Plume and wall temperature impact on the subsonic aft-body flow of a generic space launcher geometry

Abstract

Experimental and numerical simulation of launcher base flows are crucial for future launcher design. In experiments, exhaust plume simulation is often limited to cold or slightly heated gases. In numerical simulations, multi-species reactive flow is often neglected due to limited resources. The impact of these simplifications on the relevant flow features, compared to real flight scenarios, needs to be characterized in order to enhance the design process. Experimental and numerical investigations were carried out within the framework of the SFB/TRR 40 Collaborative Research Centre to study the impact of plume and wall temperature on the base flow of a generic small-scale launcher configuration. Wind tunnel tests were performed in the Hot Plume Testing Facility (HPTF) at DLR, Cologne, using subsonic ambient flow and pressurized air or hydrogen–oxygen combustion as exhaust gases. The tests were numerically rebuilt using the DLR TAU code employing a scale-resolved IDDES approach, including thermal coupling and detailed chemistry. The paper combines the experimental and numerical findings from the SFB/TRR 40 base flow studies and highlights the most prominent influences on the mean flow field, the pressure field, the dynamic wake flow motion, and the resulting aerodynamic forces on the nozzle. High-frequency pressure measurements, high-speed schlieren recordings, and time-resolved CFD results are evaluated using spectral and modal analysis of the one- and two-dimensional flow field data.

1 Introduction

Since 2008, aft-body flows of space launch vehicles in various flow regimes have been investigated using generic launcher configurations within the framework of the Collaborative Research Centre (SFB) Transregio 40 (TRR40) (Haidn et al. 2018; Adams et al. 2021). One of the primary interests has been the interaction between the high subsonic ambient freestream and the supersonic overexpanded propulsive jet during the ascent phase of a launcher. Under certain conditions during this phase, significant non-stationary flow effects can occur in the near-wake flow, leading to unsteady mechanical loads known as buffeting on base and nozzle structures. In David and Radulovic (2005), flight data from the transonic regime of an Ariane 5 ascent were analyzed for base pressure fluctuations and the corresponding dynamic loads on the nozzle’s actuators. The study indicated that the aft-body flow is mainly characterized by fluctuations in the recirculation zone at a Strouhal number of $\textrm{Sr}_D=0.2$, which is most prominent at a flight Mach number of 0.8. However, it was also noted that wind tunnel tests show significant differences in the low subsonic domain, attributed to the lack of plume simulation. Despite this, the wind tunnel model was represented by a realistic Ariane 5 geometry, including booster stages. Numerous campaigns conducted steady and unsteady pressure measurements with various geometry variations, as summarized by Geurts (2006).

The same model was subsequently utilized in the ESA TRP Unsteady Subscale Force Measurements within a Launch Vehicle Base Buffeting Environment to address remaining questions. In these studies, new tools such as high-speed PIV (Schrijer et al. 2011) and Improved Delayed Detached-Eddy Simulation (IDDES) were employed by Lüdeke et al. (2015). Hannemann et al. (2011) also reported on a feasibility study for conducting experiments including plumes, as it appeared questionable whether the results without jet simulation were representative with respect to the full-scale launcher. They developed a set of similarity parameters and stated that the most challenging similarity to achieve is the jet velocity. To address this, Hannemann et al. (2011) proposed using hot helium at 800 K to improve the situation, or ideally, the combustion of H₂/O₂ at a very low mixture ratio, as used in gas generators.

Experiments and CFD using cold air plume simulation were conducted within the CNES/ONERA research program Aerodynamics of Nozzles and Afterbodies on a generic axisymmetric backward-facing step geometry. Experimental results by Deprés et al. (2004) indicated that the distance between the base and the nozzle exit significantly influences the mean and unsteady base flow features. Associated CFD studies were performed by Deck and Thorigny (2007), Meliga et al. (2009), and Weiss et al. (2009). In a numerical study by Weiss and Deck (2013), the robustness of an axisymmetric separating/reattaching flow was investigated concerning external perturbations, such as those potentially present in wind tunnel testing.

A similar configuration was later investigated within the SFB/TRR 40. First by replacing the jet with an infinite nozzle cover in experiments by Scharnowski et al. (2013), later by experiments using a finite nozzle without jet in the work of Saile et al. (2019b) and in CFD simulations by Horchler et al. (2018). The tests of Saile et al. (2019b) were a preliminary step to characterize the wind tunnel flow and validate the experimental environment against the perturbation study by Weiss and Deck (2013). Building on this validation, Saile et al. (2019a) studied the same test setup using a cold air jet and ultimately proposed a new hypothesis on an aeroacoustic coupling effect during the ascent of space transportation systems (Saile and Gülhan 2021), which serves as a foundational point for subsequent studies in the present paper.

The similarity of wake flow physics between interaction with a cold air jet and interaction with a hot reactive jet, as encountered in real flight scenarios, however, has not yet been proven through experiments or numerical simulations. Therefore, the paper at hand presents experimental and numerical results from complementary cold and hot jet interaction tests to highlight the impact of increased plume and wall temperatures on the measurable characteristics of the subsonic aft-body flow of a generic space launcher configuration in general, and particularly at $M=0.8$. Both ambient temperature air (denoted ‘cold’) and, for the first time in Europe, hot gas generated from the internal combustion of gaseous hydrogen (GH$_{2}$) and gaseous oxygen (GO$_{2}$) were used to simulate the exhaust jet. The studies were conducted at the German Aerospace Center (DLR) on a generic geometry, following previous investigations by Saile (2019). The compilation of these results builds on the previous work conducted by Kirchheck et al. (2021), Schumann et al. (2021a), and Fertig et al. (2019).

2 Methods

2.1 Experiments

2.1.1 Test facilities

For the present study, the experimental work was performed in the Hot Plume Testing Facility (HPTF) at DLR, Cologne (Kirchheck and Gülhan 2017). This facility combines the Vertical Wind Tunnel (VMK), a GH$_{2}$/GO$_{2}$ supply facility, and a high-pressure (HP) dry air supply system (Fig. 1).

Fig. 1

Schematic of the Hot Plume Testing Facility (HPTF), at the German Aerospace Center (DLR), Cologne (taken from Kirchheck et al. 2021)

The VMK (Triesch and Krohn 1986) is a blow-down type wind tunnel with an atmospheric vertical free jet test section. It operates at a maximum pressure of 35 bar, which is maintained by a 1 000 m³ reservoir at a maximum pressure of 67 bar. It allows typical test durations of 30–60 s, and the upstream heat storage can heat the flow up to 750 K, providing sea level conditions for Mach numbers $M\le 2.8$. Supersonic velocities are set by various discrete convergent–divergent nozzles up to a Mach number of 3.2. Subsonic conditions are set using a 340 mm convergent nozzle. The test chamber is suitable for the operation of combustion tests with gaseous and solid propellant combinations in a model scale environment. For the cold gas interaction tests, the enclosed high-pressure air supply operates up to a maximum pressure of 150 bar.

The GH₂/GO₂ supply facility (Kirchheck and Gülhan 2016) was built primarily to feed wind tunnel models including integrated combustion chambers in order to provide more realistic jet composition and jet stagnation conditions during wind tunnel testing. It consists of a 300 bar gas storage and a control station employing a closed-loop mass flow controller. The maximum supply pressure is 115 bar at 399 g/s O₂ and 67 g/s H₂ maximum mass flow rates. The ratio of oxidizer to fuel mass flows (OFR) is limited by the necessary ignition ratio $\textrm{OFR}_\textrm{ign}= 0.5$ and the stoichiometric mixture ratio $\textrm{OFR}_\textrm{st}= 7.918$. Its range depends on the total mass flow rate (see Kirchheck and Gülhan 2018; Kirchheck et al. 2021, for more information on the operating envelope).

2.1.2 Test setup

The generic launcher afterbody (Fig. 2) is represented by an axisymmetric backward-facing step geometry with a base diameter $D= 67\,\textrm{mm}$ and ratios $L/D= 1.2$ and $d/D= 0.4$. It was fixed on a central support structure upstream of the divergent part of the nozzle and fed with supply gases and cabling via several support arms. Downstream of the support arms, the wind tunnel flow passes through two layers of filter screens to increase the uniformity of the flow. The model houses a combustor with a diameter $D_{cc}= 38.1\,\textrm{mm}$ and a single-element shear-flow injector similar to the design of the Penn State combustor (Marshall et al. 2005). Detailed information on design considerations and a characterization of the combustor operation is provided in Saile et al. (2015); Kirchheck and Gülhan (2018). The thrust nozzle is a 5° half-angle conical nozzle with an expansion ratio $\varepsilon =5.6298$ and throat diameter $d_{th}=11\,\textrm{mm}$. The nominal nozzle exit Mach number is $M_e=3.30$ for cold gas tests and $M_e=3.23$ for hot gas tests. It is operated in overexpanded mode at a nominal nozzle exit pressure ratio $p_e/p_\infty =0.37$. The outer model dimensions are similar to previous investigations by Saile et al. (2019b, 2019a, 2021); details on the design are provided in Kirchheck et al. (2019).

Fig. 2

Cold/hot plume interaction test setup in the Vertical Wind Tunnel (VMK) at the German Aerospace Center (DLR), Cologne (taken from Kirchheck et al. 2021)

2.1.3 Test cases

Three reference cases were defined: an ambient flow case without a jet and ambient flow cases with cold/hot jets. The selected test conditions are given in Table 1 and Fig. 3. For the ambient flow, due to the reported significant increase in base pressure fluctuations in flight and experiments at high subsonic Mach numbers (David and Radulovic 2005), $M= 0.8$ was selected as a reference for the present study. That was already the case in several other studies summarized in Deck and Thorigny (2007) as well as Meliga et al. (2009); Weiss et al. (2009); Wolf (2013); Statnikov et al. (2017); and Saile et al. (2019a, 2019b, 2021). Additional tests were conducted running several discrete Mach numbers and Mach number transients in the range of $M= [0.5 \ldots 0.95]$. Transient runs were performed at $\Delta M/\Delta t=0.01\,\textrm{s}^{-1}$. The static temperature in the freestream ($T$) is calculated using isentropic relations with an estimated ambient temperature $T_\textrm{amb}\approx 288\,\textrm{K}$. For the jet conditions, the chamber pressure ($p_{cc}$) is set around 20 bar, leading to an overexpanded jet for both the cold and hot jet cases. In the cases with air jets, the total temperature of the internal flow is $T_{cc}= T_\textrm{amb}$. For the hot jet case, $\textrm{OFR}=0.7$ was set, resulting in a chamber temperature $T_{cc}=918.7\,\textrm{K}$ from one-dimensional equilibrium calculations, performed using the Rocket Propulsion Analysis (RPA) software tool. The total mass flows were 459.9 $\textrm{g}/\textrm{s}$ for the cold jet and 89.4 $\textrm{g}/\textrm{s}$ for the hot jet case. The test conditions were constant in all cases during the last 2 seconds of the run. Evaluations are performed within $t_\textrm{eval}=[18\ldots 20]\,\textrm{s}$.

Table 1 Reference ambient and jet flow conditions

Fig. 3

Time history of ambient and jet flow conditions with respect to the evaluation time window $\varvec{t_\textrm{eval}{}}$ (reproduced from Kirchheck et al. 2019, 2021)

2.1.4 Measurements, instrumentation, and post-processing

The test setup provided access for concurrent optical and sensor measurements. Figure 4 gives an overview of the applied techniques and the instrumentation layout. Unsteady pressure sensors from Kulite^® Semiconductors Inc. were placed on the base plane of the backward-facing step and in the combustion chamber. The sensors in the base plane were mounted with a recess of 0.5 mm (XCQ-080) to provide a natural frequency above the measurement range. The combustion chamber sensor was mounted with a transmission length of 52.77 mm (XCE-062) and a 0.5 mm tube diameter. The transmission line is considered intermediately damped according to Iberall (1950), thus providing adequate frequency response in the resolved frequency range. The pressure signals were sampled at 100 kHz and 10 kHz, respectively, to capture the relevant wake flow and chamber modes (see Kirchheck et al. 2019, for an assessment of the prevailing frequencies).

Particle image velocimetry (PIV) was applied in the near-wake using a 532 nm laser with an image acquisition rate of 16 Hz, as already performed by Saile et al. (2019b). The seeding was realized using an in-house developed seeding generator with TiO₂ particles of type K1002 from Kronos™ International Inc. The particles feature a number-based average particle size $d_p=230\,\textrm{nm}$ (median particle size ${d_p}_\textrm{med}=20\,\textrm{nm}$) according to the manufacturer. Narrow-band filtering was used for the hot plume tests to increase the signal-to-noise ratio within the harsh environment of afterburning plume gases. High-speed schlieren (HSS) recordings of the near-wake region were taken at a rate of 20 kHz with a shutter speed of 2.5 $\mu \textrm{s}$. They were used to identify dynamic flow field motion leading to the measured base pressure fluctuations. The schlieren setup was a double Z-type with the knife edge aligned parallel to the flow.

Fig. 4

Layout of base and combustion chamber instrumentation and optical measurement techniques for the VMK test setup (P—pressure, T—temperature, B—base, C—pressure/combustion chamber, N—nozzle, D—main body, IO—oxygen injector, and $0\ldots 17$—sensor number)

Standard post-processing methods were applied to the high-frequency sensor and PIV measurements, leading to mean pressure ($\overline{p}$) and mean flow field data ($\overline{\varvec{u}}$), as well as time- and Mach number-dependent root-mean-square (RMS) pressure fluctuation levels ($p'_\textrm{RMS}$) using a moving one-sided interval width of 1% (equivalent to 45 000 samples or $\Delta t=0.45\,\textrm{s}$, $\Delta M=4.5\times 10^{-3}$) during Mach number transients. Pressure fluctuation frequencies were acquired from power spectral density (PSD) analysis employing the method of Welch (1967). The PSD uses a Hann window with an overlap of 0.5 and a frequency resolution of 10 Hz. The HSS recordings were similarly processed on a pixel-by-pixel basis by extracting the grayscale intensity values $I(t)$ from 10 000 samples (equivalent to a time window $\Delta t=0.5\,\textrm{s}{}$).

For a first global analysis, the HSS intensity spectra ($\textrm{PSD}_I$) were spatially averaged to $\langle \textrm{PSD}_I\rangle$ to identify the predominant frequencies in the region of interest. For further analysis of the two-dimensional distribution of the RMS intensity fluctuations, the results are plotted as spatial distribution of $I'_\textrm{RMS}$ in the image coordinate system. Finally, the two-dimensional distribution of the response of isolated frequencies $\textrm{PSD}_I(f)$ can be used to characterize the mode shapes of the dynamic wake flow motion.

2.2 Numerics

2.2.1 Numerical setup

The experiments were reconstructed and supplemented by additional parameter studies using the DLR CFD code TAU (Schwamborn et al. 2006; Hannemann et al. 2010) with 2^nd order accuracy in space and time. The numerical model (Fig. 5) comprises the internal and external volumes of the aft-body geometry as already used in Schumann (2022). The external volume is extended around the lip of the wind tunnel nozzle to account for potential effects arising from the wind tunnel nozzle shear layer. Both the internal and external volumes are divided into a region solely covered by REYNOLDS-averaged NAVIER–STOKES (RANS) equations and a scale-resolving approach combining RANS and an Improved Delayed Detached-Eddy Simulation (IDDES) method (Fig. 6).

Fig. 5

Numerical domain of the wind tunnel test setup including the internal combustor flow and the external wind tunnel flow (taken from Schumann 2022)

Fig. 6

Setup of the numerical model for precursor RANS simulations with thermal coupling and RANS–IDDES simulations (reproduced from Schumann et al. 2021a)

For the RANS computations, local time stepping is utilized for temporal discretization, and the AUSMDV upwind scheme is employed for spatial discretization. In the combined RANS–IDDES approach, dual-time stepping with backward differences and a three-stage Runge-Kutta scheme is utilized for temporal discretization, while a central hybrid low-dissipation, low-dispersion scheme developed by Probst and Reuß (2016); Fertig et al. (2019) are employed for spatial discretization. Both setups utilize a two-equation k-$\omega$ Shear Stress Transport (SST) turbulence model. Further details on the numerical methods can be found in Schumann et al. (2021a).

To determine representative wall temperatures for the IDDES computations, thermal coupling was employed in precursor RANS computations between the internal flow and the model structure, and between the model structure and the external flow (Fig. 6). The fluid–structure coupling using TAU and ANSYS Mechanical Software was performed in a two-dimensional axisymmetric setup to ensure stability and efficiency in the combustion chamber with finite-rate chemical reactions involving nine species. The coupling is realized using the heat flux at the internal model surface and the heat transfer coefficient at the external model surface. In a precursor study without external flow, an external heat transfer coefficient of $50\,\textrm{W}/\textrm{m}^2\textrm{K}$ was used. For the coupled RANS–IDDES simulations, a quasi-steady temperature distribution was assumed. To provide the temperature distribution for the hot wall cases, the external flow was considered in the coupled TAU–ANSYS simulation. Here, the heat transfer coefficient was adjusted until heat flux convergence between the flow and structure solver was achieved. Further details on the approach can be found in Fertig et al. (2019) and Schumann et al. (2021a).

For the IDDES simulation, both ambient air and the propulsive jet are modeled as single-component gases with jet flow conditions determined in precursor RANS simulations. The scale-resolving simulations are performed on a full $360^\circ$ hybrid grid with a circumferential resolution of $0.94^\circ$. Figure 7 shows the unstructured tetrahedral grid in the freestream and far-wake region with prismatic near-wall refinement and the refined structured part of the grid in the jet flow and near-wake region. This grid contains a total of approximately 33 million grid points, with a general restriction on the non-dimensional normal wall spacing of $\Delta y^+<1$. The grid resolution and design were optimized during a grid study, which focused on the validation of the implemented grid sensors and a solution sensitivity analysis to grid changes. The results of the grid study are documented in Schumann et al. (2020).

Fig. 7

Numerical grid for the scale-resolving IDDES computations; left: unstructured tetrahedral grid in the freestream and far-wake region of the RANS–IDDES regime and right: detailed view of the refined structured grid in the jet flow and near-wake region (reproduced from Schumann et al. 2021a)

2.2.2 Test cases

The test cases focused on in the current paper include the reconstruction of the wind tunnel runs with cold and hot jets from Table 1. In the hot experiment, the external model wall temperature ($T_w$) changes over time from room temperature at the beginning of the test to an equilibrium state after an operational time of about 20 $\textrm{s}$. Therefore, a case with a cold wall ($T_w= 300\,\textrm{K}$), representing the beginning of the run, and a case with a hot wall, where the temperature distribution is determined by pre-run thermal fluid–structure coupling simulations, representing the end of the run, are considered (see Table 2).

Table 2 Reference wall temperature conditions for CFD

2.2.3 IDDES validation studies

Prior to the computations described above, the numerical method was subjected to a validation study based on a similar axisymmetric backward-facing step geometry with a centric air jet. A detailed discussion on this work, featuring sensitivity studies on numerical model parameters (i.e., time step size, turbulence model, fluid modeling, circumferential grid resolution, filter length definition, and the data collection period), is available in Schumann et al. (2021b). The definition of the test case was taken from Deprés et al. (2004). It contains a main cylinder of 100 mm diameter and a second cylinder representing the generic nozzle with ratios $d/D=0.4$ and $L/D=1.2$. The mean flow field around this configuration is provided in Fig. 8 for the case with a cold jet. It shows a reattachment of the external flow on the nozzle surface at approximately $x_r/D=1.172$ for $M=0.7$.

Experimental and numerical data are used for validation, such as the base and nozzle wall pressure distribution provided in Fig. 8. Experimental data from Weiss et al. (2009); Deprés et al. (2004) and numerical data from Meliga et al. (2009) agree well with the results from the presented computational setup. Details on the validation, particularly regarding the RMS pressure coefficient distribution and the PSD of wall pressure fluctuations, can be found in Schumann et al. (2021b).

Fig. 8

Validation studies for the IDDES computations (reproduced from Schumann et al. 2021b); mean axial velocity for no jet and cold jet cases (top) and mean pressure coefficient on the main body and nozzle walls, containing data taken from Weiss et al. (2009); Deprés et al. (2004); and Meliga et al. (2009)

2.2.4 Thermal coupling

The results from the coupled simulations are shown in Fig. 9 as contour plots of the distributed gas temperature ($T_\textrm{gas}$) inside the combustion chamber volume and the distributed solid temperature ($T_\textrm{solid}$) in the material surrounding the injector, combustion chamber, and nozzle flow path. The cold and hot wall conditions, obtained from the initial boundary conditions at $t=0\,\textrm{s}$ with $T_\textrm{solid}=279.15\,\textrm{K}$ and the settled conditions at $t=20\,\textrm{s}$, are shown. The internal flow conditions are set corresponding to the experimental setup described above using $\textrm{OFR}=0.7$ at $\dot{m}=89.4\,\textrm{g}/\textrm{s}$.

Fig. 9

Thermally coupled CFD for material wall temperatures as boundary conditions for comparison with experimental heating (reproduced from Fertig et al. 2019); top: initial condition $\varvec{T_\textrm{solid}=279.15\,\textrm{K}}$ and bottom: resulting temperature distribution at $\varvec{t=20\,\textrm{s}}$ for the hot wall cases (radius $\varvec{r}$ stretched by a factor of 5)

The internal flow is characterized by a maximum temperature of $3\,550\,\textrm{K}$ inside the reaction zone and an average temperature of approximately $900\,\textrm{K}$ at $21.5\,\textrm{bar}$ at the end of the chamber. The reaction is completed about $50\,\textrm{mm}$ upstream of the nozzle throat. After $20\,\textrm{s}$, the temperature distribution inside the structure shows maximum temperatures of approximately $650\,\textrm{K}$ in the vicinity of the nozzle throat and about $630\,\textrm{K}$ in the corner between the nozzle and the base. The internal flow conditions are only marginally influenced by the surrounding wall temperature distribution, which shows a maximum at about two-thirds of the chamber length. The axial position of the maximum is shifted further downstream with respect to experimental results from Kirchheck and Gülhan (2018); Marshall et al. (2005), which might be caused by the coupling with the outer flow.

In terms of boundary conditions for the external flow, a heat transfer coefficient between $100\,\textrm{W}/\textrm{m}^2/\textrm{K}$ in the corner at $x=0$ and $1\,600\,\textrm{W}/\textrm{m}^2/\textrm{K}$ at the nozzle tip is predicted. The characteristic outflow conditions are $p_e=0.44\,\textrm{bar}$, $T_e=420\,\textrm{K}$, $M_e=3.15$, and $u_e=3.5\,\textrm{km}/\textrm{s}$. Due to a slightly lower pressure in the exit plane compared to the cold flow case reported in Fertig et al. (2017), the internal flow separation upstream of the nozzle exit plane is larger under hot flow conditions.

2.2.5 Wall heat flux modeling

Using the wall temperature distribution computed in the coupled simulation, both RANS and IDDES are employed to compute the heat flux from the walls to the fluid in the recirculating region. The resulting mean heat flux distribution on the base and nozzle walls is compared in Fig. 10, assuming an isothermal cold wall. Such a comparison is especially interesting when efficient modeling using steady-state solutions is preferred over a highly resolved unsteady approach. In the case of separating/reattaching flows, which are sensitive to the state of the boundary layer, the wall heat flux could impact the global flow topology by introducing uncertainties in the prediction of separation and reattachment locations.

Fig. 10

Heat flux data from various turbulence models (reproduced from Schumann 2022); top: heat flux along the nozzle shroud starting at the base ($\varvec{x/D=0})$ and bottom: heat flux on the annular base plane starting at the outer nozzle radius ($\varvec{r/D=0.2})$

In the present study, it was shown that the qualitative trends of wall heat flux in the base region can be predicted well using a two-equation k-$\omega$ approach, in contrast with the one-equation Spalart–Allmaras (SA) turbulence model. On the external nozzle surface (Fig. 10, top), the IDDES solution is characterized by local maxima near the base and the nozzle lip, caused by the presence of a corner vortex and the highly unsteady flow field at the reattachment location. On the base surface (Fig. 10, bottom), the radial heat flux distribution is more constant, with an increase in the vicinity of the base shoulder, caused by the unsteady flow near the separation location.

Comparing these characteristics with the results from the RANS computations, it is apparent that, generally, the RANS models perform better at the base than on the nozzle wall. The corner vortex, particularly, does not induce the characteristic heat flux peak on the nozzle surface. The k-$\omega$ model obviously underpredicts the heat flux in the corner region, while the heat flux along the nozzle wall is overpredicted. Furthermore, in this study, the SA model is considered unsuitable for predicting the heat flux distribution, as it significantly alters the flow field by provoking reattachment and shifting it much farther upstream, leading to a qualitative mismatch of the heat flux distribution.

3 Results

The following sections highlight the main impacts from hot plume and/or hot wall temperature compared to the cold jet tests. The different combinations of hot plume with cold walls and hot plume with hot walls represent the conditions of hot plume tests at the beginning of the run and hot plume tests at the end of the run, when temperatures are converged. The effects are presented and discussed in terms of instantaneous and mean flow features, base pressure and its fluctuations, the dynamic wake flow motion, and the resulting external forces on the nozzle cover.

3.1 Impact on instantaneous and mean flow features

The impact of a hot plume and hot walls on the instantaneous and mean flow features compared to the cold plume case with cold walls is investigated in WTT and CFD. This is done by means of schlieren imaging (Fig. 11) and velocity magnitude fields obtained from PIV measurements and CFD results (Fig. 12). Figure 11 displays both a short-time exposure of $2.5\,\mu \textrm{s}$ on the left symmetry, representing the instantaneous density gradient fields, and an artificial long-time exposure of $250\,\textrm{ms}$ on the right symmetry, obtained by averaging 5 000 snapshots representing the mean density gradient fields. These are provided for the reference cases listed in Table 1.

Fig. 11

Instantaneous snapshots (left symmetry) and artificial long-time exposure (right symmetry) HSS images of (a) ambient flow only, (b) cold jet only, (c) cold jet with ambient flow, and (d) hot jet with ambient flow cases (short-time exposure $\varvec{2.5\,\mu \textrm{s}}$ and artificial long-time exposure $\varvec{250\,\textrm{ms}}$)

Fig. 12

Comparison of the mean velocity magnitude field between experimental PIV data (left symmetry) and CFD computations (right symmetry) for the cases with (a) cold jet/cold walls with ambient flow and (b) hot jet/hot walls with ambient flow

In the original schlieren videos of the cases involving ambient flow and/or ambient flow with jet, a discernible oscillating movement of the shear layer originating from the base shoulder is evident. However, the specific characteristics of this movement vary between the cases. In Fig. 11, exemplary snapshots and mean density gradient fields both cannot transport this information to the reader, which is why modal analysis is applied, and analysis is presented in Sect. 3.3.3. The region of interest (ROI) related to the above mentioned oscillation is highlighted in Fig. 11 as ROI1 (in the following, each ROI applies to all cases). In the case of ambient flow without jet (Fig. 11a), the oscillation intensity in terms of lateral shear layer displacement is moderate, while its temporal appearance seems strictly periodic. This is also true for the case with a cold jet and ambient flow (Fig. 11c), whereas the oscillation intensity is strongly increased. In the case of a hot jet with ambient flow (Fig. 11d), the periodicity of the lateral movement seems to be less pronounced with amplitudes in the range of the ambient flow without jet.

This behavior impacts the dynamic motion of the jet farther downstream, including the jet/external flow shear layers, particularly in the region highlighted as ROI2. In the cold jet case (Fig. 11c), the periodic antisymmetric oscillation of the external shear layer in ROI1 (and further downstream) poses periodic lateral pressure differences on the jet boundaries, consequently leading to a strong waving motion of the supersonic jet with increasing displacement in the downstream direction. This is represented by the blur of the jet boundaries and shock structures within ROI2, visible in the mean images. This blur is particularly increased compared to the cold jet without ambient flow (Fig. 11b), where no shear layer impact is present. In the same region of interest, this blur also appears in the hot plume case (Fig. 11d), but here it is more likely due to a stochastic rather than periodic movement of the jet shear layer. In this case, the jet shear layer also shows a larger angle of growth compared to the cold plume case, which is recognizable by visually tracking structures within the shear layer (not accessible to the reader) and through a stronger widening of the blurry region of the early jet shear layer in ROI3. For the comparison of Figs. 11c and 11d, it should also be noted that the density gradients between the plume and the external flow are reversed, because of different nozzle exit temperatures at a similar nozzle exit pressure. Further, the resulting gradient in the hot plume case is stronger than in the cold plume case, which also contributes to the different visual appearances to an unknown degree.

In the case of the cold supersonic jet in ambient flow (Fig. 11c), pressure waves are clearly visible, traveling from a downstream source toward the base of the model. The occurrence of these waves is antisymmetric and seems to be connected to the oscillating movement of the supersonic jet. Similar effects are also visible in the hot plume case, but they are less pronounced and occur on a more random timebase rather than being strongly periodic. In the case of ambient flow without a jet, such waves are not detectable.

Finally, in the cases with ambient flow, the external shear layer reattaches in the vicinity of the nozzle lip, either on the nozzle wall or on the jet shear layer. The exact location of reattachment cannot be extracted from the schlieren images, but a trend can be predicted based on the bending of the external shear layer, visible in the mean images. These trends are marked in Fig. 11 by green arrows, qualitatively illustrating the impact of the type of plume on the reattachment location. In the case of ambient flow without a jet (Fig. 11a), the bend of the external shear layer occurs slightly downstream of the nozzle exit, whereas its location is shifted upstream, close to the nozzle lip, in the presence of a cold jet (Fig. 11c). In the presence of a hot jet, the bend is shifted farther downstream (Fig. 11d).

The qualitative trends observed in the schlieren images are confirmed in both experimental PIV measurements and CFD results for the axial reattachment location $x_r/D$ in Fig. 12 for the cold and hot plume cases. In WTT, reattachment occurs at $x_r/D=0.945$ in the presence of a cold plume and $x_r/D=1.265$ in the presence of a hot plume, corresponding to a 34% increase in reattachment length due to the change in plume type. In the experiment, this phenomenon appears to be mainly driven by two factors: One is a general decrease in the turbulent fluctuations upstream of the shoulder and inside the recirculation and shear-flow region, which has a strong negative correlation with the reattachment length (e.g., Isomoto and Honami 1989). A decrease in inlet turbulence intensity is to be expected due to the heating of the main cylinder wall and the associated reduction of wall shear stresses. The same is true for the recirculating flow at the nozzle wall, which impacts the shear layer directly behind the shoulder. Finally, the entrainment of hot fluid from the jet and heating of the encapsulated recirculation volume from the hot walls leads to a reduction of density of the recirculating flow, which decreases the momentum impact on the shear layer, hence delays the break-up of structures. The other main aspect appears to be an increase in jet exit velocity, effectively reducing the back pressure on the reattaching shear layer, which results in a downstream suction, hence later reattachment.

In CFD, similar phenomena result in $x_r/D=1.181$ for the cold plume and $x_r/D=1.430$ for the hot plume case, corresponding to a downstream shift of 21% due to the combustion environment. Therefore, the impact is weaker in the CFD solution, whereas in general, CFD predicts a larger reattachment length in comparison with the experiment, which is 25% in the cold plume case and 13% in the hot plume case. Since boundary conditions such as plume temperature, wall temperature, and plume composition seem to have a strong impact on the topology of the base flow as illustrated by experimental results, the CFD solution is also considered sensitive to the definition of boundary conditions. These are difficult to determine precisely in experiments under the challenging conditions of a chemically reactive hot gas environment. However, in both cases, WTT and CFD, a delayed reattachment is recorded accordingly.

3.2 Impact on base pressure

Base pressure measurements were conducted at sensor location PB0 ($r/D=0.333$, Fig. 4) in the WTT during continuous Mach number transients between $M=0.5$ and 0.95 with a slope of $0.01\,\textrm{s}^{-1}$, as well as for several discrete Mach numbers in the same range. The corresponding RMS pressure fluctuations ($p'_\textrm{RMS}$) are plotted in Fig. 13 (left) for the cold jet case in the full Mach number range. This datum complements previous WTT measurements by Saile et al. (2019a) and also numerical data by Statnikov et al. (2017), where only discrete Mach numbers were analyzed. It provides means for evaluation of the critical flight Mach number 0.8 in relation to the surrounding trajectory. Discrete measurements are provided to validate the approach of post-processing along non-constant test conditions. Finally, at Mach numbers 0.8, 0.85, and 0.9, additional hot jet tests are provided for comparison between cold and hot plume/wall temperatures. In this regard, it shows that generally, the pressure fluctuation levels are lower in the hot plume environment, which is, in this case, up to 29% compared to the cold plume case at Mach 0.8.

Fig. 13

Base and chamber pressure fluctuations from wind tunnel tests for cold and hot jet cases at various Mach numbers; left: RMS pressure fluctuation levels at PB0 and right: maximum base and combustion chamber pressure amplitude spectrum for Mach 0.8 at PB0 and PC1

Peaks in the RMS pressure fluctuations are observed at $M=0.522$, 0.651, and 0.778. In this range, similar peaks are also found in flight data by David and Radulovic (2005). However, their data show slight variations in amplitudes and frequencies along the azimuthal direction, which only allows qualitative comparison. Despite these variations, the spectra of the pressure fluctuations at different Mach numbers reveal that a significant amount of the energy content is concentrated around a specific frequency at $M=0.8$, indicating that a distinct fluid mechanical process is present. To better understand this phenomenon, the study focuses on the events occurring around this Mach number.

The PSD was obtained to examine the base and chamber pressure spectra over non-dimensional frequencies (Strouhal numbers), $\textrm{Sr}_D=fD/u$. It is shown in Fig. 13 (right) for the discrete data sets of the no jet, cold jet, and hot jet cases at Mach 0.8. It illustrates that significantly different spectra occur for the cold and hot jet cases. While for the cold jet case, the most prominent peaks appear at $\textrm{Sr}_D=0.35$ and its first and second harmonic frequencies at $\textrm{Sr}_D=0.7$ and 1.05, the highest peaks in the hot jet case are found at lower frequencies of $\textrm{Sr}_D=0.11$, 0.3, and 0.4. The no jet case is additionally provided for reference. Its amplitude level is significantly reduced compared to the cases with jet. However, it contains its main peaks at $\textrm{Sr}_D=0.11$ and 0.18 with a relative amplitude excess over the mean fluctuation level of 2.2 and 2.3, respectively.

Comparing the base pressure spectra ($\textrm{PSD}_{p_{b}}$) with those of the combustion chamber pressure ($\textrm{PSD}_{p_{cc}}$) in premultiplied form at sensor location PC1 ($r/D=0.234$, Fig. 4), it is noticeable that the peak at $\textrm{Sr}_D=0.35$ is very close to the second longitudinal chamber mode, represented by the peak of the chamber pressure spectrum at $\textrm{Sr}_D=0.335$, provided on the secondary axis in Fig. 13 (right). That longitudinal chamber mode broadens in the frequency domain due to the chambers specific internal geometry thus fully overlaps with the oscillation in the base pressure. It could, therefore, be assumed that the combustor exit conditions contribute to the increase in base pressure fluctuations if a dedicated motion of the external flow is present that might couple with an oscillating nozzle exit pressure. In relation to that, some of the peaks in the base pressure spectrum can actually be attributed to characteristic flow phenomena in the external flow and the supersonic jet, which will be considered in more detail in Sect. 3.3, Impact on Wake Flow Dynamics. In the hot jet case, the first longitudinal chamber mode around $\textrm{Sr}_D=0.92$ obviously does not induce increased pressure fluctuations at the base. A more detailed analysis of the occurring modes in the combustion chamber is presented by Kirchheck et al. (2019).

The Mach number-dependent base pressure data from WTT are supplemented by spatially resolved data of static pressure coefficient, RMS pressure coefficient, and fluctuation frequencies from numerical investigations, shown in Fig. 14 and Fig. 15. The trend illustrated in Fig. 14 (right) confirms the previously described tendency of generally lower pressure fluctuation levels associated with the hot gas environment depicted in Fig. 13. However, the curves of the RMS pressure coefficient clearly show that this deviation, particularly in the nozzle wall region, is almost exclusively caused by the change of wall temperature. This strengthens the hypothesis that wall shear stresses have a large influence on the degree of turbulence within the recirculation region. For the static pressure level, a general increase caused by the hot plume environment is noticeable in Fig. 14 (left), which is equally divided between the increase in jet and wall temperatures up to about $x/D=0.85$. The fact that this trend does not continue for $x/D>0.85$ could be due to the shift of the reattachment location discussed above in Sect. 3.1, Impact on Instantaneous and Mean Flow Features. This obviously also influences the wall pressure distribution, particularly due to the increase in the wall temperature, which is visible in Fig. 14 (left) by a downstream shift of the minimum nozzle wall pressure coefficient.

Fig. 14

Impact of plume/wall temperature on the base/nozzle wall pressure distribution from the IDDES simulations along the symmetry plane with the base at $\varvec{x/D=0}$ (reproduced from Schumann et al. 2021a; Schumann 2022); left: pressure coefficient and right: RMS pressure coefficient fluctuations

Fig. 15

Scaled premultiplied PSD of the pressure on the external nozzle surface

In Fig. 15, a scaled premultiplied PSD of the pressure on the external nozzle surface provides spatially distributed spectra for the cold and hot jet cases from the IDDES computations. They generally show that the fluctuation frequencies increase in the downstream direction, starting at the base and moving further toward the nozzle exit. One reason that applies to both the cold and hot jet cases might be attributed to the usual dissipation of eddies along the external shear layer, leading to higher frequencies caused by more frequent pressure disturbances from vortex break-up events in smaller scales. In a turbulent shear layer, this process would also lead to a broadening of the fluctuation bandwidth along the shear layer, which is also noticeable in the figure. Although more pronounced in the cold jet case, the mean frequency peaks along the nozzle wall range from $\textrm{Sr}_D=0.07$ in the base corner at $x/D=0$ to $\textrm{Sr}_D\ge 0.8$ at the end of the nozzle at $x/D=1.2$ for both cases.

Exclusively in the case of the hot jet, an additional peak in the range of $\textrm{Sr}_D=0.45$ arises in the base corner, the frequency of which also slightly increases in the downstream direction up to $\textrm{Sr}_D=0.5$ at the end of the nozzle. A possible explanation could be seen in the fact that there is a closed feedback with an instationarity at the nozzle exit, whose period becomes increasingly shorter as the source of the disturbance is approached in the downstream direction. A closer investigation of the flow field leads to the assumption that this phenomenon is related to an unsteady separation of the internal nozzle flow, which appears to be able to interact more strongly with the external shear layer due to the larger reattachment length in the hot jet environment. Its appearance corresponds to the peak at $\textrm{Sr}_D=0.4$, also found exclusively in the base pressure spectra from the hot jet WTT, shown in Fig. 13 (right).

3.3 Impact on wake flow dynamics

The dynamic wake flow motion of an axisymmetric base flow with a backward-facing step and a centric cold jet has already been extensively discussed in the literature, as stated in the introduction. Certain regularly occurring frequencies in pressure or flow data are usually associated with specific modes of the external shear layer, such as the pumping motion ($\textrm{Sr}_D= 0.1$), the flapping motion ($\textrm{Sr}_D= 0.2$), and the swinging motion of the shear layer ($\textrm{Sr}_D= 0.35$). A recent hypothesis by Saile and Gülhan (2021) combines this knowledge with research on supersonic jet instability phenomena to explain the amplification of wall pressure fluctuations or actuator loads during the ascent of space transportation vehicles. An example of this coupling of the aerodynamic near-wake motion with jet screeching is demonstrated using Ariane 5 at transonic Mach numbers, as shown in Fig. 16.

Fig. 16

Analytical estimates of screeching frequencies and wake flow modes during subsonic and transonic ascent of an exemplary launcher configuration (based on Saile (2019); Saile and Gülhan (2021))

3.3.1 Base pressure measurements

The results of the present study provide evidence to support the hypothesis presented and that it can also be applied to the results of the current wind tunnel tests for the case of the cold jet in external flow. Figure 17 illustrates this by superimposing a spectrogram of the base pressure fluctuations at various Mach numbers during a transient cold jet wind tunnel test with the analytical estimates of the typical shear layer modes and screeching frequencies of the current test setup. A coupling is assumed to occur at the junctions of the shear layer motion and screeching frequencies (and respective harmonics), where the spectrogram shows narrow-band amplification in this region. This appears to take place at the marked position in Fig. 17 near $M= 0.8$, where $\textrm{Sr}_D= 0.35$ and the first screeching frequency $f_\textrm{sc}$ intersect each other, corresponding to the evaluation of the discrete test data at $M= 0.8$ in Fig. 13 (right).

Fig. 17

Power spectral density from base pressure measurements during a continuous Mach number transient, superimposed by analytical estimates of screeching frequencies and wake flow modes

3.3.2 HSS spectral analysis

To validate that the increases in pressure fluctuation can be attributed to discrete flow motions, modal analyses of the high-speed schlieren recordings were performed at $M=0.8$, following the method described above in WTT data post-processing. These can then be compared across the cold and hot jet cases. The spatially averaged amplitude spectra of the schlieren intensity fluctuations for the no jet, cold jet, and hot jet cases are presented in Fig. 18. Here, it can be seen that for the case without a jet, in addition to the very uniform spectrum, two clearly prominent peaks appear at $\textrm{Sr}_D=0.19$ and around $\textrm{Sr}_D=0.35$, corresponding to the previously mentioned flapping and swinging motions of an axisymmetric backward-facing step flow without a jet. These peaks also appear in the hot jet case. However, the signal-to-noise ratio is lower, and the white noise level is considerably higher, which is related to the observations from the HSS images (Fig. 11). Additionally, in the hot jet case, another peak appears at $\textrm{Sr}_D=0.11$, close to what was also discovered in the base pressure spectra at $\textrm{Sr}_D=0.1$, and what is stated in the literature as the pumping motion. Accordingly, compared to the external flow without jet, the hot jet does not appear to have a significant effect on the wake flow dynamics.

Fig. 18

Spatially averaged spectrum of the HSS recordings for the no jet, cold and hot jet cases (reproduced from Kirchheck et al. 2021)

In the case of the cold jet, this is essentially different. Here, a very strong peak at $\textrm{Sr}_D=0.35$, along with its harmonics, apparently dominates the entire flow field to the extent that no further motions may occur at any other frequencies. This particular observation is consistent with the concentration of base pressure fluctuations at $\textrm{Sr}_D=0.35$ and its harmonics in Fig. 13, further supporting Saile’s coupling hypothesis not only by the pressure data but also by the intensity of periodic density fluctuations detected in the schlieren recordings of the near-wake. The results, therefore, suggest that in the hot jet environment, the intensity of the coupling mechanism is reduced compared to the cold jet environment. This might be attributed to a change in the screeching frequency when subjected to hot gas conditions, as discussed in Kirchheck et al. (2019). However, while not particularly pronounced, it still begs the question for a physical explanation.

3.3.3 Mode shape analysis

An isolation of the occurring Strouhal numbers from Fig. 18 in the form of a modal analysis allows a closer look at the shape of the respective movements to associate—ideally—the typical frequencies with the corresponding typical motion patterns. This is presented in Fig. 19 for the experimental HSS results on the no jet, cold jet, and hot jet cases for several isolated Strouhal numbers ${\textrm{Sr}_D}_\textrm{iso}$ and in Fig. 20 for the case with hot jet and hot walls from a Dynamic Mode Decomposition (DMD) of the numerical IDDES flow field solution.

The mode shapes of $\textrm{Sr}_D=0.19$ and 0.35 are presented in Fig. 19a–b for the no jet case. They show a general increase in the fluctuation amplitude in the external shear layer and in the wake of the inactive nozzle cylinder. Additionally, at $\textrm{Sr}_D=0.19$, there is an amplified region in the external shear layer suggesting a periodic lateral displacement of the shear layer. This displacement corresponds to the maximum and minimum wave positions of the characteristic motion indicated in the figure. It defines the crests of the wave at the position of maximum intensity and the throughs at the downstream and upstream ends of the intensified region. They align with the expected shape of the cross-flapping motion. At $\textrm{Sr}_D=0.35$, similar regions with smaller axial extent can be noticed in a serial arrangement along the shear layer, with a trough of a wave in between where no fluctuation amplitude is detected. This shape corresponds to the expected shape of the swinging motion of the shear layer. As observed in Fig. 18, no frequency with a characteristic longitudinal pumping motion can be identified in the range of $\textrm{Sr}_D=0.1$. However, this absence could also be a consequence of the schlieren edge setting, which leads to a higher sensitivity to lateral than axial density gradients when aligned in parallel to the model symmetry axis.

Fig. 19

Mode shapes in HSS recordings; (a)–(b) ambient flow only, (c)–(d) ambient flow with cold jet, and (e)–(f) ambient flow with hot jet (reproduced from Kirchheck et al. 2019, 2021)

Fig. 20

Dynamic mode decomposition (DMD) of CFD results on the wake flow field with hot exhaust plume (reproduced from Schumann 2022)

In the case of the cold jet, a very strong excitation of the swinging motion is illustrated in Fig. 19c and d at $\textrm{Sr}_D=0.35$. High displacement values and strong density gradients lead to a very clear representation of the mode shape even far downstream in the wake. The conservation of this motion in the downstream direction accordingly also leads to a swinging motion of the supersonic jet, which is also evident from this illustration. Furthermore, the shape of the first harmonic motion at $\textrm{Sr}_D=0.7$ is indicated, characterized by a decomposition of the original waveform into a smaller amplitude wave of half the wavelength. It should also be noted that even the expansion shock wave at the exit of the nozzle is clearly excited at the swinging motion frequency, which was visible in the range of the longitudinal chamber mode in the pressure spectra in Fig. 13. As a matter of fact, it should, therefore, not be excluded that the considerable flow excitation in the cold jet case is not exclusively caused by the coupling of the external flow with the jet screeching but potentially also by chamber pressure fluctuations imposed on the supersonic jet, its shock structure, and consequently also the jet shear layer.

The HSS evaluation of the hot jet case in Fig. 19e and f, as expected from the averaged spectra in Fig. 18, shows similar mode shapes for the peaks at $\textrm{Sr}_D=0.2$ and 0.35, representing the cross-flapping and swinging motions. Besides an increase in the general noise level in the external shear layer as well as in the jet area, no further amplification of the jet shock structure appears in this case. Particularly, there is no amplification upstream of the first Mach disk, where oscillations are most likely expected to originate from internal rather than external excitation. Therefore, the two most prominent frequencies show no evidence of any excitation of their motions due to coupling mechanisms with the jet shear layer or combustor instabilities.

The DMD of the numerical IDDES solution for the hot jet case supports this observation by reproducing the dominant modes from the schlieren recordings at $\textrm{Sr}_D=0.2$ and $\textrm{Sr}_D=0.35$ and providing a closer look at the three-dimensional flow field data. Interestingly, in this case, the longitudinal cross-pumping at $\textrm{Sr}_D=0.1$ is also identified, as well as the higher frequency mode at $\textrm{Sr}_D=0.45$, which was already mentioned in relation to the spatial distribution of nozzle wall pressure fluctuations in the hot jet case in Fig. 15. From the DMD analysis, this higher frequency mode can be characterized as a higher frequency swinging of the shear layer that, as mentioned above, could be triggered by an unsteady nozzle separation.

3.4 Impact on nozzle forces

From the DMD of the numerical IDDES solution, additional phase information on the identified modes is available. This is relevant when considering the resulting net force on the nozzle, which is decisive in terms of actuator loads for thrust vector-controlled nozzle configurations. The net force is zero for a symmetric mode and nonzero for asymmetric modes, such as the cross-flapping and swinging motions at $\textrm{Sr}_D=0.2$ and $\textrm{Sr}_D=0.35$ (Fig. 20). However, if the loads imposed on the nozzle extension are considered in terms of structural design, then the symmetrical modes, i.e., the longitudinal cross-pumping at $\textrm{Sr}_D=0.1$ and the second swinging mode at $\textrm{Sr}_D=0.45$, and thus the total gross load, need to be taken into account.

To adapt to the increased actuator loads during the ascent of Ariane 5 at the critical Mach number 0.8 (David and Radulovic 2005), forces on the nozzle are considered as net forces in this section. They are evaluated separately for the y and z components and then combined to form a total force $F = 0.5(F_y + F_z)$. In Fig. 21, the total force and its components are compared for the cold jet case and the two hot jet cases with cold and hot walls, with respect to their premultiplied power density spectrum as a result of the IDDES computations.

Fig. 21

Impact of plume and wall temperature on the dynamics of the pressure forces, acting on the nozzle (reproduced from Schumann 2022)

In the cold jet case, there are prominent peaks in the spectrum of the combined force around $\textrm{Sr}_D=0.28$ and $\textrm{Sr}_D=0.35$, with the highest peak being at $\textrm{Sr}_D=0.35$, consistent with the observations obtained from the experiment. As also observed in the experiment, no peak appears at $\textrm{Sr}_D=0.2$, which is different for both hot jet cases. Particularly for the hot jet case with cold walls, different peaks occur below and above $\textrm{Sr}_D=0.2$, yielding a combined force with a peak amplitude around this value. However, due to limited resolution at low frequencies, distinguishing between them becomes challenging. Nevertheless, these observations align closely with experimental results. In this case, the peaks at $\textrm{Sr}_D=0.35$ and $\textrm{Sr}_D=0.45$ also appear in the spectrum of the combined force. These peaks are noticeable in both the cold wall and hot wall cases, but they are more pronounced in the cold wall scenario. This observation aligns with the previous findings indicating that hot walls result in decreased fluctuation amplitudes and, consequently, lower wall shear stresses. The absence of the pumping motion in the spectrum at $\textrm{Sr}_D=0.1$ can be attributed to its symmetrical shape, by which the forces on opposing sides of the nozzle cancel each other out.

Thus, the spectrum of nozzle forces in the different cases shows good agreement not only with the numerical results from the wall pressure fluctuations, which is intrinsic, but also with the HSS evaluation presented above. It should be noted, however, that the significant excitation of the swinging motion frequency at $\textrm{Sr}_D=0.35$ in the cold jet experiment is not fully represented by the numerical simulation. This discrepancy suggests that other factors, such as the previously mentioned combustion chamber pressure fluctuations, could contribute to the peculiarity of the experimental results, since this influence is not considered in the numerical simulation. Furthermore, the hypothesis on the coupling of the wake flow modes with instability phenomena of the supersonic jet is based on the fact that jet instabilities are generated inside the jet shear layer at a position as far as about three Mach disks downstream of the nozzle exit. Properly replicating such coupling mechanisms requires extremely high resolution of the jet shear layer to prevent pressure disturbances from dissipating during propagation to the receiving locations of instability, namely, the nozzle exit plane and the base shoulder. This fact strengthens the statement that the coupling mechanism could be confirmed by the present experimental data.

In addition to the information on fluctuation amplitudes and frequencies, Fig. 22 provides insight into the circumferential distribution of the point of application of the combined forces. It shows nearly homogeneous distributions for all three cases, indicating that no preferred directional pattern of force introduction develops over time. This further illustrates that not only are the fluctuation amplitudes lower in the case with a hot jet and hot walls compared to the cases involving a cold/hot jet and cold walls, as shown in Fig. 21, but also the average force over time is approximately 20% lower with increased wall temperatures. This observation is consistent with the reduction in the RMS wall pressures for the hot jet with hot walls observed in the experiment (Fig. 13, left), as well as with the numerical results (Fig. 15).

Fig. 22

Impact of plume and wall temperature on the pressure forces, acting on the nozzle (reproduced from Schumann 2022)

4 Conclusions

The present study provides an overview of the different impacts of plume and/or wall temperature on various measurements of the aft-body flow of a generic space launcher geometry in subsonic flight. These measurements were conducted on a wind tunnel model in ambient flow using either room temperature air or hydrogen–oxygen combustion as a propulsive jet simulation. Scale-resolving CFD calculations complemented the experimental tests, including detailed chemistry and thermal coupling between the internal flow, the model structure, and the external flow. The comparison of the cold and hot jet scenarios is based on a characterization of a cold plume reference case, examining mean flow features, base pressure and base pressure fluctuations, as well as the dynamic motion of the wake flow field.

Differences are revealed in all areas, which may potentially be traced back to the influence of the hot jet itself or the hot walls resulting from the internal flow. One of the main influences of the hot jet is the entrainment of hot gases into the recirculation region due to the interaction of the external and jet shear layers. The entrainment of low-density fluid leads to a reduction of viscosity in the bulk recirculation region. This reduction in viscosity is associated with a decreased eddy dissipation process in the external shear layer, resulting in delayed reattachment. This delay in reattachment is further supported by the hot nozzle walls, which reduce wall shear stresses and, consequently, the turbulence introduced into the recirculation region and its surrounding shear layer. Additionally, the higher jet exit velocities are expected to modify the pressure gradient by decreasing the back pressure on the external shear layer, further inhibiting the reattachment of the shear layer. The delayed reattachment leads to a decrease in static pressure on the nozzle walls, resulting in reduced RMS pressure fluctuations. Combined with the reduction of wall shear stresses, this also leads to a decrease in the forces acting on the nozzle cover. Specifically, the reattachment length is increased by 34%, and RMS pressure fluctuations are reduced by up to 29% in the hot jet experiment. These findings largely validate similar trends observed in the CFD results, such as the reduction of combined nozzle forces, particularly evident in the case with hot walls.

Regarding the dynamic flow motion, in the cold reference case, a pronounced interaction between the swinging motion of the shear layer and jet screeching at $\textrm{Sr}_D=0.35$ results in resonance across the entire wake flow region. This resonance amplifies the fluctuations and leads to significant pressure disturbances. However, significant deviations are observed in the hot jet cases. Unlike the cold jet case, the hot jet cases do not exhibit similar resonance phenomena. Instead, the dynamic properties in the hot jet scenarios more closely resemble those of the reference case without a propulsive jet. The governing Strouhal numbers of $\textrm{Sr}_D=0.1$, 0.2, and 0.35 appear, consistent with typical flow motions known from the literature. In the hot jet cases, these typical modes are present, but their intensity and interactions differ. A second swinging motion is detected in both WTT and CFD. This additional mode is attributed to the interaction of the external shear layer with an increased nozzle flow separation, which is due to a reduced nozzle exit pressure compared to the cold jet case.

Identified as potential influences on the development of the resonance mechanism are a slightly increased jet screeching frequency in the hot jet case, as well as a significant alteration of the first longitudinal chamber mode (1 L). However, it is not expected that these factors alone would provide sufficient evidence to explain why resonance is not present in the hot jet cases. Instead, it is suggested to further build up knowledge on the sensitivities of the cold jet resonance mechanism. For example, further parameter investigations, such as a variation of the relative reattachment length in relation to the nozzle exit plane, might provide valuable insights. Given that reattachment is significantly altered in the hot jet environment, understanding its necessity for the cold jet flow coupling could also shed light on its relevance for realistic hot jet scenarios. This approach would help in understanding the underlying mechanisms governing resonance phenomena in different flow conditions and provide valuable insights for future studies in this area.

Finally, valuable information about temperature impacts on relevant characteristics of rocket wake flows is provided based on hydrogen–oxygen combustion at low oxidizer–fuel ratios. However, the temperatures reached in the experiment are far below those of realistic rocket combustion chambers. This justifies the question of whether the trends presented in this paper would continue for higher jet reservoir conditions. This highlights the significance of accounting for the effects of hot plumes and hot walls in characterizing rocket wake flows for an accurate design process. The limited similarity observed between cold and hot jet cases in various aspects underscores the need for further improvement in our understanding of the underlying physical mechanisms.