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Notes on Numerical Fluid Mechanics and Multidisciplinary Design 146

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Nguyễn Gia Hào

Academic year: 2023

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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.

Transportation Systems

1 Introduction

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 [9]. From the solution of the cell problem, the effective coefficients were determined and included in the boundary conditions.

Fig. 1 Temperature distributions for a combined (transpiration, convective, film) cooling concept of a rocket combustion chamber throat area using the developed numerical framework with  cou-pled domains
Fig. 1 Temperature distributions for a combined (transpiration, convective, film) cooling concept of a rocket combustion chamber throat area using the developed numerical framework with cou-pled domains

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 [17]. 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.

Fig. 7 Pressure signal at the nozzle wall (left) and hysteresis behavior of the separation position inside the nozzle as calculated by LES
Fig. 7 Pressure signal at the nozzle wall (left) and hysteresis behavior of the separation position inside the nozzle as calculated by LES

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 [39]. The impact of the 1 L resonance in the LOX injector on the LOX jet is visualized on the right side in Fig.15.

Fig. 10 Free shear layer enclosing the recirculation region of the generic rocket base and the hot plume at transonic flow conditions in VMK
Fig. 10 Free shear layer enclosing the recirculation region of the generic rocket base and the hot plume at transonic flow conditions in VMK

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.

Fig. 17 Comparison with experimental observations - deformed geometry and damage contour after 47 cycles obtained from simulation (top) and cut view of the fatigue experiment after 48 cycles showing a macroscopic crack in the center cooling channel (bottom
Fig. 17 Comparison with experimental observations - deformed geometry and damage contour after 47 cycles obtained from simulation (top) and cut view of the fatigue experiment after 48 cycles showing a macroscopic crack in the center cooling channel (bottom

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 [51]. 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 [58].

Fig. 21 Near-injector flame of a gas/gas (left) and gas/liquid (right) CH4/O2 Combustor
Fig. 21 Near-injector flame of a gas/gas (left) and gas/liquid (right) CH4/O2 Combustor

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.

Thrust-Chamber Demonstrators

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

1 Motivation

Transpiration cooling experiments for metal nozzle applications were performed in [13] and numerical simulations for metal nozzles can be found in [18]. 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

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.

Table 1 Flow and porous material parameters for test scenario 1
Table 1 Flow and porous material parameters for test scenario 1

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).

Table 2 Flow parameters for test scenario 2
Table 2 Flow parameters for test scenario 2

5 Conclusion

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.

Combustion Chambers

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.

Fig. 2 Specimen setup and characterization
Fig. 2 Specimen setup and characterization

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.

Table 1 Summary of the derived steady-state test case parameters with the according inlet tem- tem-perature and pressure
Table 1 Summary of the derived steady-state test case parameters with the according inlet tem- tem-perature and pressure

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 [12]. 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.

Fig. 5 Numerical setup
Fig. 5 Numerical setup

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.

Fig. 7 Measured (symbol) and simulation (lines) temperature boundary profiles in streamwise direction at their corresponding axial position for various blowing ratios F in %
Fig. 7 Measured (symbol) and simulation (lines) temperature boundary profiles in streamwise direction at their corresponding axial position for various blowing ratios F in %

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 [11].

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.

Dual-Bell Nozzle

Coolant Supply

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 [13].

Fig. 5 Conical nozzle with heating system and stagnation chamber Table 2 Details of the conical nozzle [13]
Fig. 5 Conical nozzle with heating system and stagnation chamber Table 2 Details of the conical nozzle [13]

4 Results Conical Nozzle 4.1 Reference Flow

Parametric Study

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 [7].

Correlation

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.

Table 5 Influence of an increasing parameter (left) on the cooling efficiency (right) [7, 8]
Table 5 Influence of an increasing parameter (left) on the cooling efficiency (right) [7, 8]

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.

6 Conclusion

The images or other third-party material in this chapter are included in the chapter's Creative Commons license, unless otherwise indicated in a credit line for the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by law or exceeds the permitted use, you must obtain permission directly from the copyright holder.

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

Film Cooling

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.

Table 1 Free-stream conditions for the DNS and thermophysical parameters of superheated steam and helium
Table 1 Free-stream conditions for the DNS and thermophysical parameters of superheated steam and helium

3 Numerical Method

4 Results

  • 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 [19] for a discussion of the differences in the hot gas boundary layer coming from nearby.

Fig. 3 Main flow characteristics of supersonic film cooling with laminar slot injection [25]
Fig. 3 Main flow characteristics of supersonic film cooling with laminar slot injection [25]

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

Resonators

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 [20]. 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).

Fig. 1 Sketch of a Helmholtz resonator, with highlighted oscillating fluid mass in the neck region.
Fig. 1 Sketch of a Helmholtz resonator, with highlighted oscillating fluid mass in the neck region.

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.

Fig. 9 Temporal averaged EHT over amplitude  for various Stokes’ length l s + corresponding to different frequencies
Fig. 9 Temporal averaged EHT over amplitude for various Stokes’ length l s + corresponding to different frequencies

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).

Fig. 14 Semi-logarithmic presentation of the enhancement of longitudinal heat transfer  turb
Fig. 14 Semi-logarithmic presentation of the enhancement of longitudinal heat transfer turb

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.

BFS Model

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.

Fig. 2 Illustration of the planar space launcher model with a 2D Dual-Bell nozzle and the measurement domains
Fig. 2 Illustration of the planar space launcher model with a 2D Dual-Bell nozzle and the measurement domains

Measurement Techniques

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.

3 Results

Steady-State Sea Level Mode

Steady-State Altitude Mode

Transition

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.

Fig. 4 Schlieren recordings of transitioning of DB2 from sea level to altitude mode (top to bottom).
Fig. 4 Schlieren recordings of transitioning of DB2 from sea level to altitude mode (top to bottom).

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
    • Instrumentation
  • 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.

Table 1 Flow conditions of ambient and jet flow
Table 1 Flow conditions of ambient and jet flow

4 Summary

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 .

Fig. 4 Photograph and 3D sectional view of the model combustor HOC1; 1 injector body, 2 pressure port, 3 wall temperature measurement module, 4 ignition module, 5 wall temperature measurement module, 6 nozzle assembly, 7 strain compensation elements, 8 sup
Fig. 4 Photograph and 3D sectional view of the model combustor HOC1; 1 injector body, 2 pressure port, 3 wall temperature measurement module, 4 ignition module, 5 wall temperature measurement module, 6 nozzle assembly, 7 strain compensation elements, 8 sup

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 [19].

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).

Fig. 10 Internal and external flow properties for all test cases in time; constant flow conditions are maintained within the evaluation time window t eval = [ 18
Fig. 10 Internal and external flow properties for all test cases in time; constant flow conditions are maintained within the evaluation time window t eval = [ 18

5 Conclusions

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.

Fig. 1 Schematic of the interaction of the wake flow with a dual-bell nozzle operating at sea-level mode (a) and altitude mode (b)
Fig. 1 Schematic of the interaction of the wake flow with a dual-bell nozzle operating at sea-level mode (a) and altitude mode (b)

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.

Fig. 2 Geometry parameters of the generic axisymmetric configurations (a). Setup for the flow control configuration (b)
Fig. 2 Geometry parameters of the generic axisymmetric configurations (a). Setup for the flow control configuration (b)

4 Conclusions

Note that the frequency coincides perfectly with the peak detected in the pressure fluctuations and the results reported in the literature [13]. 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 [1]. Then the surface temperature distribution obtained from the structure solver is prescribed as a boundary condition for the subsequent run of the flow simulation.

Fig. 1 Geometry and setup of the simulations
Fig. 1 Geometry and setup of the simulations

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.

Fig. 3 Surface heat flux and temperature distribution in the solid with heat flux trace lines and the surrounding flow (left) and heat flux together with heat transfer coefficient and surface temperature along the 2nd cylinder (right)
Fig. 3 Surface heat flux and temperature distribution in the solid with heat flux trace lines and the surrounding flow (left) and heat flux together with heat transfer coefficient and surface temperature along the 2nd cylinder (right)

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.

Fig. 1 Similarity analysis of centerline concentration of C 6 H 14 , C 5 H 12 and FK. Evaluated from database of Baab et al
Fig. 1 Similarity analysis of centerline concentration of C 6 H 14 , C 5 H 12 and FK. Evaluated from database of Baab et al

3 Numerical Consideration and Thermodynamic Modeling

Thermodynamic Modeling

However, it cannot be assessed which physical effect is dominant and what primarily causes the deviations from the adiabatic assumption.

Hình ảnh

Fig. 6 Correlation of wall pressure fluctuations at x/h = 7 and the vertical velocity component downstream of a backward-facing step at Ma ∞ = 0.8
Fig. 8 PIV measurement during hot plume interaction test in the VMK
Fig. 11 Schematic overview of the different disintegration regimes with increasing injection tem- tem-perature
Fig. 12 Critical point and real gas effects on non-adiabatic reacting flow
+7

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