On subsonic near-wake flows of a space launcher configuration with various base geometries

The failure of Ariane 5 during flight 157 was partially attributed to the buffet/buffeting effect. Here, buffet refers to the excitation of aerodynamic forces in the wake and buffeting the structural response. In resonance, the interaction between aerodynamic and structural loads can have disastrous consequences. The studies of David and Radulovic (2005), Schwane (2015) have found that flow conditions are especially detrimental for Ariane 5 in the transonic flow regime, in particular, at Mach 0.8.

The failed flight has triggered many studies to improve and extend the understanding of base flow phenomena. Investigations on similar base geometry representations for Ariane 5 have been conducted by Wong et al. (2007), Schrijer et al. (2011), Hannemann et al. (2011), Schwane (2015). On generic configurations, the governing mechanisms for buffeting have been analyzed among others by Fuchs et al. (1979), Deprés et al. (2004), Deck and Thorigny (2007), Weiss et al. (2009), Weiss and Deck (2013), Schrijer et al. (2014), Scharnowski (2013), Scharnowski et al. (2015), Scharnowski et al. (2016), Statnikov et al. (2016), Statnikov et al. (2017), van Gent et al. (2017b), and van Gent et al. (2017a). Statnikov et al. (2017) extended existing knowledge about governing mechanisms by means of ‘dynamic mode decomposition’ and isolated three different modes of excitation in the base region: ‘cross-pumping’ of the separation bubble and ‘cross-flapping’ and ‘swinging’ of the shear layer.

Few of the references above are experimental and even fewer with a supersonic exhaust jet (Deprés et al. 2004; Weiss and Deck 2013; van Gent et al. 2017b, 2019), meaning there is generally a lack experimental data. However, van Gent et al. (2017b), van Gent et al. (2019) actually conducted extensive work similar to the study at hand, meaning these results can be applied for validation purposes and comparisons. In that study, the impact of the nozzle length was studied for an ambient flow in the transonic regime and in the supersonic regime. For the transonic case, it was found that for comparable overall conditions (geometry+flow conditions) ‘neither an increase in nozzle length nor the presence of an exhaust plume’ lead to ‘a significant change in the mean reattachment length.’ Further, it was concluded that the plume ‘cannot accurately be modeled by replacing the plume with a solid geometry.’

The first statement cannot be generally supported by the predecessor studies of the current work. A comparison between the jet-off- (Saile et al. 2019b) and jet-on-case (Saile et al. 2019a) shows clear differences when the jet is turned on. It decreased from \(L_r/D=1.18\) to 0.94, which corresponds to a retraction by \(20\%\) (Saile 2019). There, this was attributed to a base suction effect as previously described by Schoones and Bannink (1998), Deprés et al. (2004); Wolf (2013).

However, the second statement though can be supported. According van Gent et al. (2017b), van Gent et al. (2019), the plume cannot be correctly modeled with a solid plume-like sting since, on the one hand, the shape of the plume is not known a priori, and on the other hand, since the jet accelerates the outer flow due to entrainment. For the work at hand, a third aspect comes into play which concerns a presumable feedback mechanism with the jet leading to a strong excitation.

The feedback taking place in the near-wake region was suggested in Saile et al. (2019a); Saile (2019), and the excitation in question can be found in particular for Mach 0.8 when the jet is turned on. It is found that the excitation is outstanding in comparison to other investigated subsonic ambient Mach numbers (Saile et al. 2019a, b), which provides the motivation for the current study. Thus, the following questions are addressed:Thus, the objective here is to study the impact of the relative nozzle length on the flow field of a simplified space launcher configuration. More generally, among other studies such as the ones noted above, the overarching idea here is to provide data to the community as a small contribution for the development of further design guidelines for space launchers such as asked in the three bullet points above.

As in the previous studies of this series (Saile et al. 2019a, b), this task is approached by conducting experiments in the ‘Vertical Test Section Cologne’ (VMK) on a base model representing generic space launcher configurations. The base model geometry is modified from test to test by changing the nozzle length. Experiments are executed at Mach 0.8 for a Reynolds number of \(1.4\cdot 10^6\). Data are captured by means of particle image velocimetry (PIV), and the results mainly concern the mean and turbulent quantities for the velocity. A POD analysis is applied to extract dominant velocity modes. To underline some points over the course of the discussion, the probability density estimate function (PDF) derived by applying a kernel smoothing density (ksd) function is given of a point just upstream of the nozzle exit and selected instantaneous velocity distributions are shown. Additionally, the dynamic mechanisms of the near-wake are captured with high-speed schlieren images and the results are analyzed with respect to the spectral content.

The paper is structured as following: Hereafter in Sect. 2, the methods for data acquisition and analysis are presented followed by the description of the results in Sect. 3. A conclusion and outlook is given in Sect. 4.

The experiments were conducted in VMK (Triesch and Krohn 1986; DLR 2019; Saile et al. 2015), which is a blow-down type wind tunnel with a free test section. The current setup is comparable to the experiments presented in detail in Saile et al. (2019b) using again the subsonic wind tunnel nozzle with an exit diameter of \(340\,\mathrm {mm}\) into which the wind tunnel model is integrated (Fig. 1). The main components mimic generically the base geometry of Ariane 5, and for completeness, and its details are presented again in Fig. 2. This baseline model is modified by attaching adapters of various lengths to the base enabling measurements with a relative nozzle length of \(L/D=0.45\), 0.6, 0.75, 0.9, 1.05, and 1.20 (similar to the approach in Saile et al. (2013), van Gent et al. (2017b)). The nozzle remains the same for all base geometries. It has a conical contour, and to avoid the occurrence of condensed oxygen in the cold exhaust jet, it was chosen to limit the expansion ratio to \(\epsilon =7.37\) (nozzle exit Mach number of 3.59 for air).

The ambient flow Mach number is kept at 0.8 for all configurations and further details to the flow conditions are listed in Table 1. It contains the exit Mach number \(Ma_C\), exit velocity \(U_C\), exit Reynolds number \(Re_C\) based on the diameter of the main cylinder. Additionally, the chamber pressure \(p_{0,b}\) and temperature \(T_{0,b}\) of the wind tunnel model are listed. The exit Mach number was calculated under the assumption of an isentropic expansion by means of the reservoir and ambient pressure; the velocity is directly taken from the PIV results. Due to corrupted results just upstream in the vicinity of the base separation point, the ambient flow (Table 1) was determined farther downstream from the base. The ambient flow is averaged over an area between \(0.15<x/D<0.2\) and \(0.7<r/D<0.8\).

The preceding studies additionally provide data of the incoming boundary layer for Mach 0.8 and a relative nozzle length of \(L/D=1.2\). Since only adapters have been added to the base of the model, it is assumed that the changes regarding the incoming boundary layer are negligible. For more details, please refer to Ref. (Saile et al. 2019a, b).

The current experimental settings seek to simulate the conditions of Ariane 5 at an altitude of \(4.3\,\mathrm {km}\). This altitude is equivalent to an ambient Mach number of 0.8, which is correspondingly kept similar between the real-flight configuration and the experiments. Due to the sheer size of Ariane 5, it is not possible to establish a diameter-based Reynolds number similarity (\(70\cdot 10^6\) vs. \(1.4\cdot 10^6\) for the tests at hand). However, the near-wake flow of both configurations is turbulent and can be attributed to the trans-or post-critical regime Morkovin (1964) capturing similar fluid dynamic effects. Further, the incoming boundary layer is thin with respect to the step height (from the main cylinder to the nozzle). For such flows, Roshko and Lau (1965) and Westphal et al. (1984) found the recirculation region to be similar.

Nevertheless, due to the geometric differences and due to the usage of cold air to simulate the exhaust jet, the corresponding flow similarity can only be partial. For instance, similarity can be established with respect to the shape of the plume: an over-expanded nozzle flow is present for both conditions. Accordingly, the pressure ratio between the ambient flow and jet agrees with a reasonable degree, meaning a ratio of 0.25 can be found for Ariane 5 vs. of 0.36 for the experiments. In other words, the displacement effect can be considered as similar.

The largest deviation without doubt is induced by the conditions in the combustion chamber/reservoir. To compensate for the difference regarding the specific heats \(\kappa\), which influences the pressure change caused by a change in the flow direction for a supersonic flow, Goethert and Barnes (1960) suggested to keep \(\kappa Ma_j^2/\sqrt{Ma_j^2-1}\) similar. With 5.2 vs. 5.6 for Ariane 5, this quantity agrees quite well. Note that \(Ma_j\) corresponds to the jet Mach number. Next, the difference concerning the chamber temperatures is addressed, which directly influences the jet velocity. The jet velocity is about six to seven times larger for Ariane 5. Interrelated to that is the base suction effect. Thus, it must be assumed that shear layer evolution defers and the overall length of the mean recirculation bubble is presumably underestimated. Note that the Ariane 5-related flight data are based on a system analysis executed and provided by the DLR Institute of Space Systems. Further details in that respect and with respect to the similarity considerations are presented in Saile (2019).

The PIV measurement setup features a minor difference regarding the field of view (FOV), but other than that, the setup was kept just as in Saile et al. (2019a), meaning a classical 2D-2C setup was used. The light sheet is generated with an Ultra CFR Nd:YAG laser system of Big Sky Laser. Each laser pulse contains \(190\,\mathrm {mJ}\) at a wavelength of \(532\,\mathrm {nm}\). The sheet thickness was in the range of \(0.5\,\mathrm {mm}\). Perpendicular to the laser sheet, a PCO1600 camera system by PCO AG was set up at a distance of about \(200\,\mathrm {mm}\) for the acquisition of the particle images. The LabSmith timing unit by LC880 controls the trigger pulses for both components with an accuracy of \(100\,\mathrm {ps}\). The camera was equipped with the Makro-Planar 2/35 ZF lens by Carl Zeiss AG. The FOV to capture a global view of the wake resolves about \(134\times 100\,{mm^2}\). To accommodate for the base geometry adaptation, the FOVs are equally shifted downstream with increasing base adapter lengths. Due to the high depth of focus, the choice for the aperture setting has turned out to be unfortunate. The wind tunnel nozzle is faintly visible in the background of the raw images for occasionally weak seeding. For this reason, results are not discussed in that flawed range, meaning if they are located upstream from \(x/D<0.15\) and related to the incoming freestream (\(r/D>0.5\)). The FOV for the relative nozzle length \(L/D=1.2\) is depicted in Fig. 1, which also shows the coordinate system originating in the symmetry axis on the base. Seeding was accomplished with an in-house developed seeding generator providing titanium dioxide particles. Titanium dioxide of the type K1002 from Kronos International, Inc. was used, which exhibits according to the manufacturer a number based average diameter and density of \(d_{p}=0.23\, {\mu m}\) and \(\rho _p=3800kgm^{-3}\), respectively. The particles were injected through an orifice into the flow upstream of position ‘A’ (Fig. 1). The jet was not seeded.

The analysis of the images was executed with PIVview V3.60 by PIVTEC GmbH. The relative motion between camera and wind tunnel model was measured for a close-up FOV to be \(<40\,\mu m\) (Saile 2019). For the current larger FOV, no motion could be detected between the raw images. Thus, it can be considered as negligible and was consequently not corrected. In total, a number of 345 images per run were evaluated with a window size of \(32\times 16\,\mathrm {px}\) with an overlap of \(4\times 4\,\mathrm {px}\). In physical units, one interrogation window without overlap has a size of \(2.68\times 1.34\,{mm^2}\). The multi-grid interrogation method with grid refinement was applied, the ‘Whittaker’ reconstruction (Raffel et al. 2007) was used for the sub-pixel peak fit and on the final pass, a B-spline interpolation scheme of \(3^{rd}\) order was applied to cover the aspect of adaptive image deformation. The data were not interpolated.

An uncertainty analysis has been executed which is based on an approach suggested by Lazar et al. (2010) and Benedict and Gould (1996). The analysis takes into account the equipment-related uncertainty, the uncertainty due to the particle lag and the sampling uncertainty. In that order, the individual average contributions to the \(95\%\) confidence interval are found to be \(\pm 0.24\%\), \(\pm 2.11\%\), and \(\pm 0.85\%\) with respect to the incoming ambient flow velocity for the configuration with \(L/D=0.45\), which featured the largest uncertainties in comparison to the other configurations. ‘On average’ relates to a box drawn in the near-wake downstream from the base between \(0.15\le x/D\le 1.2\) and \(0.2\le r/D\le 0.5\). In total, the individual contributions amount to an averaged uncertainty of \(\pm 2.4\%\). The averaged \(95\%\) confidence interval for the turbulent intensity components due to sampling errors was determined to be \(<\pm 1\%\). Further details are available in Saile (2019). Additionally, the results have been checked for peak-locking, which in consequence was ruled out, and with respect to the signal-to-noise ratio.

The methodological approach for the Proper Orthogonal Decomposition (POD) follows the traces of Wolf (2013), who refers Nguyen et al. (2010) for the governing equations. Both are using the method of snapshots or strobes as introduced by Sirovich (1987). In total, 345 instantaneous velocity snapshots were captured during an experiment and subsequently used for the POD analysis.

The underlying idea of the POD can be found in Eqn. 1, which is that the fluctuations of the velocity field \(\varvec{u'}(\varvec{x},t)\) can be expressed as an expansion series of a time-varying scalar coefficient \(\zeta _k(t)\) and a time-independent base function \(\varvec{\psi }_k(\varvec{x})\). The base function \(\varvec{\psi }_k(\varvec{x})\) is equivalent to the \(k^{th}\) eigenmode, and for the PIV results, can be interpreted as the \(k^{th}\) flow field layer describing one of K eigenmodes as the governing motions on top of the mean flow field \(\varvec{\overline{u}}(\varvec{x})\). The number of modes K corresponds to the number of time steps or snapshots N. Another output of the POD decomposition is the relative kinetic energy \(\lambda _k/\sum \lambda _k\), which is used to rank the modes in descending order. The snapshot method (Sirovich 1987) yields at the computationally efficient determination of the corresponding POD basis functions \(\varvec{\psi }\) and time-varying coefficients \(\zeta\) for discrete experimental results such as given by PIV.VMK is equipped with a Z-type schlieren setup, which was used to capture the density gradients of the supersonic jet in the near-wake. The images were recorded with a Photron FASTCAM-APX RS camera, while the recording frequency was set to \(17\,\mathrm {kHz}\) with the shutter time at \(5.0e^{-5}\,\mathrm {s}\). Each image is made up of \(320\times 240\,\mathrm {px}\) and the magnification corresponds to \(0.316\,\mathrm {mm/px}\). The high recording frequency allowed the application of a spectral analysis to gain insights into the periodic behavior of the near-wake flow as shown later in context of Fig. 13. For the spectral analysis, the power spectral density was determined by using Welch’s overlapped segment averaging estimator (Welch 1967). Each segment consisted of 2048 samples (with an overlap of \(75\%\)) onto which a Hamming window was applied resulting in a minimal spectral resolution of \(8.3\,\mathrm {Hz}\) up to a maximal resolution of \(8.5\,\mathrm {kHz}\).

The research questions of the current study posed above suggest the following answers: Yes, the excitation in the near-wake is dependent on the nozzle length, and yes, a most unfavorable base geometry appears to exist. For the investigated configurations, it can be found for a relative nozzle length of \(L/D=0.9\). Then, upstream pointing velocity fluctuations are as frequent as downstream pointing fluctuations. It further corresponds to the configuration for which the reattachment on the mean does not take place along the solid nozzle wall, but just at the tip of the nozzle (without overhang). It was further suggested that an engulfment-entrainment process driven by a large-scale vortex and the jet is the driver for the relatively strong fluctuations. This is supported by the finding that the predominant oscillation takes place with a Strouhal number of 0.36, which is associated with the interrelated near-wake dynamics called shear layer swinging. Consequently, it appears recommendable to avoid such a configuration due to its presumable impact as loads on the base structures of the space launcher.