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Error analysis in a high accuracy sampled-data velocity stabilising system using Volterra series
(2015)
Stably stratified Taylor–Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier–Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.
Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time-step size. Exploiting the Lagrangian nature of the Boltzmann equation’s material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which circumvents this restriction. While many lattice Boltzmann methods for compressible flows were restricted to two dimensions due to the enormous number of discrete velocities in three dimensions, the SLLBM uses only 45 discrete velocities. Based on compressible Taylor-Green vortex simulations we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques other than the filtering introduced by the interpolation, even when the time-step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time-step sizes is dictated by physics rather than spatial discretization.
This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method , the method operates in a static, non-moving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to non-uniform grids.
Off-lattice Boltzmann methods increase the flexibility and applicability of lattice Boltzmann methods by decoupling the discretizations of time, space, and particle velocities. However, the velocity sets that are mostly used in off-lattice Boltzmann simulations were originally tailored to on-lattice Boltzmann methods. In this contribution, we show how the accuracy and efficiency of weakly and fully compressible semi-Lagrangian off-lattice Boltzmann simulations is increased by velocity sets derived from cubature rules, i.e. multivariate quadratures, which have not been produced by the Gauß-product rule. In particular, simulations of 2D shock-vortex interactions indicate that the cubature-derived degree-nine D2Q19 velocity set is capable to replace the Gauß-product rule-derived D2Q25. Likewise, the degree-five velocity sets D3Q13 and D3Q21, as well as a degree-seven D3V27 velocity set were successfully tested for 3D Taylor–Green vortex flows to challenge and surpass the quality of the customary D3Q27 velocity set. In compressible 3D Taylor–Green vortex flows with Mach numbers on-lattice simulations with velocity sets D3Q103 and D3V107 showed only limited stability, while the off-lattice degree-nine D3Q45 velocity set accurately reproduced the kinetic energy provided by literature.
Rosenbrock–Wanner methods for systems of stiff ordinary differential equations are well known since the seventies. They have been continuously developed and are efficient for differential-algebraic equations of index-1, as well. Their disadvantage that the Jacobian matrix has to be updated in every time step becomes more and more obsolete when automatic differentiation is used. Especially the family of Rodas methods has proven to be a standard in the Julia package DifferentialEquations. However, the fifth-order Rodas5 method undergoes order reduction for certain problem classes. Therefore, the goal of this paper is to compute a new set of coefficients for Rodas5 such that this order reduction is reduced. The procedure is similar to the derivation of the methods Rodas4P and Rodas4P2. In addition, it is possible to provide new dense output formulas for Rodas5 and the new method Rodas5P. Numerical tests show that for higher accuracy requirements Rodas5P always belongs to the best methods within the Rodas family.
This paper presents a novel approach to address noise, vibration, and harshness (NVH) issues in electrically assisted bicycles (e-bikes) caused by the drive unit. By investigating and optimising the structural dynamics during early product development, NVH can decisively be improved and valuable resources can be saved, emphasising its significance for enhancing riding performance. The paper offers a comprehensive analysis of the e-bike drive unit’s mechanical interactions among relevant components, culminating—to the best of our knowledge—in the development of the first high-fidelity model of an entire e-bike drive unit. The proposed model uses the principles of elastic multi body dynamics (eMBD) to elucidate the structural dynamics in dynamic-transient calculations. Comparing power spectra between measured and simulated motion variables validates the chosen model assumptions. The measurements of physical samples utilise accelerometers, contactless laser Doppler vibrometry (LDV) and various test arrangements, which are replicated in simulations and provide accessibility to measure vibrations onto rotating shafts and stationary structures. In summary, this integrated system-level approach can serve as a viable starting point for comprehending and managing the NVH behaviour of e-bikes.
Design of a Medium Voltage Generator with DC-Cascade for High Power Wind Energy Conversion Systems
(2021)
This paper shows a new concept to generate medium voltage (MV) in wind power application to avoid an additional transformer. Therefore, the generator must be redesigned with additional constraints and a new topology for the power rectifier system by using multiple low voltage (LV) power rectifiers connected in series and parallel to increase the DC output voltage. The combination of parallel and series connection of rectifiers is further introduced as DC-cascade. With the resulting DC-cascade, medium output voltage is achieved with low voltage rectifiers and without a bulky transformer. This approach to form a DC-cascade reduces the effort required to achieve medium DC voltage with a simple rectifier system. In this context, a suitable DC-cascade control was presented and verified with a laboratory test setup. A gearless synchronous generator, which is highly segmented so that each segment can be connected to its own power rectifier, is investigated. Due to the mixed AC and DC voltage given by the DC-cascade structure, it becomes more demanding to the design of the generator insulation, which influences the copper fill factor and the design of the cooling system. A design strategy for the overall generator design is carried out considering the new boundary conditions.
Trends of environmental awareness, combined with a focus on personal fitness and health, motivate many people to switch from cars and public transport to micromobility solutions, namely bicycles, electric bicycles, cargo bikes, or scooters. To accommodate urban planning for these changes, cities and communities need to know how many micromobility vehicles are on the road. In a previous work, we proposed a concept for a compact, mobile, and energy-efficient system to classify and count micromobility vehicles utilizing uncooled long-wave infrared (LWIR) image sensors and a neuromorphic co-processor. In this work, we elaborate on this concept by focusing on the feature extraction process with the goal to increase the classification accuracy. We demonstrate that even with a reduced feature list compared with our early concept, we manage to increase the detection precision to more than 90%. This is achieved by reducing the images of 160 × 120 pixels to only 12 × 18 pixels and combining them with contour moments to a feature vector of only 247 bytes.
Suitability of Current Sensors for the Measurement of Switching Currents in Power Semiconductors
(2021)
This paper investigates the impact of current sensors on the measurement of transient currents in fast-switching power semiconductors in a double pulse test (DPT environment. We review previous research that assesses the influence of current sensors on a DPT circuit through mathematical modeling. The developed selection aids can be used to identify suitable current sensors for transient current measurements of fast-switching power semiconductors and to estimate the error introduced by their insertion into the DPT circuit. Afterwards, this analysis is extended by including further elements from real DPT applications to increase the consistency of the error estimation with practical situations and setups. Both methods are compared and their individual advantages and drawbacks are discussed. Finally, a recommendation on when to use which method is derived.
This paper investigates the effect of voltage sensors on the measurement of transient voltages for power semiconductors in a Double Pulse Test (DPT) environment.We adapt previously published models that were developed for current sensors and apply them to voltage sensors to evaluate their suitability for DPT applications. Similarities and differences between transient current and voltage sensors are investigated and the resulting methodology is applied to commercially available and experimental voltage sensors. Finally, a selection aid for given measurement tasks is derived that focuses on the measurement of fast-switching power semiconductors.
Integrating physical simulation data into data ecosystems challenges the compatibility and interoperability of data management tools. Semantic web technologies and relational databases mostly use other data types, such as measurement or manufacturing design data. Standardizing simulation data storage and harmonizing the data structures with other domains is still a challenge, as current standards such as the ISO standard STEP (ISO 10303 ”Standard for the Exchange of Product model data”) fail to bridge the gap between design and simulation data. This challenge requires new methods, such as ontologies, to rethink simulation results integration. This research describes a new software architecture and application methodology based on the industrial standard ”Virtual Material Modelling in Manufacturing” (VMAP). The architecture integrates large quantities of structured simulation data and their analyses into a semantic data structure. It is capable of providing data permeability from the global digital twin level to the detailed numerical values of data entries and even new key indicators in a three-step approach: It represents a file as an instance in a knowledge graph, queries the file’s metadata, and finds a semantically represented process that enables new metadata to be created and instantiated.
This study addresses the common occurrence of cell-to-cell variations arising from manufacturing tolerances and their implications during battery production. The focus is on assessing the impact of these inherent differences in cells and exploring diverse cell and module connection methods on battery pack performance and their subsequent influence on the driving range of electric vehicles (EVs). The analysis spans three battery pack sizes, encompassing various constant discharge rates and nine distinct drive cycles representative of driving behaviours across different regions of India. Two interconnection topologies, categorised as “string” and “cross”, are examined. The findings reveal that cross-connected packs exhibit reduced energy output compared to string-connected configurations, which is reflected in the driving range outcomes observed during drive cycle simulations. Additionally, the study investigates the effects of standard deviation in cell parameters, concluding that an increased standard deviation (SD) leads to decreased energy output from the packs. Notably, string-connected packs demonstrate superior performance in terms of extractable energy under such conditions.