The effects of an exhaust plume and nozzle length on the flow organization of axisymmetric base flows have been studied experimentally at Mach numbers of 0.76 and 2.2 using particle image velocimetry. From the measured velocity data, the mean pressure field was computed. The application of different nozzle lengths resulted in flow cases in which the shear layer impinges on the model, on the flow downstream of the model, or intermittently on the model and on the flow. The results showed that, for intermediate nozzle lengths, the overall pressure level downstream of the base decreased in the transonic flow cases and increased in the supersonic flow cases, indicating an entrainment effect in transonic flow and a displacement effect in supersonic flow. An increase in nozzle length was found to lead to a higher local pressure at the nozzle exit, which seemed to result in more overexpanded plumes in the transonic flow cases and less underexpanded plumes in the supersonic flow cases. @en

The present study characterises the spatio-temporal filtering associated with pseudo-tracking. A combined theoretical and numerical assessment is performed that uses the relatively simple flow case of a two-dimensional Taylor vortex as analytical test case. An additional experimental assessment considers the more complex flow of a low-speed axisymmetric base flow, for which time-resolved tomographic PIV measurements and microphone measurements were obtained. The results of these assessments show how filtering along Lagrangian tracks leads to amplitude modulation of flow structures. A cut-off track length and spatial resolution are specified to support future applications of the pseudo-tracking approach. The experimental results show a fair agreement between PIV and microphone pressure data in terms of fluctuation levels and pressure frequency spectra. The coherence and correlation between microphone and PIV pressure measurements were found to be substantial and almost independent of the track length, indicating that the low-frequency behaviour of the flow could be reproduced regardless of the track length. It is suggested that a spectral analysis can be used inform the selection of a suitable track length and to estimate the local error margin of reconstructed pressure values.@en

Pressure reconstruction based on particle image velocimetry (PIV) refers to the determination of pressure data from pictures of small tracer particles added to a flow. The technique possesses a unique combination of beneficial characteristics in that it non-intrusively provides simultaneous pressure and velocity data in the flow field without the need for instrumentation or other preparation the model. The present research provides a structured overview of different approaches to PIV-based pressure reconstruction and characterises their (relative) performance, particularly when applied to a transonic base flow. The unsteady, large-scale behaviour of this flow constitutes is subject of active research in the context of launcher aerodynamics to which experimental pressure field data would make a valuable contribution. Two techniques are analysed in depth through theoretical analyses, a simulated experiment based on a numerical simulation and several wind tunnel experiments: pseudo-tracking for the determination of instantaneous pressure fields and the Reynolds-averaging approach for the determination of time-averaged pressure fields. Various PIV-based methods for instantaneous pressure determination are capable of reconstructing the main features of instantaneous pressure fields, including methods that reconstruct pressure fields from a single velocity snapshot. Highly accurate pressure fields can be obtained by tracking individual particles in combination with advanced processing techniques. In view of this outcome, it is recommended to let the choice for a specific technique be guided by the desired accuracy, resolution and dimensionality of the pressure results, while taking taking into account practical considerations, in particular limitations in the capabilities of available measurement equipment and the complexity of the measurement system. Without such intent, the potential difficulties and complexity of data acquisition were demonstrated with the use of a 12-camera/2-laser PIV system. For instantaneous pressure reconstruction through pseudo-tracking new insights were obtained on its spatio-temporal filtering behaviour and the propagation of velocity measurement errors. A cut-off peak-response is specified as a function of the temporal track length and spatial resolution. Novel approaches are suggested to determine suitable temporal track lengths on the basis of the variation in material acceleration with track length and on the basis of pressure power spectra. Such spectra were also used estimate the local error margin of reconstructed pressure values. For the implementation of pseudo-tracking, it is recommended to first construct tracks by a combination of a second-order integration method and linear interpolation, using an integration time step that is sufficiently small to meet the Courant–Friedrichs–Lewy condition. The material acceleration may subsequently be estimated from the tracks by means of least-square fitting of a first-order polynomial or central differencing depending on the type of input data. When calculating mean pressure fields with the Reynolds-averaging approach, it is recommended to only include the terms that are associated with the mean flow and Reynolds stresses. The impact of neglecting spatial and temporal density variations may be estimated as the difference between pressure solutions calculated with and without density-gradient terms. After validation, the approach was employed to study the effects of an exhaust plume and nozzle length on transonic and supersonic axisymmetric base flows. Amongst others, the results showed that depending on the nozzle length the presence of a plume may cause a decrease in base pressure in the transonic flow cases and an increase in base pressure in the supersonic flow cases, indicating the effects of entrainment and displacement, respectively. The results furthermore highlight the need of considering during vehicle design, that a longer nozzle in which a plume expands further, not only corresponds to a lower exit pressure in the plume, but also to a different ambient pressure near the nozzle exit.@en

Pseudo-tracking refers to the construction of imaginary particle paths from PIV velocity fields and the subsequent estimation of the particle (material) acceleration. In view of the variety of existing and possible alternative ways to perform the pseudo-tracking method, it is not straightforward to select a suitable combination of numerical procedures for its implementation. To address this situation, this paper extends the theoretical framework for the approach. The developed theory is verified by applying various implementations of pseudo-tracking to a simulated PIV experiment. The findings of the investigations allow us to formulate the following insights and practical recommendations: (1) the velocity errors along the imaginary particle track are primarily a function of velocity measurement errors and spatial velocity gradients; (2) the particle path may best be calculated with second-order accurate numerical procedures while ensuring that the CFL condition is met; (3) least-square fitting of a first-order polynomial is a suitable method to estimate the material acceleration from the track; and (4) a suitable track length may be selected on the basis of the variation in material acceleration with track length.@en

The feasibility of computing the flow pressure on the basis of PIV velocity data has been demonstrated abundantly for low-speed conditions. The added complications occurring for high-speed compressible flows have, however, so far proved to be largely inhibitive for the accurate experimental determination of instantaneous pressure. Obtaining mean pressure may remain a worthwhile and realistic goal to pursue. In a previous study, a Reynolds-averaging procedure was developed for this, under the moderate-Mach-number assumption that density fluctuations can be neglected. The present communication addresses the accuracy of this assumption, and the consistency of its implementation, by evaluating of the relevance of the different contributions resulting from the Reynolds-averaging. The methodology involves a theoretical order-of-magnitude analysis, complemented with a quantitative assessment based on a simulated and a real PIV experiment. The assessments show that it is sufficient to account for spatial variations in the mean velocity and the Reynolds-stresses and that temporal and spatial density variations (fluctuations and gradients) are of secondary importance and comparable order-of-magnitude. This result permits to simplify the calculation of mean pressure from PIV velocity data and to validate the approximation of neglecting temporal and spatial density variations without having access to reference pressure data.

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The present work is conducted in the framework of the ESA TRP “Launcher Base Flows and Shock Interactions Regions Improved Load Characterization”, where high speed PIV measurements and unsteady pressure measurements performed in the DNW-HST on a 1:60 scale Ariane 5 are compared to simulations using IDDES and ZDES for the same configuration and flow conditions. The goal of the investigation is to identify how well the computations are capable of predicting the salient features of the transonic buffeting phenomenon. In order to make a valid comparison, it is confirmed that both the experimental as well as the numerical data is properly converged in order to extract flow statistics. It is found that due to the spatial filtering inherent to the PIV processing the measured velocity fluctuations are modulated. Furthermore a POD analysis shows that both the numerics and the experiments return the same modes (both for velocity field and pressure distribution) which indicates that both approaches contain similar large scale flow dynamics.@en

PIV measurements have been carried out to study the effect of exhaust plume and nozzle length on the flow topology and mean pressure distribution of axisymmetric base flows at freestream Mach numbers 0.76 and 2.20. Four different nozzle lengths with and without exhaust plume have been tested. The use of different nozzle lengths leads to flow cases in which the shear layer impinges on the model (solid reattachment), on the flow downstream of the model (fluidic reattachment), and intermittently on the model and on the flow (hybrid reattachment). An increase in nozzle length and the presence of an exhaust plume led to an increase in mean reattachment length at Mach 2.20, whereas no significant change in reattachment length was observed at Mach 0.76. The flow cases with the longest nozzles for which solid reattachment occurred showed significantly higher turbulent kinetic energy levels, at Mach 2.20, but significantly lower levels at Mach 0.76. Comparisons of flow cases with a long nozzle without a plume and flow cases with a short nozzle but with a plume suggest that the presence of the plume cannot accurately be modelled by replacing the plume with a solid geometry. Pressure results showed that the location of the low-pressure region downstream of the base remains rather invariant for different flow cases with and without plume and for different nozzle lengths. An increase in nozzle length leads to higher local pressure at the nozzle exit and therefore results in a less under-expanded or more over-expanded plume.@en

A test case for pressure field reconstruction from particle image velocimetry (PIV) and Lagrangian particle tracking (LPT) has been developed by constructing a simulated experiment from a zonal detached eddy simulation for an axisymmetric base flow at Mach 0.7. The test case comprises sequences of four subsequent particle images (representing multi-pulse data) as well as continuous time-resolved data which can realistically only be obtained for low-speed flows. Particle images were processed using tomographic PIV processing as well as the LPT algorithm ‘Shake-The-Box’ (STB). Multiple pressure field reconstruction techniques have subsequently been applied to the PIV results (Eulerian approach, iterative least-square pseudo-tracking, Taylor’s hypothesis approach, and instantaneous Vortex-in-Cell) and LPT results (FlowFit, Vortex-in-Cell-plus, Voronoi-based pressure evaluation, and iterative least-square pseudo-tracking). All methods were able to reconstruct the main features of the instantaneous pressure fields, including methods that reconstruct pressure from a single PIV velocity snapshot. Highly accurate reconstructed pressure fields could be obtained using LPT approaches in combination with more advanced techniques. In general, the use of longer series of time-resolved input data, when available, allows more accurate pressure field reconstruction. Noise in the input data typically reduces the accuracy of the reconstructed pressure fields, but none of the techniques proved to be critically sensitive to the amount of noise added in the present test case.

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Quantification of surface pressure is critical for the efficient design of aerospace structures. One way of measuring pressure is PIV/PTV-based pressure reconstruction [1]. In this approach, PIV/PTV data are used to determine the material acceleration and subsequently pressure via the momentum equation. In recent years, the technique has become increasingly feasible and appealing due to the development of (time-resolved) volumetric diagnostic capabilities, such as tomographic PIV [2] and Lagrangian particle tracking [3]. The performance of a variety of state-of-the-art techniques was recently assessed for the case of a transonic base flow within the collaborative European framework programs 'NIOPLEX' [4]. Since the NIOPLEX test case considers a simulated experiment, it does not necessarily demonstrate the actual capabilities of PIV/PTV-based pressure reconstruction techniques for realistic measurement conditions. The present study overcomes this limitation by reconstructing pressure from actual PIV/PTV measurements of a flow that is similar to the NIOPLEX test case, i.e. an axisymmetric step albeit in a low-speed flow, facilitating comparison. Reference measurements are obtained using microphones and static pressure sensors to provide a source for comparison@en