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

Experimental and numerical simulation of launcher base ﬂows is crucial for future launcher design. In experiments, the 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 sim-pliﬁcations 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 in the frame of the SFB/TRR 40 Collaborative Research Centre in order 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, us-ing 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.

Plume and wall temperature impact on the subsonic aft-body flow of a generic space launcher geometry Daniel Kirchheck1 • Jan-Erik Schumann2 • Markus Fertig 3 • Dominik Saile 1 • Volker Hannemann 2 • Thino Eggers 3 • Ali Gülhan 1 1 Introduction Since 2008, aft-body flows of space launch vehicles in various flow regimes have been investigated on generic launcher configurations within the frame of the Collaborative Research Centre (SFB) Transregio 40 (TRR40) (Haidn et al. 2018;Adams et al. 2021).Since 2016, one of the key interests has been laid in the interaction of the high subsonic ambient freestream with the supersonic overexpanded propulsive jet during the ascent phase of a launcher.Under certain flow conditions in this phase, significant non-stationary flow effects within the nearwake flow may occur, resulting in unsteady mechanical loads known as buffeting on base and nozzle structures (David and Radulovic 2005).
In order to improve the knowledge on their driving mechanisms and consequently enhance predictability of qualitative and quantitative loads for future launcher design, these effects have been studied at the German Aerospace Center (DLR).It was achieved through a complementary experimental and numerical approach on a generic Ariane 5 geometry, using ambient temperature air (denoted 'cold') and hot gas generated from the combustion of gaseous hydrogen (GH2) and gaseous oxygen (GO2) for the exhaust jet (Kirchheck et al. 2021;Schumann et al. 2021a).
Previous studies in this domain predominantly utilized air jets (Deprés et al. 2004;Deck and Thorigny 2007;Meliga et al. 2009;Weiss et al. 2009;Wolf 2013;Statnikov et al. 2017;Horchler et al. 2018;Saile et al. 2019a).However, to the knowledge of the authors, the similarity of the wake flow physics between interaction with a cold air jet and a hot reactive jet, as present in real flight scenarios, has not been proven yet, neither by experiments nor numerical simulations.Therefore, the paper presents experimental and numerical results from cold and hot jet interaction tests in order 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.

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).It combines the Vertical Wind Tunnel Facility (VMK), a GH2/GO2 supply facility and a high-pressure (HP) dry air supply system (Fig. 1).
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 m 3 reservoir at a maximum pressure of 67 bar.It allows typical test durations of 30 s to 60 s and the upstream heat storage can heat the flow up to 750 K, providing sea level conditions for Mach numbers M ≤ 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 Fig. 1 Schematic of the Hot Plume Testing Facility (HPTF), at the German Aerospace Center (DLR), Cologne (taken from Kirchheck et al. 2021) 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 OFR ign = 0.5 and the stoichiometric mixture ratio OFR 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).

Test Setup
The generic launcher afterbody (Fig. 2) is represented by an axisymmetric backward-facing step geometry with base diameter D = 67 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 two layers of filter screens to increase uniformity of the flow.The model houses a combustor with diameter D cc = 38.1 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 expansion ratio ε = 5.6298.The outer model dimensions are similar to previous investigations by Saile et al. (2019bSaile et al. ( ,a, 2021)), details on the design are provided in Kirchheck et al. (2019).

Test Cases
Three reference cases were defined: an ambient flow case without jet and ambient flow cases with cold/hot jet.The selected test conditions are given in Table 1 and Fig. 3.For the ambient flow, due to the reported significant increase of base pressure fluctuations in flight and experiments at high subsonic Mach numbers (David and Radulovic 2005), M ∞ = 0.8 was selected as 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); Saile et al. (2019bSaile et al. ( ,a, 2021)).Additional tests were conducted at several discrete and transient Mach number runs in the range of M ∞ = [0.5 . . .0.95].The static temperature in the freestream (T ∞ ) is calculated using isentropic relations with an estimated ambient temperature T amb ≈ 288 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 amb .For the hot jet case, OFR = 0.7 was set, resulting in a chamber temperature T cc = 918.7 K from one-dimensional equilibrium calculations, performed using the Rocket Propulsion Analysis (RPA) software tool.The total mass flows were 459.9 g/s for the cold jet and 89.4 g/s for the hot jet case.The test conditions were constant in all cases during the last two seconds of the run.Evaluations are performed within t eval = [18 . . .20] s.

Measurements, Instrumentation and Post-processing
The test setup provided access for concurrent optical and sensor measurements.
Figure 4 gives an overview on 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 with a recess of 0.5 mm (XCQ-080) and in the combustion chamber with a transmission length of 52.77 mm (XCE-062).They were sampled at 100 kHz and 10 kHz respectively in order 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.Narrow band filtering was used for the hot plume tests in order to increase the signal to noise ratio within the harsh environment of after-burning plume gases.Finally, 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 µs.They were used to identify dynamic flow field motion leading to the measured base pressure fluctuations.Additionally steady pressure and temperature measurements, as well as Infrared Thermography (IRT) were performed that are not part of the discussion in the present paper.Standard post-processing methods were applied to the high-frequency sensor and PIV measurements leading to mean pressure (p) and mean flow field data (u), as well as time and Mach number dependent root mean square (RMS) pressure RMS ) and pressure fluctuation frequencies 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 10 Hz frequency resolution.The HSS recordings were similarly processed on a pixel-by-pixel basis by extracting the grayscale intensity values I(t) from 10 000 samples (0.5 s) image ensembles.
For a first global analysis, the HSS intensity spectra PSD I were spatially averaged to ⟨PSD I ⟩ 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 ′ RMS in the image coordinate system.Finally, the two-dimensional distribution of the response of isolated frequencies PSD I (f ) can be used to characterize the mode shapes of the dynamic wake flow motion.

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 in order to account also for potential effects routing from the wind tunnel nozzle shear layer.Both the internal and external volumes are divided into a region that is 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).For the RANS computations, local time stepping is used for the temporal discretization and the AUSMDV upwind scheme is used for the spatial discretization.For the combined RANS-IDDES approach, dual time stepping with backwarddifferences and a three-stage Runge Kutta scheme is used for the temporal discretization, while a central hybrid low-dissipation, low-dispersion scheme by Probst and Reuß (2016); Fertig et al. (2019) is used for the spatial discretization.Both setups employ a two-equation k-ω Shear Stress Transport (SST) turbulence model.More 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 used 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 provide sufficient stability and efficiency in the combustion chamber with finite rate chemical reactions including 9 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 W/m 2 K was used.For the coupled RANS-IDDES simulations a quasi steady temperature distribution was assumed.In order 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 varied until heat flux convergence between flow and structure solver was obtained.Details on the approach are provided in Fertig et al. (2019); Schumann et al. (2021a).
For the IDDES simulation, ambient air and the propulsive jet are both modeled as single component gases with jet flow conditions determined in precursor RANS simulations.The scale-resolving simulations are performed on a full 360 • hybrid grid with a circumferential resolution of 0.94 • .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 containing a total of approximately 33 Million grid points with a general restriction on the non-dimensional normal wall spacing of ∆y + < 1.The grid resolution and design was optimized during a grid study.It 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).

Test Cases
The test cases focused on in the current paper include 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 s.Therefore, a case with cold wall (T w = 300 K) representing the beginning of the run and a case with 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).

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 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 is used for validation of e. g. 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 with regard to the RMS pressure coefficient distribution and PSD of wall pressure fluctuations can be found in Schumann et al. (2021b).

Thermal Coupling
The results from the coupled simulations are shown in Fig. 9 as contour plots of the distributed gas temperature T gas inside the combustion chamber volume and the distributed solid temperature T 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 s with T solid = 279.15K and the settled conditions at t = 20 s are shown.The internal flow conditions are  (2004); Meliga et al. (2009) set corresponding to the experimental setup described above using OFR = 0.7 at ṁ = 89.4g/s.
The internal flow is characterized by a maximum temperature of 3 550 K inside the reaction zone and an average temperature of approximately 900 K at 21.5 bar at the end of the chamber.The reaction is completed about 50 mm upstream of the nozzle throat.After 20 s, the temperature distribution inside the structure shows maximum temperatures of approximately 650 K in the vicinity of the nozzle throat and about 630 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 third of the chamber length.The axial position of the maximum is shifted further downstream w. r. t. 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 W/m 2 /K in the corner at x = 0 and 1 600 W/m 2 /K at the nozzle tip are predicted.The characteristic outflow conditions are p e = 0.44 bar, T e = 420 K, M e = 3.15, and u e = 3.5 km/s.Due to a slightly lower pressure in the exit plane

Wall Heat Flux Modeling
Using the wall temperature distribution computed in the coupled simulation, both RANS and IDDES are used 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 comparison is obviously interesting when efficient modeling using steady state solutions is preferred over a highly resolved unsteady approach.In case of separating/reattaching flows, which are sensible to the state of the boundary layer, the wall heat flux could impact the global flow topology by uncertainties in the prediction of separation and reattachment locations.
In the present study, it could be shown that the qualitative trends of wall heat flux in the base region can be predicted well using a two-equation k-ω approach in contrast to the one-equation Spalart-Allmaras (SA) turbulence model.On the external nozzle surface (Fig. 10, top), the IDDES solution is characterized by local maximums near the base and the nozzle lip, which are caused by the presence of a corner vortex and the highly unsteady flow field at the reattachment location.On the base surface (Fig. 10  constant, with an increase at the vicinity of the base shoulder that is 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-ω model obviously underpredicts the heat flux in the corner region while the heat flux along the nozzle wall is overpredicted.Further, in this study, the SA model is considered unsuitable for prediction of the heat flux distribution, since it significantly alters the flow field by provoking reattachment and shifting it much farther upstream, which leads to a qualitative mismatch of the heat flux distribution.

Results
The following sections highlight the main impacts found in WTT and CFD investigations.In contrast to the cold jet environment, they are caused by the presence of a hot jet, on the one hand in combination with cold walls representing the beginning of the wind tunnel test, or hot walls representing the converged conditions at the end of the test.The effects are presented and discussed from the aspects of instantaneous and mean flow features, base pressure and base pressure fluctuations, the dynamic wake flow motion, and the resulting external forces on the nozzle cover.

Impact on Instantaneous and Mean Flow Features
The impact of a hot plume and/or hot walls on the instantaneous and mean flow features compared to the cold plume case with cold walls are investigated in WTT by means of Schlieren imaging and the velocity magnitude fields, obtained from PIV and directly from the CFD results in Fig. 11  In sequences of snapshots for 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 these cases.In 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 cold jet and ambient flow (Fig. 11c), whereas the oscillation intensity is strongly increased.In 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 layer.In the cold jet case (Fig. 11c), the periodic antisymmetric oscillation 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.It is represented by the increasing blur of the jet boundaries and shock structure in the mean image compared to the cold jet without ambient flow (Fig. 11b).This blur is also present in the hot plume case (Fig. 11d), but here more likely due to a stochastic rather than periodic movement of the jet shear layer.In this case, the shear layer also shows a larger angle of growth compared to the cold plume case, which additionally contributes to the blurring in the downstream region.
In case of the cold supersonic jet in ambient flow (Fig. 11c), pressure waves are clearly visible, traveling from a downstream source towards 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 less pronounced and rather on a random timebase than strongly periodically.In case of ambient flow without 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.This trend is marked in Fig. 11 by a white arrow, qualitatively illustrating the impact of the type of plume on the reattachment location.Therefore, compared to the ambient flow without jet (Fig. 11a), where the bend of the external shear layer occurs slightly downstream of the nozzle exit, its location is shifted upstream, close to the nozzle lip, in the presence of a cold jet (Fig. 11c).In presence of a hot jet, the bend is shifted farther downstream (Fig. 11d).
The qualitative trends compared to 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 presence of a cold plume and x r /D = 1.265 in 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 driven by several factors.These factors include the entrainment of high-temperature, lowdensity fluid from the internal flow into the recirculation region.Additionally, an increase in the external nozzle wall temperature leads to a reduction in wall shear stress, thereby decreasing turbulence introduced into the recirculation region and facilitating the dissipation of structures in the external shear layer.Furthermore, an increase in jet exit velocity reduces the back pressure on the reattaching shear layer, resulting in downstream suction of the shear layer.
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 like 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.

Impact on Base Pressure
Base pressure measurements were conducted in the WTT during continuous Mach number transients between M = 0.5 and 0.95 with a slope of 0.01 s −1 as well as for several discrete Mach numbers in the same range.The corresponding RMS pressure fluctuations p ′ RMS are plotted in Fig. 13 (left) for the cold jet case in the full Mach number range.This data 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 and 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.Peaks of the RMS pressure fluctuations are found at Mach numbers 0.522, 0.651, and 0.778.However, in order to evaluate the relevance of pressure fluctuations with respect to flight, e. g. with regard to structural modes, the frequency spectra and the dynamic pressure at the respective trajectory point must also be considered.For this reason, focus was on Mach 0.8 in the present study.A Fast Fourier Transform (FFT) was performed to examine the maximum base pressure fluctuation amplitudes distributed over non-dimensional frequencies (Strouhal numbers), Sr D = f D/u.It is shown in Fig. 13 (right) for the discrete data sets discussed in the previous paragraph.It illustrates that at the critical Mach number of 0.8, significantly different spectra occur for the cold and hot jet cases.While for the cold jet case, very distinct amplitude peaks appear at Sr D = 0.35 and its first and second harmonic frequencies at Sr D = 0.7 and 1.05, the highest peaks in the hot jet cases are found at lower frequencies of Sr D = 0.11, 0.3 and around Sr D = 0.4 at M = 0.8.
Comparing the base pressure spectra with those of the combustion chamber pressure, it is noticeable that the peak at Sr D = 0.35 is very close to the second longitudinal chamber mode, represented by the peak of the chamber pressure spectrum at Sr D = 0.335, also included in Fig. 13 (right).It is therefore reasonable to assume that the combustor exit conditions contribute to the increase in base pressure fluctuations.However, some of the peaks can also be attributed to characteristic flow phenomena in the external flow and the supersonic jet, which will be considered in more detail in Section 3.3, Impact on Wake Flow Dynamics.In contrast to that, the first longitudinal chamber mode under hot gas conditions around 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 which are 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, which 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 Section 3.1, Impact on Instantaneous and Mean Flow Features.This obviously also influences the wall pressure distribution, in particular due to the increase of the wall temperature, which is visible in Fig. 14 (left) by a downstream shift of the minimum nozzle wall pressure coefficient.
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 towards 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 Sr D = 0.07 in the base corner at x/D = 0 to Sr D ≥ 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 Sr D = 0.45 arises in the base corner, the frequency of which also slightly increases in the downstream direction up to 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 is 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 stronger interact with the external shear layer due to the larger reattachment length in the hot jet environment.Its appearance corresponds to the peak at Sr D = 0.4, also found exclusively in the base pressure spectra from the hot jet WTT, shown in Fig. 13 (right).

Impact on Wake Flow Dynamics
The dynamic wake flow motion of an axisymmetric base flow with backward-facing step and centric cold jet has already been broadly discussed in 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 (Sr D = 0.1), the flapping motion (Sr D = 0.2), and the swinging motion of the shear layer (Sr D = 0.35).A recent hypothesis by Saile and Gülhan (2021) combines this knowledge with research on supersonic jet instability phenomena to explain amplification of wall pressure fluctuations or actuator loads during the ascent of space transportation vehicles by a coupling of the aerodynamic near-wake motion with jet screeching using Ariane 5 at transonic Mach numbers as an example (see Fig. 16).

Base Pressure Measurements
The results of the present study give reason to believe that the presented hypothesis can be confirmed and also applied to the results of the current wind tunnel tests for the case of the cold jet in external flow.

HSS Spectral Analysis
In order to validate that the increases of pressure fluctuation that occur can be attributed to discrete flow motions, modal analyzes of the high-speed Schlieren recordings were performed at M = 0.8, according to the method described above in WTT data post-processing.These in turn can 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 jet, in addition to the very uniform spectrum, two clearly prominent peaks appear at Sr D = 0.19 and around Sr D = 0.35, which correspond to the previously mentioned flapping and swinging motions of an undisturbed axisymmetric backward-facing step flow.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 Sr D = 0.11, close to what was also discovered in the base pressure spectra at Sr D = 0.1 and what is stated in literature as the pumping motion.Accordingly, compared to the undisturbed external flow, the hot jet does not appear to have a significant effect on the wake flow dynamics.
In the case of the cold jet, this is essentially different.Here, a very strong peak at 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 Sr D = 0.35 and its harmonics in Fig. 13, further supporting Saile's coupling hypothesis by not only 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.

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 in order to associate -ideally -the typical frequencies with the corresponding typical motion patterns.That 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 Sr D 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 Sr D = 0.19 and 0.35 are presented in Fig. 19a-b for the no jet case.They show a general increase of the fluctuation amplitude in the external shear layer and the wake of the inactive nozzle cylinder.In addition to that, Sr D = 0.19 contains an amplified region in the external shear layer that suggests a periodic lateral displacement of the shear layer, which approximately leads to the maximum and minimum wave positions, being the wave crests of the characteristic motion indicated in the figure.It corresponds to the expected shape of the cross-flapping motion.At Sr D = 0.35, similar regions with smaller axial extent can be noticed in a serial arrangement along the shear layer, with a through of a wave in between at which no fluctuation amplitude is detected.It corresponds to the expected shape of the swinging motion of the shear layer.Also as observed in Fig. 18, no frequency with a characteristic longitudinal pumping motion can be identified in the range of Sr D = 0.1, however, this 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.
In case of the cold jet, a very strong excitation of the swinging motion is illustrated in Fig. 19c-d at 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 Sr D = 0.7 is indicated, which is characterized by a decomposition of the original waveform into a smaller amplitude wave of half the wavelength.Also, it should 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 to be 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 combustion 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-f, as expected from the averaged spectra in Fig. 18, shows similar mode shapes for the peaks at Sr D = 0.2 and 0.35, representing the cross-flapping and swinging motions.Next to an increase of 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 not upstream of the first Mach disc, 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 jet shear layer or combustor instabilities.
The DMD of the numerical IDDES solution for the hot jet case adds up on this observation by reproducing the dominating modes from the Schlieren recordings at Sr D = 0.2 and Sr D = 0.35 and providing an even closer look on the threedimensional flow field data.Interestingly, in this case also the longitudinal crosspumping at Sr D = 0.1 is identified, as is the higher frequency mode at Sr D = 0.45, which was already mentioned with respect to the spatial distribution of nozzle wall pressure fluctuations in the hot jet case in Fig. 15.From the DMD analysis, it can be characterized as a higher frequency swinging of the shear layer that, as mentioned above, could be triggered by an unsteady nozzle separation.

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 that is decisive in terms of actuator loads for thrust vector controlled nozzle configurations.It is zero in case of a symmetric mode and non-zero in case of asymmetric modes, which are the cross-flapping and swinging In order to adopt 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 added up to form a combined 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 from the IDDES computations.
In the cold jet case, there are prominent peaks in the spectrum of the combined force around Sr D = 0.28 and Sr D = 0.35, with the highest peak being at Sr D = 0.35, which is consistent with the observations obtained from the experiment.As also observed in the experiment, no peak shows up at Sr D = 0.2, which is different for both of the hot jet cases.Here, particularly for the hot jet case with cold walls, different peaks occur below and above 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, also the peaks at Sr D = 0.35 and Sr D = 0.45 appear in the spectrum of the combined force.They 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 previous findings indicating that hot walls result in decreased fluctuation amplitudes and, consequently, lower wall shear stresses.The fact that the pumping motion does  not appear in the spectrum at Sr D = 0.1 can be attributed to its symmetrical shape, by which the forces on opposing sides of the nozzle are canceled out by each other.
Thus, the spectrum of nozzle forces in the different cases shows a 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 enormous excitation of the swinging motion frequency at Sr D = 0.35 in the cold jet experiment is not fully represented by the numerical simulation.This fact leaves room for interpretation that other aspects such as the previously mentioned combustion chamber pressure fluctuations could also contribute to the peculiarity of the experimental results, since this influence is not considered in the numerical simulation, for example.Further, the hypothesis on a coupling of the wake flow modes with instability phenomena of the supersonic jet bases on the fact that jet instabilities are generated inside the jet shear layer at a position as far as about three Mach discs downstream of the nozzle exit.A proper rebuilding of such coupling mechanisms therefore requires an extremely high resolution of the jet shear layer in order to prevent pressure disturbances from dissipating during propagation to the receiving locations of instability, being the nozzle exit plane and the base shoulder.This in 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 close to homogeneous distributions for all three cases, meaning that no preferred directional pattern of force introduction develops in 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).

Conclusions
The present study provides an overview on different impacts of plume and/or wall temperature on various measurements on the aft-body flow of a generic space launcher geometry in subsonic flight.These were measured on a wind tunnel model in ambient flow using room temperature air or hydrogen-oxygen-combustion as propulsive jet simulation and scale-resolving CFD calculations, complementing 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 bases on a characterization of a cold plume reference case, regarding 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 more or less traced back to the influence of the hot jet itself or to the hot walls resulting from the internal flow.As one of the main influences from the existence of a hot jet, entrainment of hot gases into the recirculation region by interaction of the external and jet shear layers is identified.The entrainment of low density fluid leads to a reduction of viscosity in the bulk recirculation region, which is connected with a reduced eddy dissipation process in the external shear layer, and with that a delayed reattachment.This delay in reattachment is further supported by the hot nozzle walls, leading to a reduction of the wall shear stresses, hence turbulence introduced into the recirculation region and its surrounding shear layer.Finally, the higher jet exit velocities are expected to modify the pressure gradient in posing a decreased back pressure on the external shear layer that further strengthens the inhibition of the shear layer reattachment.The delayed reattachment leads to a decrease in static pressure on the nozzle walls, resulting in reduced RMS pressure fluctuations.Additionally, in combination with the reduction of wall shear stresses, this 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, there is a pronounced interaction between the swinging motion of the shear layer and jet screeching at Sr D = 0.35, resulting in resonance across the entire wake flow region.However, in the hot cases, significant deviations are observed, as no similar phenomena can be detected.By contrast, the dynamic properties more closely follow those of the reference case without propulsive jet, so that essentially the governing Strouhal numbers of Sr D = 0.1, 0.2, and 0.35 occur in combination with their typical flow motions known from literature.In addition to the typical modes, a second swinging motion is detected in WTT and CFD which is attributed to an interaction of the external shear layer with an increased nozzle flow separation 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 (1L).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.It is rather suggested to further build up knowledge on the sensitivities of the cold jet resonance mechanism, as for example further parameter investigations like a variation of the relative reattachment length in relation to the nozzle exit plane might provide.As described above, the reattachment is significantly altered in the hot jet environment, so that an improved understanding of its necessity for the cold jet flow coupling would also provide insight in the relevance for realistic hot jet scenarios.
Finally, valuable information about temperature impacts on relevant characteristics of rocket wake flows is provided on the basis of hydrogen-oxygen-combustion at low oxidizer-fuel-ratio.The temperatures reached in the experiment however are far below those of realistic rocket combustion chambers, which justifies the question on a further continuation of the trends presented in this paper for higher jet reservoir conditions.This highlights the significance of accounting for the effects of hot plume 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.

Fig. 2
Fig.2Cold/hot plume interaction test setup in the Vertical Wind Tunnel Facility (VMK) at the German Aerospace Center (DLR), Cologne (taken fromKirchheck et al. 2021)

Fig. 4
Fig. 4 Layout of base and combustion chamber instrumentation and optical measurement techniques for the VMK test setup

Fig. 5 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. 7
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; right: detailed view of the refined structured grid in the jet flow and near-wake region (reproduced from Schumann et al. 2021a)

Fig. 8
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);Meliga et al. (2009)

Fig. 9
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 T solid = 279.15K; bottom: resulting temperature distribution at t = 20 s for the hot wall cases (radius r stretched by a factor of 5)

Fig. 10
Fig. 10 Heat flux data from various turbulence models (reproduced from Schumann 2022); top: heat flux along the nozzle shroud starting at the base (x/D = 0); bottom: heat flux on the annular base plane starting at the outer nozzle radius (r/D = 0.2)

Fig. 11 Fig. 12
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 2.5 µs, artificial long time exposure 250 ms)

Fig. 13
Fig. 13 Base pressure fluctuations from wind tunnel tests for cold and hot jet cases at variaous Mach numbers; left: RMS pressure fluctuation levels; right: maximum base and combustion chamber pressure amplitude spectrum 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 x/D = 0 (reproduced from Schumann et al. 2021a; Schumann 2022); left: pressure coefficient; right: RMS pressure coefficient fluctuations

Fig. 17
Fig. 17Power spectral density from base pressure measurements during a continuous Mach number transient, superimposed by analytical estimates of screeching frequencies and wake flow modes

Fig. 21
Fig. 21 Impact of plume and wall temperature on the dynamics of the pressure forces, acting on the nozzle (reproduced from Schumann 2022) Hot plume, hot wall

Fig. 22
Fig. 22 Impact of plume and wall temperature on the pressure forces, acting on the nozzle (reproduced from Schumann 2022)

Table 1
Reference ambient and jet flow conditions Kirchheck et al. 2019Kirchheck et al. , 2021) )et flow conditions with respect to the evaluation time window t eval (reproduced fromKirchheck et al. 2019Kirchheck et al. , 2021) )

Table 2
Reference wall temperature conditions for CFD a distribution determined from pre-run coupled simulations , bottom), the radial heat flux distribution is more t = 0.85 k-ω, Pr t = 0.75 k-ω, Pr t = 0.95 SA, Pr t = 0.85