Exact solutions to non-classical steady nozzle flows of Bethe-Zel'dovich-Thompson fluids

Steady nozzle flows of Bethe-Zel'dovich-Thompson fluids - substances exhibiting non-classical gasdynamic behaviour in a finite vapour-phase thermodynamic region in close proximity to the liquid-vapour saturation curve - are examined. Non-classical flow features include rarefaction shock waves, shock waves with either upstream or downstream sonic states and split shocks. Exact solutions for a mono-component single-phase fluid expanding from a reservoir into a stationary atmosphere through a conventional converging-diverging nozzle are determined within the quasi-one-dimensional inviscid flow approximation. The novel analytical approach makes it possible to elucidate the connection between the adiabatic, possibly non-isentropic flow field and the underlying local isentropic-flow features, including the possible qualitative alterations in passing through shock waves. Contrary to previous predictions based on isentropic-flow inspection, shock disintegration is found to occur also from reservoir states corresponding to a single sonic point. The global layout of the flow configurations produced by a monotonic decrease in the ambient pressure, namely the functioning regime, is examined for reservoir conditions resulting in single-phase flows. Accordingly, a classification of steady nozzle flows into 10 different functioning regimes is proposed. Flow conditions determining the transition between the different classes of flow are investigated and each functioning regime is associated with the corresponding thermodynamic region of reservoir states

Effects of Molecular Complexity and Reservoir Conditions on the Discharge Coefficient of Adapted Planar Nozzles

The transonic flow at throat section of a convergent-divergent nozzle is studied in adapted conditions to assess the influence of the fluid molecular complexity and total thermodynamic state on the discharge coefficient. The standard Sauer method is applied to solve the transonic perturbation potential equation in the vicinity of the nozzle throat. An analytic expression is derived that allows one to compute the discharge coefficient in terms of the nozzle curvature at the throat section and of the value of the fundamental derivative of gasdynamics at sonic conditions, which depends on the fluid molecular complexity and on the thermodynamic state in the reservoir. A linear dependence of the discharge coefficient on the sonic value of the fundamental derivative of gasdynamics is exposed

A deep neural network reduced order model for unsteady aerodynamics of pitching airfoils

A machine learning framework is developed to compute the aerodynamic forces and moment coefficients for a pitching NACA0012 airfoil incurring in light and deep dynamic stall. Four deep neural network frameworks of increasing complexity are investigated: two multilayer perceptrons and two convolutional neural networks. The convolutional framework, in addition to the standard mean squared error loss, features an improved loss function to compute the airfoil loads. In total, five models are investigated of increasingly complexity. The convolutional model, coupled with the loss function based on force and moment coefficients and embedding the attention mechanism, is found to robustly and efficiently predict pressure and skin friction distributions over the airfoil over the entire pitching cycle. Periodic conditions are implemented to grant the physical smoothness of the model output both in space and time. An analysis of the training dataset point distributions is performed to point out the effects of adopting low discrepancy sequences, such as Latin hypercube, Sobol', and Halton, compared to random and uniform sequences. The current model shows improved performances in predicting forces and pitching moment in a broad range of operating conditions

Numerical simulations of ice accretion on wind turbine blades: are performance losses due to ice shape or surface roughness?

Ice accretion on wind turbine blades causes both a change in the shape of its sections and an increase in surface roughness. These lead to degraded aerodynamic performances and lower power output. Here, a high-fidelity multi-step method is presented and applied to simulate a 3 h rime icing event on the National Renewable Energy Laboratory 5 MW wind turbine blade. Five sections belonging to the outer half of the blade were considered. Independent time steps were applied to each blade section to obtain detailed ice shapes. The roughness effect on airfoil performance was included in computational fluid dynamics simulations using an equivalent sand-grain approach. The aerodynamic coefficients of the iced sections were computed considering two different roughness heights and extensions along the blade surface. The power curve before and after the icing event was computed according to the Design Load Case 1.1 of the International Electrotechnical Commission. In the icing event under analysis, the decrease in power output strongly depended on wind speed and, in fact, tip speed ratio. Regarding the different roughness heights and extensions along the blade, power losses were qualitatively similar but significantly different in magnitude despite the well-developed ice shapes. It was found that extended roughness regions in the chordwise direction of the blade can become as detrimental as the ice shape itself

Shock Tube Flows Past Partially Opened Diaphragms

Unsteady compressible flows resulting from the incomplete burst of the shock tube diaphragm are investigated both experimentally and numerically for different initial pressure ratios and opening diameters. The intensity of the shock wave is found to be lower than that corresponding to a complete opening. A heuristic relation is proposed to compute the shock strength as a function of the relative area of the open portion of the diaphragm. Strong pressure oscillations past the shock front are also observed. These multi-dimensional disturbances are generated when the initially normal shock wave diffracts from the diaphragm edges and reflects on the shock tube walls, resulting in a complex unsteady flow field behind the leading shock wave. The limiting local frequency of the pressure oscillations is found to be very close to the ratio of acoustic wave speed in the perturbed region to the shock tube diameter. The power associated with these pressure oscillations decreases with increasing distance from the diaphragm since the diffracted and reflected shocks partially coalesce into a single normal shock front. A simple analytical model is devised to explain the reduction of the local frequency of the disturbances as the distance from the leading shock increases

Efficient Lagrangian particle tracking algorithms for distributed-memory architectures

This paper focuses on the solution of the dispersed phase of Eulerian–Lagrangian one-way coupled particle laden flows. An efficient two-constraint domain partitioning for 2D and 3D unstructured hybrid meshes is proposed and implemented in distributed memory architectures. A preliminary simulation, using a set of representative particles, is performed first to suitably tag the cells with a weight proportional to the probability of being crossed by a particle. In addition, an innovative parallel ray-tracing location algorithm is presented. A global identifier is assigned to each particle resulting in a significant reduction of the overall communication among processes. The proposed approaches are verified against two steady reference cases for ice accretion simulation: a NACA 0012 profile and a NACA 64A008 swept horizontal tail. Furthermore, a cloud droplet impact test case starting from an unsteady flow around a 3D cylinder is performed to evaluate the code performances on unsteady problems