Table 1 - uploaded by James Braun
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Sutherland law coefficients for viscosity and thermal conductivity.
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The pressure gain across a rotating detonation combustor offers an efficiency rise and potential architecture simplification of compact gas turbine engines. However, the combustor walls of the rotating detonation combustor are periodically swept by both detonation and oblique shock waves at several kilohertz, disrupting the boundary layer, resultin...
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... thermodynamic properties were based on a real gas model with a temperature-dependent coefficient polynomial for each individual species with the coefficients found in Bride et al. [26]. The Sutherland law was used to model the viscosity for each individual species, and the constants are depicted in Table 1. For this study, a one-step Arrhenius reaction with three reactive species (H 2 O, O 2 and H 2 ) [11] was used. ...
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... Through 3-D numerical simulation results, Dubrovskii et al. [42] reported that the maximum heat flux of the inner wall near the bottom of the RDC was about 1.7 MW/m 2 , while the maximum heat flux of the outer wall was about 0.95 MW/m 2 at a distance of 150-200 mm from the bottom of the RDC. In order to quantitatively predict the convective heat flux in an RDE, Braun et al. [43] established a reducedorder model using unsteady Reynolds-averaged Navier-Stokes CFD with premixed hydrogen and air as the propellant. The peak time-averaged heat flux was predicted to be about 6 MW/m 2 at the triple point, followed by a downstream decrease in the oblique shock. ...
Accurately predicting the thermal characteristics and heat transfer distribution of the rotating detonation engine (RDE) and acquiring a clear understanding of the performance and mechanism of the rotating detonation are of great significance for achieving the safe and reliable long-duration operation of RDEs. Using RP-3 as fuel, a long-duration experimental study is performed on a 220 mm-diameter RDC to investigate the details with respect to the thermal environment. The heat flux at the typical location and the average heat flux of both the inner and outer cylinders are measured, respectively. Meanwhile, the peak pressure of the rotating detonation wave (RDW) and specific thrust are analyzed. When the ER is between 0.5 and 1 (oxidizer 2 kg/s), the stable rotating detonation mode is obtained, and the detonation duration is set as 40 s to accurately calculate the heat released by the detonation combustion. The heat flux in the upstream region of the RDW location ranges from 2.40 × 105 W/m2 to 3.17 × 105 W/m2, and the heat flux in the downstream area of the RDW location ranges from 1.05 × 106 W/m2 to 1.28 × 106 W/m2. The results demonstrate the important role of the detonation combustion zone, and the thrust performance of RDC can be improved by making the RDW move forward along the RDC axis, which is the optimal direction of detonation combustion. Through a comparison of average heat flux under different conditions, it is found that the heat released by the RDC is directly related to its thrust. In addition, the average heat flux of the inner cylinder is about three times that of the outer cylinder for the two-phase RDC with a Tesla valve intake structure, indicating that the high-temperature combustion product is closer to the inner wall. Therefore, more thermal protection should be allocated to the inner cylinder, and a more systematic analysis of the two-phase flow field distribution in the annular combustion chamber should be carried out to improve the thrust performance. In this paper, the average heat flux of the inner and outer cylinders of the RDC as well as the typical local heat flux of the outer cylinders is quantitatively measured by means of experiments, which not only deepens the understanding of RDC flow field distribution, but also provides quantitative boundary conditions for the thermal protection design of RDCs.
... The same time step as the 3D simulations and identical reaction mechanism was employed. The mesh was a structured square mesh with a discretization of 0.5 mm by 0.5 mm (based on a mesh and time step sensitivity, the grid could accurately track CJ speeds, temperatures and pressures, all the way up to 0.5 mm grid spacing [39] and similar to other reported values). Fig. 2 plots two simulations, in which the back pressures were modified to mimic a change in pressure ratio, ranging from 0.1 bar to 5 bar. ...
... In contrast, a detonation wave rides the outer wall and circumferentially upstream of that detonation wave, fresh mixture cools the walls. By analyzing two different total pressure simulations Fig. 15b demonstrates the effect of total upstream pressure, which has the highest impact on the heat load variation [39]. Upstream a net cooling effect is observed as the reactants help to cool the combustor. ...
... The multi-step reactions require a tenfold timestep decrease and a small mesh size to obtain accurate results. All three reaction schemes predict similar CJ speed but the temperature of the one-step reaction overshoots CJ temperature by 7 % [39]. Fig. 19. ...
... Energy losses in air-breathing rotating detonation engines (RDEs) have been the focus of many studies, and the performance deficits stemming from energy losses have been documented [11][12][13][14]. Strakey et al. showed that average heat loss to the walls is in the 12% to 18% range for air-breathing RDEs [15]. ...
... Similar to the 4-inch chamber, the 3-inch chamber simulations also exhibited a decrease in performance in the isothermal cases. These trends for the rocket chamber are similar to observations made in air-breathing simulations [11][12][13][14][15]. Figure 5 shows the temperature of an unwrapped slice near the outer chamber wall of the 4-inch RDRE. The top slice is from the adiabatic case, the middle is from the simulation with a wall temperature of 873 K, and the bottom slice from the case with a wall temperature of 300 K. ...
Rotating detonation rocket engines (RDRE) have the potential to achieve higher performance and efficiency than conventional rocket engines. High-fidelity computational fluid dynamics (CFD) simulations aid the design, discovery, and description of physical phenomena exhibited in RDREs. To date, many simulations overpredict global performance metrics, such as chamber pressure, thrust, and ISP, when compared with experimental measurements. In this study, we investigate the thermal losses within the RDRE chamber using high-fidelity CFD and conjugate heat transfer simulations. Results show that switching from an adiabatic to an isothermal wall boundary condition recovers as much as 8% of RDRE simulation performance overprediction. We further analyze the effect that cooled chamber walls have on RDRE dynamics. Surrogate, transient conjugate heat transfer simulations provide estimates of the heat flux to the chamber walls and are compared with the high-fidelity simulations. Both the heat transfer and high-fidelity simulations show a wall heat flux on the order of 10 MW/m^2 to 20 MW/m^2 .
... Numerical results have also contributed to the definition of the thermal load in RDC combustors. Braun et al. [14] developed a reduced order model for the definition of the RDC flow field as a function of prescribed initial pressure and temperature of the unburnt gas mixture. Then, considering the boundary layer integral method and dedicated correlations, the heat flux and heat transfer coefficient have been calculated. ...
... Heat flux time averaged profiles along the RDC axial direction have been provided only by a few of the works presented in the introduction and the results have been summarized in Fig. 2. The results presented show some common trends. Generally, Braun et al. [14] and Theuerkauf et al. [8] showed lower values of heat flux at low axial positions. This is assumed to be caused by the cooling effects of the unburnt gases. ...
In the last decade, the Rotating Detonation Combustor (RDC) has received growing attention among the different Pressure Gain Combustion concepts due to the simplicity of the design and the potential ease of integration in gas turbines. However, multiple technological challenges are still associated with its development. Researchers have pointed out concerns related to the heat loads determined by the high temperature and the complex flow field occurring in this kind of combustion chamber based on a small but meaningful set of experimental and numerical results. An investigation of the open literature has shown a strong sensitivity of the heat loads with multiple designs and operational parameters. The aim of this work is to provide a fundamental review of the primary drivers affecting heat load in a typical RDC in order to define basic cooling requirements for possible actual design of the combustor. Along with this, a simplified approach has been implemented for the estimation of the requirements for cold side convection cooling with respect to different heat load scenarios, shedding light on the compatibility of pure convection cooling for Rotating Detonation Combustors. Finally, the results are used to determine guidelines for the design of a cooled and efficient RDC.
... Numerical results have also contributed to the definition of the thermal load in RDC combustors. Braun et al. [14] developed a reduced order model for the definition of the RDC flow field as a function of prescribed initial pressure and temperature of the unburnt gas mixture. Then, considering the boundary layer integral method and dedicated correlations, the heat flux and heat transfer coefficient have been calculated. ...
... Heat flux time averaged profiles along the RDC axial direction have been provided only by a few of the works presented in the introduction and the results have been summarized in Fig. 2. The results presented show some common trends. Generally, Braun et al. [14] and Theuerkauf et al. [8] showed lower values of heat flux at low axial positions. This is assumed to be caused by the cooling effects of the unburnt gases. ...
In the last decade, the Rotating Detonation Combustor (RDC) has received growing attention among the different Pressure Gain Combustion concepts due to the simplicity of the design and the potential ease of integration in gas turbines. However, multiple technological challenges are still associated with its development. Researchers have pointed out concerns related to the heat loads determined by the high temperature and the complex flow field occurring in this kind of combustion chamber based on a small but meaningful set of experimental and numerical results. An investigation of the open literature has shown a strong sensitivity of the heat loads with multiple designs and operational parameters. The aim of this work is to provide a fundamental review of the primary drivers affecting heat load in a typical RDC in order to define basic cooling requirements for possible actual design of the combustor. Along with this, a simplified approach has been implemented for the estimation of the requirements for cold side convection cooling with respect to different heat load scenarios, shedding light on the compatibility of pure convection cooling for Rotating Detonation Combustors. Finally, the results are used to determine guidelines for the design of a cooled and efficient RDC.
... Analysing the strengths and weaknesses of each of the approaches mentioned earlier, a research framework was developed to obtain a reduced-order numerical (ROM) model to achieve the most effective solution for the problem concerned. A ROM provides similar accuracy as 3D CFD models in solving complex scenarios but requires significantly less computational resources and time [40]. This study aimed to develop a (1 + 1)D reduced-order numerical model that could (1) be validated by the results of an experimental investigation, (2) provide the same accuracy as a 3D finite element (FE) model for different operating and design parameters and (3) be applied to establish an energy-efficient large-scale design for injecting flue gas into mine tailings. ...
... Once a layer of tailings has fully reacted, a new layer of tailings can be built up with a new set of injection pipes. provides similar accuracy as 3D CFD models in solving complex scenarios but requires significantly less computational resources and time [40]. This study aimed to develop a (1 + 1)D reduced-order numerical model that could (1) be validated by the results of an experimental investigation, (2) provide the same accuracy as a 3D finite element (FE) model for different operating and design parameters and (3) be applied to establish an energyefficient large-scale design for injecting flue gas into mine tailings. ...
One method to accelerate carbon sequestration within mine tailings from remote mines involves the injection of diesel generator exhaust into dry stack tailings. The techno-economic feasibility of this approach heavily depends on understanding the flow characteristics inside the perforated injection pipes embedded within the tailings. Two distinctive yet dynamically coupled transport phenomena were identified and evaluated: (i) gas transport inside the pipe and (ii) gas injection into the porous body of the tailings. This paper presents two models to investigate these transport phenomena, a three-dimensional (3D) and a one-plus-one-dimensional (1 + 1)D model. An experimental investigation of the pressure profile through the injection pipe was carried out to validate the models at the experimental scale. To apply the (1 + 1)D model to larger scales, the results were compared with those of the 3D model, as the (1 + 1)D model required significantly less computational resources and time. To include the effect of the perforations in the pipe on the pressure profile of the (1 + 1)D model, an analytical fluid velocity profile was developed in relation to geometric and physical parameters. The performance of the (1 + 1)D model with an impact factor was then evaluated against the 3D model results for the inlet pressure, pressure profile and gas outflow distribution under various conditions than those investigated experimentally. The developed (1 + 1)D model can be used to design an energy-efficient approach for large-scale implementation with a wide range of desired operating parameters.
... The fluid and particle properties used in this CFD model are presented in Table 4. The values presented in Table 5 were selected based on the data available in the literature ( Ref 1,11,35,[55][56][57]. ...
The production of Inconel 718 coatings using the cold spray process is often challenging due to the limited plastic deformation of particles upon impact associated with its mechanical properties. This leads to the requirement of high spray parameters to achieve dense coating build-up that may result in high and complex residual stresses that can also affect negatively the substrate and lead to nozzle clogging. In this work, the role of the coating and particle impact temperatures is investigated while ensuring they are decoupled from the particle impact velocity. This allows starting to explore potential ways to produce a sound and quality Inconel 718 coating at reduced spray parameters. To decouple and evaluate the role of the particle impact temperature, powder preheating units with downstream injection are used to decouple the particle impact temperature from the particle impact velocity. Three initial particle temperatures are studied: 25, 400 and 750 °C. The effect of the coating temperature on the deposition process is investigated by controlling this temperature independently of the gas stagnation temperature through the use of induction heating. Deposition efficiency, porosity, and micro-hardness are used to assess the coating quality. The coating time–temperature history is measured to better understand its influence on the deposition of Inconel 718. In this work, an enhanced understanding of the effect of both particle and coating temperatures on the coating process is obtained, and the findings allow the establishment of a potential approach to produce dense coatings using reduced spray parameters.
... Reduced order models have been used in previous works to predict the heat flux [8]. Most of these models are based on the adiabatic supersonic expansion that occurs behind the front and is constrained by the slip lines. ...
... Shock waves can have a strong influence on the boundary layer properties [8], [10] and thus on the heat transfer. Conceptually, a greater number of waves dictates that a location on the combustor wall would be swept at a greater frequency, hence increasing the flux. ...
Rotating Detonation Engines (RDEs) offer improvement over existing propulsion and energy generation systems via pressure gain combustion. In this study, water-based calorimetry is performed on a straight annular RDE with methane (natural gas)-oxygen propellants. Measurements are performed at mass flows ranging from 0.1 to 0.5 kg/s and equivalence ratios of 0.8 to 1.4. The distribution of the heat flux was resolved and compared with flow field results from an optically accessible heatsink RDE. The peak heat-flux was observed to vary from 3.4 to 9.0 MW/m2 and confirmed to be within the detonation region of the combustor. The mode of the detonation waves in the combustor is shown to strongly influence the heat transfer rate. The total heat load to the wall is shown to account for 10.4 to 29.3 % of total flow enthalpy.
... This requires kinematic viscosities of the H 2 gas calculated from dynamic viscosities and gas densities at each elevation. The dynamic viscosities of H 2 in this calculation are obtained from the temperature-dependent Sutherland constants for hydrogen gas from Braun et al. (2018) and ideal gas densities corresponding to the atmospheric H 2 pressures. The terminal velocities depend on the diameter of the pebbles. ...
We use new experiments and a theoretical analysis of the results to show that the isotopic fractionation associated with laser-heating aerodynamic levitation experiments is consistent with the velocity of flowing gas as the primary control on the fractionation. The new Fe and Mg isotope data are well explained where the gas is treated as a low-viscosity fluid that flows around the molten spheres with high Reynolds numbers and minimal drag. A relationship between the ratio of headwind velocity to thermal velocity and saturation is obtained on the basis of this analysis. The recognition that it is the ratio of flow velocity to thermal velocity that controls fractionation allows for extrapolation to other environments in which molten rock encounters gas with appreciable headwinds. In this way, in some circumstances, the degree of isotope fractionation attending evaporation is as much a velocimeter as it is a barometer.
... The detonation speed was ~ 1950 m/s, and is within 2% of the Chapman Jouguet speed. Additional verifications for a similar computational grid with the H2-air reaction mechanism can be found in [40]. To assess the validity of a single-step hydrogen-air mechanism, different reaction mechanisms in a detonation tube were analyzed. ...
This paper details an energy conversion unit for the combined power extraction and thrust increase from high subsonic to hypersonic flows. The energy transfer is achieved through a wavy hub surface that promotes shocks and expansion fans. First, a design procedure and the non-dimensional steady-state performance characteristics (the reduced torque, non-dimensional mass flow, and non-dimensional speed) are presented (including an exergetic analysis) at on– and off-design conditions through time-averaged Reynolds Averaged Navier Stokes simulations. A cycle analysis was performed on a Mach 3 vehicle to demonstrate the feasibility of this technology. Second, energy extraction is achieved from the highly unsteady exhaust of rotating detonation combustors without needing an additional intermediate diffuser or nozzle. The rotating boundary conditions were computed from a reactive unsteady simulation. The influence of three shock parameters (pressure ratio across the shock, shock wave Mach number, and the number of waves) is investigated through a sensitivity study to assess the robustness of the new device. Furthermore, depending on the sense of rotation of the bladeless turbine relative to the rotation of the incoming shock and the helix angle, we can define two different modes of operation in which power extraction was achieved, namely, the shock mode and reversed mode.
