Parabolic trough solar collector is the most proven industry-scale solar generation technology today available. The thermal performance of such devices is of major interest for optimising the solar field output and increase the efficiency of power plants. In this paper, a detailed numerical heat transfer model based on the finite volume method for these equipment is presented. In the model, the different elements of the receiver are discretised into several segments in both axial and azimuthal directions and energy balances are applied for each control volume. An optical model is also developed for calculating the non-uniform solar flux distribution around the receiver. This model is based on finite volume method and ray trace techniques and takes into account the finite size of the Sun. The solar heat flux is determined as a pre-processing task and coupled to the energy balance model as a boundary condition for the outer surface of the receiver. The set of algebraic equations are solved simultaneously using direct solvers. The model is thoroughly validated with results from the literature. First, the optical model is compared with known analytical solutions. After that, the performance of the overall model is tested against experimental measurements from Sandia National Laboratories and other un-irradiated receivers experiments. In all cases, results obtained shown a good agreement with experimental and analytical results.Peer ReviewedPreprin

The direct numerical simulation of the flow over a sphere is performed. The computations are carried out in the sub-critical regime at Re = 3700 (based on the free-stream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation is used for simulating the flow. At this Reynolds number, flow separates laminarly near the equator of the sphere and transition to turbulence occurs in the separated shear layer. The vortices formed are shed at a large-scale frequency, S_t = 0.215, and at random azimuthal locations in the shear layer, giving a helical-like appearance to the wake. The main features of the flow including the power spectra of a set of selected monitoring probes at different positions in the wake of the sphere are described and discussed in detail. In addition, a large number of turbulence statistics are computed and compared with previous experimental and numerical data at comparable Reynolds numbers. Particular attention is devoted to assessing the prediction of the mean flow parameters, such as wall-pressure distribution, skin friction, drag coefficient, among others, in order to provide reliable data for testing and developing statistical turbulence models. In addition to the presented results, the capability of the methodology used on unstructured grids for accurately solving flows in complex geometries is also pointed out.

The presence of low-frequency fluctuations in the wake of bluff bodies have been observed in several investigations. Even though the flow past a circular cylinder at Re = 3900 (Re = UrefD/ν) has been the object of several experimental and numerical investigations, there is a large scattering in the average statistics in the near wake. In the present work, the flow dynamics of the near wake region behind a circular cylinder has been investigated by means of direct numerical simulations and statistics have been computed for more than 858 shedding cycles. The analysis of instantaneous velocity signals of several probes located in the vortex formation region, point out the existence of a low-frequency fluctuation at the non-dimensional frequency of fm = 0.0064. This large-scale almost periodic motion seems to be related with the modulation of the recirculation bubble which causes its shrinking and enlargement over the time. Two different configurations have been identified: (i) a high-energy mode with larger fluctuations in the shear-layer and in the vortex formation region (Mode H) and (ii) a low-energy mode with weaker fluctuations in the shear layer (Mode L). The influence of such a low-frequency in the wake topology has been studied not only by means of the phase-average flow field for each mode, but also by the analysis of the time-average first- and second-order statistics of each wake mode. The results are compared with the long-term averaged solution and with results in the existing literature.

Large-eddy simulations (LES) of the flow past a circular cylinder are used to investigate the flow topology and the vortex shedding process at Reynolds numbers Re=2.5×105-8.5×105Re=2.5×105-8.5×105. This range encompasses both the critical and super-critical regimes. As the flow enters the critical regime, major changes occur which affect the flow configuration. Asymmetries in the flow are found in the critical regime, whereas the wake recovers its symmetry and stabilizes in the super-critical regime. Wake characteristic lengths are measured and compared between the different Reynolds numbers. It is shown that the super-critical regime is characterised by a plateau in the drag coefficient at about CD˜0.22CD˜0.22, and a quasi-stable wake which has a non-dimensional width of dw/D˜0.4dw/D˜0.4. The periodic nature of the flow is analysed by means of measurements of the unsteady drag and lift coefficients. Power spectra of the lift fluctuations are computed. Wake vortex shedding is found to occur for both regimes investigated, although a jump in frequencies is observed when the flow enters the super-critical regime. In this regime, non-dimensional vortex-shedding frequency is almost constant and equal to St=fvsD/Uref˜0.44St=fvsD/Uref˜0.44. The analysis also shows a steep decrease in the fluctuating lift when entering the super-critical regime. The combined analysis of both wake topology and vortex shedding complements the physical picture of a stable and highly coherent flow in the super-critical regime.Peer ReviewedPostprint (author's final draft

It is well known that the flow past a circular cylinder at critical Reynolds number combines flow separation, turbulence transition, reattachment of the flow, and further turbulent separation of the boundary layer. The transition to turbulence in the boundary layer causes the delaying of the separation point and an important reduction of the drag force on the cylinder surface known as the drag crisis. In the present work, large-eddy simulations of the flow past a cylinder at Reynolds numbers in the range 2.5 × 10⁵-6.5 × 10⁵ are performed. It is shown how the pressure distribution changes as the Reynolds number increases in an asymmetric manner, occurring first on one side of the cylinder and then on the other side to complete the drop in the drag up to 0.23 at Re = 6.5 × 10⁵. These variations in the pressure profile are accompanied by the presence of a small recirculation bubble, observed as a small plateau in the pressure, and located around ϕ = 105^∘ (measured from the stagnation point). This small recirculation bubble anticipated by the experimental measurements is here well captured by the present computations and its position and size measured at every Reynolds number. The changes in the wake configuration as the Reynolds number increases are also shown and their relation to the increase in the vortex shedding frequency is discussed. The power spectra for the velocity fluctuations are computed. The analysis of the resulting spectrum showed the footprint of Kelvin-Helmholtz instabilities in the whole range. It is found that the ratio of these instabilities frequency to the primary vortex shedding frequency matches quite well the scaling proposed by Prasad and Williamson [“The instability of the separated shear layer from a bluff body,” Phys. Fluids 8, 1347 (1996); “The instability of the shear layer separating from a bluff body,” J. Fluid Mech. 333, 375–492 (1997)] (f_KH/f_vs ∝ Re^0.67).