Open Access This book is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, provided you give proper credit to the original author(s) and source, link to the Creative Commons license, and indicate whether changes have been made. This book summarizes the main achievements of the Collaborative Research Center Transregio 40 (TRR40), funded by the German Research Foundation (Deutsche Forschungsgemeinschaft DFG) from July 2008 to June 2020.
In the first phase, the main emphasis was placed on exploratory research aimed at fundamental modeling, development of critical methods and tools, and analysis of innovative concepts. The final funding phase, most projects aimed at creating an integrated simulation environment, demonstrating technologies and demonstrating hardware.
2 Research Area A: Structural Cooling
Transpiration Cooled Ceramic Structures
Since the modification does not model the interaction of different scales resulting from surface pore size and flow transport, a more sophisticated approach based on scaling techniques has been developed . From the solution of the cell problem, the effective coefficients were determined and included in the boundary conditions.
Supersonic Film Cooling
The cooling effectiveness showed the best performance expected for higher densities and thus mass flow rates, also because the laminar/turbulent transition of the film is delayed due to smaller turbulent structures; see Fig.4 (blow ratio of one) where the transition to turbulence is placed downstream of the scale (above the yellow wall). Therefore, the temperature of the facing boundary layer wall must be included for any comprehensive scaling formula used for film cooling design.
Damping Performance of Resonators
4 Snapshot of film cooling flow field: vortices colored by the temperature (blue - cold, red - hot) and mass fraction of the cool helium (yellow: 1, blue: zero) on the bottom wall and the exhaust face. Cooling the wall upstream of the blowing leads to a clearly higher shear and thus to a stronger turbulence production in the free shear layer downstream of the step.
3 Research Area B: Aft-Body Flows
Nozzle Flow Separation Studies
The investigation of two fundamental configurations of heat transfer in an oscillatory flow revealed that, first, acoustic pulsations enhance wall-normal heat transfer and, second, as an oscillatory resonator flow is characterized by thin hydrodynamic and thermal boundary layers, longitudinal heat transfer increases dramatically . Figure 5 interprets this finding physically: turbulence increases the thermal penetration depth of the wall into the channel (non-dimensional width −1≤η≤1).
Interaction of Rocket Plume and External Flow
7 Pressure signal at the nozzle wall (left) and hysteresis behavior of the separation position in the nozzle as calculated by LES. To simulate the interactions of the hot propellant jet, a completely new Hot Plume Testing Facility (HPTF) was established at the Vertical Wind Tunnel Cologne (VMK) that duplicated key hot plume similarity parameters.
Modeling of Buffeting
Scaling hybrid RANS-LES shows a surprisingly strong impact of hot plume and hot walls on the backbody flow. Figure 10 shows the heated turbulent structures at the bottom of the launcher as they reattach to the nozzle shield and interact with the hot plume.
4 Research Area C: Combustion Chamber
- Dynamic Processes in Trans-Critical Jets
- Injection, Mixing and Combustion Under Real-Gas Conditions
- Boundary Layer Heat Transfer Modelling
- Combustion Stability of Rocket Engines
Based on this approach, the influence of diffusion flame structures on room flow (see Fig.14: Principles) on acoustics has been studied . The impact of the 1 L resonance in the LOX injector on the LOX jet is visualized on the right side in Fig.15.
5 Research Area D: Thrust Nozzle
Thermal Barrier Coatings and Component Life Prediction
The results showed that the height of the deformation profile increased almost linearly with the number of load cycles until the cooling channel structure failed due to the so-called doghouse effect, see Fig.17. The comparison with the experiment, which is shown in Figure 17, revealed that the number of cycles to failure, the position of maximum deformation and degradation, and the final failure mode, i.e. the doghouse effect, were accurately predicted by the simulation.
Cooling Channel Flows
Fluid Structure Interaction
Fluid structure interaction (FSI) experiments were performed in a very high temperature environment such that massive deformations occurred with and without plastic behavior . Additional numerical flow analysis was part of a coupled fluid-structure interaction simulation performed in the D10 project (see Martin et al. in this volume).
6 Research Area K: Thrust-Chamber Assembly
Combustion and Heat Transfer
Figure 21 shows the marked differences of the regions near the flame injector with a single injector for the liquid and gaseous oxygen supply cases. Such simulations have also been performed, see Figure 24, which shows the predicted temperature distribution in the center of the plane of the Thrust Chamber Demonstrator (TCD1) of the K4 project .
Dual Bell Nozzle
This effect reduces the margin of stable operation in one particular mode in the presence of minor pressure and flow fluctuations around the nozzle. Recently, K2 has focused on a combination of a classic convectively cooled base nozzle and a film cooled nozzle extension with a double bell contour which was tested at DLR test facility P8, see Fig.25.
26 Hot gas temperature field of the TCD1 demonstrator illustrated in several axial and side slices, as well as for the surface of the stoichiometric mixture. The resulting hot gas temperature field as well as selected axial parts of the structure and coolant temperatures of such a CHT simulation of the TCD1 demonstrator are illustrated in Fig.26.
7 Central Research and Education Support
Special summer program lectures on launcher-related topics have been delivered during the summer program. As a service to all the projects involved, TRR40 underwent a rigorous evaluation of the turbulence modeling activities involved in the computational fluid dynamics projects.
Chemnitz, A., et al.: Modification of eigenmodes in a cold flow combustion chamber by acoustic resonators, J. Kaller, T., et al.: Turbulent flow through a high aspect ratio cooling channel with asymmetric wall heating.
Transpiration cooling experiments for metal nozzle applications were performed in  and numerical simulations for metal nozzles can be found in . Numerical simulations of channel flow of subsonic hot gas exposed to transpiration cooling were performed by Jiang et al.
2 Mathematical Modeling
Hot Gas Domain
For more details, in particular on the modeling of the Reynolds stress tensor and the mean and turbulent heat flux, we refer to previous work [4,6,17]. To this end, the RANS equations (1) are extended with additional Ns. species equations for the partial densities ρα, i.e. the vector of conserved quantities is now determined by.
Porous Medium Domain
For walls W, HG, downstream of the porous sample, the adiabatic boundary conditions take into account the wall temperature change due to cooling. Note that atW,PM no boundary conditions need to be imposed on the density ρf because viscous effects are neglected in the continuity equation and in the Darcy-Forchheimer equation.
Coupling conditions at the interface Int for HG use the normal component of the Darcy velocityvD,na and the fluid temperatureTf of the porous medium at the interface such that. For supersonic nozzle flow, the mass fractions of the coolant Xα, are set to the interface for calculating ρα=ρ·Xα,cwithρ from (8).
3 Numerical Methods
For non-uniform injection and thermal equilibrium, the local pressure continuity is lost due to the factoro¯in (8), but due to. Contrary to previous work [4,6,8], we use the reservoir pressure pRas as an appropriate parameter to ensure that the given mass flow rate at the interface is met and the continuity of the pressure distribution at the interface is established.
4 Numerical Results
Non-uniform Injection into a Subsonic Hot Gas Channel Flow
In fig.2 (left) we show the temperature distribution at the wall in the hot gas domain, where the porous medium is mounted. The cooling film in the wake of the sample is more uniform compared to the lateral wave pattern.
Uniform Injection into a Supersonic Nozzle Flow
For x>70 mm, the temperature is higher than TW due to the adiabatic boundary condition in the wake of the porous medium and therefore no cooling film can be observed. The temperature peak in the lower part of the boundary layer (wall distance less than 2 mm) decreases from 945 K (no cooling) to 853 K (slit injection) and 746 K (circumferential injection).
Dahmen, W., Gerber, V., Gotzen, T., Müller, S., Rom, M., Windisch, C.: Numerical simulation of transpiration cooling with a mixture of thermally perfect gases. König, V., Rom, M., Müller, S., Schweikert, S., Selzer, M., von Wolfersdorf, J.: Numerical and experimental investigation of transpiration cooling with C/C characteristic outflow distributions.
This led to more robust samples, making it possible to characterize fully instrumented samples and use these identical samples in the hot gas channel for transpiration cooling experiments. Thus, in a real combustion chamber, an additional efficiency gain is expected by adapting the refrigerant mass flow distribution to the local heat load and replenishing the refrigerant film laid by upstream transpiration cooling only when needed [2,9,10].
2 Experimental Setup
Stacked Transpiration Cooling Specimen
Visible on the edges of the C/C samples, a galvanic copper layer is used to prevent lateral mass flow and to solder the individual sample into the sample holder. Four surface thermocouples at the outlet of the C/C sample (see Fig.2), one thermocouple at the back and five thermocouples at different depths in the sample.
Hot Gas Channel and Measurement Setup
For quantitative analysis of the infrared data an in-situ calibration according to Martiny et al. Using the differential method, the latter relate the surface temperature reductions to reductions in the measured radiation intensity recorded as digital levels, a unit of intensity for the infrared camera linked to the chosen integration time.
3 Numerical Setup
For the hot gas domain, the inlet boundary conditions are given by the measured inlet temperature and velocity profiles and the average outlet pressure provided by the vacuum pump . The iteratively modified boundary conditions provided by the porous domain are the surface temperatures of the sample TP M,s for the solid and TP M,f for the liquid and the exit velocity vector −→vP M,out.
4 Results and Interpretation of the Serial Transpiration Cooling Experiment
While the measured temperature profiles and the infrared thermography show slight differences with the numerical data, the good agreement of the simulated data for blowing ratios up to F =0.5% is even more remarkable. For the non-cooled sample 3, the surface temperature has already increased over the gap and continues to increase over the first parts of the sample.
5 Summary and Outlook
The aim of these experiments was to show the influence of different contour bending geometries on the film cooling efficiency in the bell extension. For further application of film cooling in new nozzle concepts, film cooling experiments in a double bell nozzle were carried out.
2 Film Cooling Theory
Film Cooling Efficiency
Here η is a function of the wall heat fluxes q˙ measured in the experiment and the heat transfer coefficients α of hot gas ∞ and hot gas-refrigerant mixture m. Since it is not feasible to experimentally determine the ratio of the heat transfer coefficients, this ratio was often assumed to be one in previous projects [5, 13].
Film Cooling Model
This factor depends on the local orifice radius r(x), the swelling ratioF= ρρ∞cuuc∞, the injection slot heights, the orifice radius at the injection point, and the height of the local hot gas boundary layer δ(x) that starts to grow at the injection point. By accounting for the compressibility and pressure gradient of the nozzle flow, the boundary layer height is calculated using the model of Stratford and Beavers .
3 Experimental Setup 3.1 Test Facility
Conical Nozzle 1
Wall heat fluxes and static pressures are measured in the nozzle extension using type E thermocouples and Kulite pressure transducers.
6 Dual-bell nozzle at the test facility (left) and sectional view of the nozzle (right) Table 3 Details of the dual-bell nozzle. To enable experiments without coolant injection, the injection port can be replaced by an insert which provides a smooth inner nozzle wall contour .
4 Results Conical Nozzle 4.1 Reference Flow
Figure 9 exemplarily shows for carbon dioxide as the cooling gas a comparison of the wall heat flux with and without cooling injection. Therefore, the injection conditions, hot gas conditions, and cooling gas conditions were changed separately .
The strong cooling effect of the gas injected slightly downstream of the injection slot is clearly visible from the strong reduction in heat flux. The measured heat fluxes with and without cooling allow the determination of the cooling efficiency according to Eq.
5 Results Dual-Bell Nozzle
Experiments Without Film Cooling
The heat fluxes for the sharp edge are about 20% higher than for the rounded bend contour. It can result from changes in the expansion fan and local acceleration of the flow, which leads to changes in the boundary layer height.
Experiments with Film Cooling
Thus, a sharp-edged contour bend is recommended for film cooling application in the double bell nozzle.
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Turbulence gives rise to a much stronger wall-normal heat conduction compared to the laminar envelope, resulting in a faster heating of the cooling stream. But the turbulent kinetic energy is lower in the downstream cooling region of the fissure with helium.
2 Flow Configuration
The static pressure pc is taken constant over the slot height and the density ρcis derived from the equation of state. Note that all reported refrigerant exit conditions (i.e. pressure matched, over or under expanded) are based on the free stream pressure, not the pressure behind the stage without a secondary stream.
3 Numerical Method
- Influence of Coolant Mass Flow Rate
- Influence of Coolant Mach Number
- Influence of the Upstream Wall Temperature
- Lip-Thickness Influence
- Influence of the Coolant Velocity Profile
- Correlation of Data
- Comparison with Wall-Normal Blowing
As evident from Fig.5, the present investigation shows no significant influence of coolant Mach number. The reader is referred to  for a discussion of the differences in the hot gas boundary layer coming from nearby.
5 Conclusions and Outlook
Keller, M., Kloker, M.J.: Direct numerical simulation of foreign gas film cooling in supersonic boundary layer flow. Ludescher, S., Olivier, H.: Experimental investigations of film cooling in a conical nozzle. under rocket engine-like flow conditions.
Impact on Temperature Distribution and Damping Performance of Acoustic
1 Introduction and Placement in SFB
Cardenas developed analytical correlations for the acoustic damping properties of a quarter-wave resonator, which indicate that the effect of temperature inhomogeneities is significant . In this context, the turbulent pulsating nature of the flow in the resonator poses a crucial challenge for the modeling of heat transfer.
2 Impact of Temperature Inhomogeneities on Damping Performance
5 Reflection coefficient gain for harmonic (square) excitation and results for three randomly generated broadband excitations obtained by CFD/SI (dashed lines). 6 Analytical model reflection coefficient gain (solid lines) and average results obtained from broadband excitation system identification (dashed lines).
3 Impact of Acoustic Oscillations on Heat Transfer
Wall Normal Heat Transfer
The figures in this section show the enhancement in heat transfer (EHT) versus non-dimensional pulsation amplitude for different Stokes' lengths l+s. Indeed, an examination of the time-resolved heat transfer (Fig. 10) indicates the relevance of large flow rates.
Longitudinal Heat Transfer
The graph reveals that the entire cross-sectional area of the channel (η=z/h) contributes to the longitudinal heat transfer. Figure 16 shows a qualitative match between the numerical results (colored lines) and the analytical predictions (black dotted lines).
4 Summary and Conclusions
Des, J.E., Keller, J.O., Arpaci, V.S.: Enhancement of heat transfer in the oscillating turbulent flow of a pulse combustor tailpipe. Miranda, A.C.: Influence of enhanced heat transfer in pulsatile flow on the damping characteristics of resonator rings.
The first contour is designed with a transition to occur at low supersonic freestream conditions. However, the results of the second contour are used to compare the transition behavior at sub- and supersonic free-stream conditions.
This nozzle operated at a total pressure of approximately pn,0≈ 9.8 bar at transonic transient free-stream conditions and at approximately pn,0 ≈3.5 bar at supersonic transient free-stream conditions.
Steady-State Sea Level Mode
Steady-State Altitude Mode
Future experiments should verify the validity of the Dual-Bell stability model provided in Fig.7. Thus, in sub- or transonic flow conditions, a natural transition of the Dual-Bell nozzle flow is possible, which was verified by the underlying experiments.
Flow of a Generic Space Launcher
A double-bell nozzle increases the efficiency of a space rocket propulsion system using altitude adjustment. The second part focuses on the twin-bell nozzle configuration, investigating the Reynolds number sensitivity.
2 Experimental and Numerical Setup 2.1 Geometry and Test Cases
- Experimental Setup
- Wind Tunnel and Jet Simulation Facility
- Numerical Setup
- URANS Setup
- Zonal RANS/LES Setup
- Passive Flow Control on TIC Configuration
- Analysis of Dual-Bell Transition—Effect of Reynolds Number
- Analysis of Dual-Bell Transition—Influence of Afterbody Geometry
In all three cases, the outer flow separates at the shoulder of the main body and the shear layer bends toward the nozzle fairing. The appearance of the flip-flop mode in the supersonic regime is therefore related to the reattachment of the external flow to the nozzle body.
Barklage, A., Radespiel, R.: Effect of boundary layer condition on the passage of a double-bell nozzle. Estorf, M., Wolf, T., Radespiel, R.: Experimental and numerical investigations of the performance of the Braunschweig hypersonic Ludwig tube.
Figure 1 shows its dependence on the temperature of the combustion chamber and the molecular mass of the exhaust gas. They were carried out to prove the feasibility of the plant concept to follow wind tunnel test campaigns.
2 The Hot Plume Testing Facility (HPTF)
Vertical Wind Tunnel Cologne (VMK)
The model extension is held by a central upstream support, which is integrated into the low-velocity section of the subsonic nozzle and followed by two planes of metal filter screens. 3 Operating range of the GH2/GO2 supply facility in terms of total chamber pressure PCC and oxidizer fuel ratio OFR as maximum working envelope (thick solid line) and model design envelope (filled area) with design reference conditions RC0, RC1 and RC2.
GH2/GO2 Supply Facility
3 Characterization of HPTF for Wind Tunnel Testing
HPTF Characterization Test Setup
HPTF Characterization Test Results
A variation of the oxidizer-fuel ratio was performed at a constant injector geometry between ratios of 0.7-2.5 (Fig. 7, RC0→C01). 6 Spectogram of the pressure fluctuations in the combustion chamber at standard reference condition RC0; the first longitudinal mode (L1) is estimated as .
4 Cold and Hot Plume Interaction Testing
GH2/GO2 Wind Tunnel Model
The asymmetrical rear-facing step is a generic representation of the main stage of the Ariane 5 with respect to the L/Dandd/Don ratios on a scale of 1/80. The internal geometry of the plenum and single shear flow injector has been designed and explored in previous work .
Test Program and Test Conditions
9 Wind tunnel model with combustion chamber for plume interaction testing mounted on an upstream waist. Then a cold exhaust jet is added, just as in previous investigations by Saile et al.
Wind Tunnel Test Results
- Cold Plume Interaction
- Hot Plume Interaction
As expected from the mean HSS power spectra, the ambient flow case with hot jet interaction behaves similarly to the ambient flow without jet with respect to the frequencies of the cross-flap and yaw motion. 14 Amplitude distribution of the power spectrum for ambient flow with hot jet; aSrD=0.20 (cross flapping motion); bSrD=0.35 (swinging motion).
In particular, this is true in the jet and the far line of the bluff body, where the shear layers interact strongly. Acknowledgments Financial support was provided by the German Research Foundation (Deutsche Forschungsgemeinschaft-DFG) in the framework of the Sonderforschungsbereich Transregio 40.
Wake for a Generic Space Launcher with a Dual-Bell Nozzle
1 Schematic of the interaction between the wake flow and a double bell nozzle operating at sea level mode (a) and altitude mode (b). Subsequently, the influence of flow control on the wake and buffet loads is outlined.
2 Computational Approach
- Geometry and Flow Conditions
- Zonal RANS/LES Flow Solver
- Computational Mesh
- Supersonic Configuration
- Transonic Configuration
- Wake Flow Topology
- Analysis of the Wake Dynamics
- Flow Control
The purpose of the jets is to reduce the coherence in the track to reduce the buffet loads. Afterwards, the influence of the flow control on the wake flow dynamics and buffet loads is discussed.
Note that the frequency coincides perfectly with the peak detected in the pressure fluctuations and the results reported in the literature . While in both configurations there is a peak at the characteristic dimensionless frequency, the amplitude is strongly reduced in the controlled case confirming that the coherence of the pressure fluctuations, i.e. the antisymmetric mode, is reduced by the jets leading to reduced buffet loads.
Vehicle Base Flows with Hot Plumes
For certain geometry designs and flow conditions, this shear layer is then reattached at the end of the nozzle structure and creates a recirculation zone at the bottom of the vehicle. In addition to the higher temperatures of the cloud itself, the structure of the nozzle also heats up during the flight.
2 Numerical Method and Setup
For the determination of the temperature distribution at the surface and in the solid, the RANS simulation is connected to ANSYS Mechanical V19 . Then the surface temperature distribution obtained from the structure solver is prescribed as a boundary condition for the subsequent run of the flow simulation.
3 Results of Thermal Flow Structure Coupling
The heat fluxes obtained from the structure solver were then applied to the following RANS simulation. Therefore, in a second attempt the heat transfer coefficient is spatially described in the structure solver at the red limit.
4 Investigation of Aft-Body Flow Fields
This indicates an additional effect that is independent of the fan characteristics, but solely due to the increased temperature in the recirculation region. For the DES studies, the pressure fluctuations can be assessed and presented on the right side of the figure.
Within High-Pressure Injections
Physical analysis of the supercritical regime and binary mixing systems shows that adiabatic mixing may not be globally applicable. With this in mind, an extended analysis of the mixing data is performed regarding the applicability of the adiabatic mixing model.
2 Phenomenological Considerations on Mixing Jets
To this end, the sound speed database for the subsonic high-pressure nozzles of Baab et al. In contrast, the n-pentane test cases 2 and 3 show a systematic deviation from the adiabatic mixing line.
3 Numerical Consideration and Thermodynamic Modeling
However, it cannot be assessed which physical effect is dominant and what primarily causes the deviations from the adiabatic assumption.