Fachbereich Ingenieurwissenschaften und Kommunikation
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Fundamental hydrogen storage properties of TiFe-alloy with partial substitution of Fe by Ti and Mn
(2020)
TiFe intermetallic compound has been extensively studied, owing to its low cost, good volumetric hydrogen density, and easy tailoring of hydrogenation thermodynamics by elemental substitution. All these positive aspects make this material promising for large-scale applications of solid-state hydrogen storage. On the other hand, activation and kinetic issues should be amended and the role of elemental substitution should be further understood. This work investigates the thermodynamic changes induced by the variation of Ti content along the homogeneity range of the TiFe phase (Ti:Fe ratio from 1:1 to 1:0.9) and of the substitution of Mn for Fe between 0 and 5 at.%. In all considered alloys, the major phase is TiFe-type together with minor amounts of TiFe2 or \b{eta}-Ti-type and Ti4Fe2O-type at the Ti-poor and rich side of the TiFe phase domain, respectively. Thermodynamic data agree with the available literature but offer here a comprehensive picture of hydrogenation properties over an extended Ti and Mn compositional range. Moreover, it is demonstrated that Ti-rich alloys display enhanced storage capacities, as long as a limited amount of \b{eta}-Ti is formed. Both Mn and Ti substitutions increase the cell parameter by possibly substituting Fe, lowering the plateau pressures and decreasing the hysteresis of the isotherms. A full picture of the dependence of hydrogen storage properties as a function of the composition will be discussed, together with some observed correlations.
Long-term variability of solar irradiance and its implications for photovoltaic power in West Africa
(2020)
This paper addresses long-term changes in solar irradiance for West Africa (3° N to 20° N and 20° W to 16° E) and its implications for photovoltaic power systems. Here we use satellite irradiance (Surface Solar Radiation Data Set-Heliosat, Edition 2.1, SARAH-2.1) to derive photovoltaic yields. Based on 35 years of data (1983–2017) the temporal and regional variability as well as long-term trends of global and direct horizontal irradiance are analyzed. Furthermore, at four locations a detailed time series analysis is undertaken. The dry and the wet season are considered separately.
4GREAT is an extension of the German Receiver for Astronomy at Terahertz frequencies (GREAT) operated aboard the Stratospheric Observatory for Infrared Astronomy (SOFIA). The spectrometer comprises four different detector bands and their associated subsystems for simultaneous and fully independent science operation. All detector beams are co-aligned on the sky. The frequency bands of 4GREAT cover 491-635, 890-1090, 1240-1525 and 2490-2590 GHz, respectively. This paper presents the design and characterization of the instrument, and its in-flight performance. 4GREAT saw first light in June 2018, and has been offered to the interested SOFIA communities starting with observing cycle 6.
In recent years, a plethora of observations with high spectral resolution of sub-millimetre and far-infrared transitions of methylidene (CH), conducted with Herschel and SOFIA, have demonstrated this radical to be a valuable proxy for molecular hydrogen that can be used for characterising molecular gas within the interstellar medium on a Galactic scale, including the CO-dark component. We report the discovery of the 13CH isotopologue in the interstellar medium using the upGREAT receiver on board SOFIA. We have detected the three hyperfine structure components of the ≈2 THz frequency transition from its X2Π1∕2 ground-state towards the high-mass star-forming regions Sgr B2(M), G34.26+0.15, W49(N), and W51E and determined 13CH column densities. The ubiquity of molecules containing carbon in the interstellar medium has turned the determination of the ratio between the abundances of the two stable isotopes of carbon, 12C/13C, into a cornerstone for Galactic chemical evolution studies. Whilst displaying a rising gradient with galactocentric distance, this ratio, when measured using observations of different molecules (CO, H2CO, and others), shows systematic variations depending on the tracer used. These observed inconsistencies may arise from optical depth effects, chemical fractionation, or isotope-selective photo-dissociation. Formed from C+ either through UV-driven or turbulence-driven chemistry, CH reflects the fractionation of C+, and does not show any significant fractionation effects, unlike other molecules that were previously used to determine the 12C/13C isotopic ratio. This makes it an ideal tracer for the 12C/13C ratio throughout the Galaxy. By comparing the derived column densities of 13CH with previously obtained SOFIA data of the corresponding transitions of the main isotopologue 12CH, we therefore derive 12C/13C isotopic ratios toward Sgr B2(M), G34.26+0.15, W49(N) and W51E. Adding our values derived from 12∕13CH to previous calculations of the Galactic isotopic gradient, we derive a revised value of 12C/13C = 5.87(0.45)RGC + 13.25(2.94).
The temperature of photovoltaic modules is modelled as a dynamic function of ambient temperature, shortwave and longwave irradiance and wind speed, in order to allow for a more accurate characterisation of their efficiency. A simple dynamic thermal model is developed by extending an existing parametric steady-state model using an exponential smoothing kernel to include the effect of the heat capacity of the system. The four parameters of the model are fitted to measured data from three photovoltaic systems in the Allgäu region in Germany using non-linear optimisation. The dynamic model reduces the root-mean-square error between measured and modelled module temperature to 1.58 K on average, compared to 3.03 K for the steady-state model, whereas the maximum instantaneous error is reduced from 20.02 to 6.58 K.
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.
Turbulent compressible flows are traditionally simulated using explicit Eulerian time integration applied to 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 elegantly circumvents this restriction. Previous lattice Boltzmann methods for compressible flows were mostly restricted to two dimensions due to the enormous number of discrete velocities needed in three dimensions. In contrast, this Rapid Communication demonstrates how cubature rules enhance the SLLBM to yield a three-dimensional velocity set with only 45 discrete velocities. Based on simulations of a compressible Taylor-Green vortex we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques, 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 for the first time to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time step sizes is only dictated by physics, while being decoupled from the spatial discretization.
The general method of topological reduction for the network problems is presented on example of gas transport networks. The method is based on a contraction of series, parallel and tree-like subgraphs for the element equations of quadratic, power law and general monotone dependencies. The method allows to reduce significantly the complexity of the graph and to accelerate the solution procedure for stationary network problems. The method has been tested on a large set of realistic network scenarios. Possible extensions of the method have been described, including triangulated element equations, continuation of the equations at infinity, providing uniqueness of solution, a choice of Newtonian stabilizer for nearly degenerated systems. The method is applicable for various sectors in the field of energetics, including gas networks, water networks, electric networks, as well as for coupling of different sectors.
Alkaline methanol oxidation is an important electrochemical process in the design of efficient fuel cells. Typically, a system of ordinary differential equations is used to model the kinetics of this process. The fitting of the parameters of the underlying mathematical model is performed on the basis of different types of experiments, characterizing the fuel cell. In this paper, we describe generic methods for creation of a mathematical model of electrochemical kinetics from a given reaction network, as well as for identification of parameters of this model. We also describe methods for model reduction, based on a combination of steady-state and dynamical descriptions of the process. The methods are tested on a range of experiments, including different concentrations of the reagents and different voltage range.
Solving differential-algebraic equations (DAEs) efficiently by means of appropriate numerical schemes for time-integration is an ongoing topic in applied mathematics. In this context, especially when considering large systems that occur with respect to many fields of practical application effective computation becomes relevant. In particular, corresponding examples are given when having to simulate network structures that consider transport of fluid and gas or electrical circuits. Due to the stiffness properties of DAEs, time-integration of such problems generally demands for implicit strategies. Among the schemes that prove to be an adequate choice are linearly implicit Rung-Kutta methods in the form of Rosenbrock-Wanner (ROW) schemes. Compared to fully implicit methods, they are easy to implement and avoid the solution of non-linear equations by including Jacobian information within their formulation. However, Jacobian calculations are a costly operation. Hence, necessity of having to compute the exact Jacobian with every successful time-step proves to be a considerable drawback. To overcome this drawback, a ROW-type method is introduced that allows for non-exact Jacobian entries when solving semi-explicit DAEs of index one. The resulting scheme thus enables to exploit several strategies for saving computational effort. Examples include using partial explicit integration of non-stiff components, utilizing more advantageous sparse Jacobian structures or making use of time-lagged Jacobian information. In fact, due to the property of allowing for non-exact Jacobian expressions, the given scheme can be interpreted as a generalized ROW-type method for DAEs. This is because it covers many different ROW-type schemes known from literature. To derive the order conditions of the ROW-type method introduced, a theory is developed that allows to identify occurring differentials and coefficients graphically by means of rooted trees. Rooted trees for describing numerical methods were originally introduced by J.C. Butcher. They significantly simplify the determination and definition of relevant characteristics because they allow for applying straightforward procedures. In fact, the theory presented combines strategies used to represent ROW-type methods with exact Jacobian for DAEs and ROW-type methods with non-exact Jacobian for ODEs. For this purpose, new types of vertices are considered in order to describe occurring non-exact elementary differentials completely. The resulting theory thus automatically comprises relevant approaches known from literature. As a consequence, it allows to recognize order conditions of familiar methods covered and to identify new conditions. With the theory developed, new sets of coefficients are derived that allow to realize the ROW-type method introduced up to orders two and three. Some of them are constructed based on methods known from literature that satisfy additional conditions for the purpose of avoiding effects of order reduction. It is shown that these methods can be improved by means of the new order conditions derived without having to increase the number of internal stages. Convergence of the resulting methods is analyzed with respect to several academic test problems. Results verify the theory determined and the order conditions found as only schemes satisfying the order conditions predicted preserve their order when using non-exact Jacobian expressions.
This paper addresses long-term historical changes in solar irradiance in West Africa (3 to 20° N and 20° W to 16° E) and the implications for photovoltaic systems. Here, we use satellite irradiance (Surface Solar Radiation Data Set – Heliosat, Edition 2.1 – SARAH-2.1) and temperature data from a reanalysis (ERA5) to derive photovoltaic yields. Based on 35 years of data (1983–2017), the temporal and regional variability as well as long-term trends in global and direct horizontal irradiance are analyzed. Furthermore, a detailed time series analysis is undertaken at four locations. According to the high spatial resolution SARAH-2.1 data record (0.05°×0.05°), solar irradiance is largest (up to a 300 W m−2 daily average) in the Sahara and the Sahel zone with a positive trend (up to 5 W m−2 per decade) and a lower temporal variability (<75 W m−2 between 1983 and 2017 for daily averages). In contrast, the solar irradiance is lower in southern West Africa (between 200 W m−2 and 250 W m−2) with a negative trend (up to −5 W m−2 per decade) and a higher temporal variability (up to 150 W m−2). The positive trend in the north is mostly connected to the dry season, whereas the negative trend in the south occurs during the wet season. Both trends show 95 % significance. Photovoltaic (PV) yields show a strong meridional gradient with the lowest values of around 4 kWh kWp−1 in southern West Africa and values of more than 5.5 kWh kWp−1 in the Sahara and Sahel zone.
This dataset contains data from two measurement campaigns in autumn 2018 and summer 2019 that were part of the BMWi project "MetPVNet", and serve as a supplement to the paper "Dynamic model of photovoltaic module temperature as a function of atmospheric conditions", published in the special edition of "Advances in Science and Research", the proceedings of the 19th EMS Annual Meeting: European Conference for Applied Meteorology and Climatology 2019.
Data are resampled to one minute, and include:
PV module temperature
Ambient temperature
Plane-of-array irradiance
Windspeed
Atmospheric thermal emission
The data were used for the dynamic temperature model, as presented in the paper
Demand forecast
(2020)
Network aggregation
(2020)