shows superior accuracy over traditional 2D RANS method and 3D RANS method in performance prediction of compressor cascade.

Quasi-3D two-phase model for dam-break flow over movable bed based on a non-hydrostatic depth-integrated model with a dynamic rough wall law

The assumptions of equilibrium flow conditions neglecting the flow acceleration for vertical velocity distributions and of the equilibrium wall law applied to the bottom boundary condition, in which the flow acceleration is neglected in the vicinity of the bed, are questionable when used to calculate sediment transport for flows that vary rapidly over time and space. Examples of such flows include dam-break flows and flows around structures. This study proposes a two-phase depth-integrated model for large-scale geophysical flow applications involving sediment transport phenomena and bed morphology. The model for the fluid phase is based on the non-hydrostatic quasi-3D method, and uses a dynamic rough wall law that employs continuity and momentum equations for the bottom boundary conditions.It was confirmed that the proposed model reduces to the previous bedload formulae for uniform flow conditions under the weak sediment transport condition. The model was applied in an experiment involving a dam-break flow on a movable bed channel with a suddenly enlarged section. The comparison between the experimental results and the results calculated with the proposed model and previous models demonstrates the validity of the proposed model. The comparison also highlights the advantages of introducing a quasi-3D two-phase model to evaluate vertical velocity distributions and non-equilibrium sediment motions.

Analysis of AFPM machines with cylindrically shaped magnets using quasi-3D method

PurposeThe purpose of this paper is the fast and accurate modelling of surface-mounted Axial-Flux Permanent-Magnet (AFPM) machines equipped with cylindrical magnets using quasi-3D approach. Furthermore, the accuracy of the method is improved by using leakage coefficient, saturation coefficient and an appropriate permeance function.Design/methodology/approachQuasi-3D approach is used for fast and accurate modelling of AFPM machines. Air-gap flux density distribution, induced back EMF, and produced cogging torque are calculated using the proposed method with reasonable accuracy.FindingsThe results obtained by quasi-3D approach compared to Finite-Element-Analyses (FEA) shows how accurate, fast and efficient this method is. It is proved that, this method can be successfully applied to evaluate the performance of the AFPM machines.Originality/valueEffectiveness and accuracy of quasi-3D approach is assessed on different AFPM machines. Furthermore, to increase the accuracy of computations, the effects of the magnetic potential drop at iron parts of the machine are taken into account by using a saturation coefficient. Besides, the influence of the slot opening on the flux density distribution is taken into account by using an appropriate relative permeance function.

Discussion on applying an analytical method to optimize the anti-freeze design parameters for underground water pipelines in seasonally frozen areas

Adopting the quasi-three-dimensional (Quasi-3D) numerical method to optimize the anti-freeze design parameters of an underground pipeline usually involves heavy numerical calculations. Here, the fitting formulae between the safe conveyance distance (SCD) of a water pipeline and six influencing factors are established based on the lowest water temperature (LWT) along the pipeline axis direction. With reference to the current widely used anti-freeze design approaches for underground pipelines in seasonally frozen areas, this paper first analyzes the feasibility of applying the maximum frozen penetration (MFP) instead of the mean annual ground surface temperature (MAGST) and soil water content (SWC) to calculate the SCD. The results show that the SCD depends on the buried depth if the MFP is fixed and the variation of the MAGST and SWC combination does not significantly change the SCD. A comprehensive formula for the SCD is established based on the relationships between the SCD and several primary influencing factors and the interaction among them. This formula involves five easy-to-access parameters: the MFP, buried depth, pipeline diameter, flow velocity, and inlet water temperature. A comparison between the analytical method and the numerical results based on the Quasi-3D method indicates that the two methods are in good agreement overall. The analytic method can be used to optimize the anti-freeze design parameters of underground water pipelines in seasonally frozen areas under the condition of a 1.5 safety coefficient.

Quasi-3D modeling of surface potential and threshold voltage of Triple Metal Quadruple Gate MOSFETs

In this paper we present electrostatic model of 3D Triple Metal Quadruple Gate (TMQG) MOSFET of rectangular cross-section based on quasi-3D method. The analytical equations for channel potential and characteristic length have been derived by decomposing TMQG into two 2D perpendicular cross-sections (triple metal double gate, TMDG) and the effective characteristic length of TMQG is found using equivalent number of gates (ENG) method. For each of the TMDG, 2D Poisson's equation is solved by parabolic approximation and proper boundary conditions to calculate channel potential. The threshold voltage expression is developed using inversion carrier charge sheet density method. The developed models for channel potential and threshold voltage are validated using numerical simulations of TMQG. The developed model provides the design guidelines for TMQG with improved HCEs and SCEs.