Search Results (62)

The characteristic structure of the two-dimensional adjoint Euler equations is examined. The behavior is similar to that of the original Euler equations, but with the information traveling in the opposite direction. The compatibility conditions obeyed by the adjoint variables along characteristic lines are derived. It is also shown that adjoint variables can have discontinuities across characteristics, and the corresponding jump conditions are obtained. It is shown how this information can be used to obtain exact predictions for the adjoint variables, particularly for supersonic flows. The approach is illustrated by the analysis of supersonic flow past a double-wedge airfoil, for which an analytic adjoint solution is obtained in the near-wall region. The solution is zero downstream of the airfoil and piecewise constant around it except across the expansion fan, where the adjoint variables change smoothly while remaining constant along each Mach wave within the fan. Full article

In this study we perform a computational numerical analysis to examine the flow characteristics of a system composed of a rocket engine, supersonic diffuser, and ejector system. When the nozzle expansion ratio of a rocket engine increases, it is necessary to maintain high-vacuum conditions during ground hot testing, which requires a supersonic diffuser and ejector system. The integrated model, consisting of multiple systems and a single-ejector system model, exhibits a difference in the initial volume to be evacuated. Although some differences are observed during the initial vacuum transition process, both models maintain the same final vacuum pressure (4 kPa). During the initial vacuum process, if the injection pressure of the ejector decreases below the design pressure, vacuum degradation occurs because of momentum deficiency, followed by pressure perturbations as the vacuum process resumes. Once the rocket engine ignites and flow is supplied to the suction region, two flow regions exist around the ejector nozzle exit. As these flows mix and move downstream, flow separation occurs in the expansion region. When the injection pressure of the ejector falls below the design pressure, the flow separation region moves forward, and this shift helps maintain the designed vacuum suction conditions. Full article

Decarbonization of industrial processes by using high-temperature heat pumps is one of the most important pillars towards sustainable energy goals. Most heat pumps are based on the standard Carnot cycle which includes an expansion valve leading to irreversible dissipation and energetic losses. Especially for high-temperature applications, these losses increase significantly, and a replacement of the conventional throttle valve with an ejector, which is an alternative expansion device, for partial recovery of some of the pressure lost during the expansion, is investigated in this paper. However, designing such a device is complicated as the flow inside is subject to multiphase and supersonic conditions. Therefore, this paper aims to streamline an approach for designing ejectors for high-temperature heat pumps using numerical simulations. To showcase the application of the design procedure, an ejector, which is used to upgrade a standard cycle high-temperature heat pump with the synthetic refrigerant R1233zdE, is developed. To design the ejector heat pump, an interaction between a fast 1D design tool, a 1D heat pump cycle simulation, and a 2D CFD simulation is proposed. An ejector is designed for a sink temperature of 130 °C, which can potentially increase the COP of the heat pump by around 20%. Preliminary measurements at off-design conditions at 100 °C sink temperature are used to validate the design procedure. The pressure distribution inside the ejector is well captured, with relative errors around 4%. However, the motive nozzle mass flow was underpredicted by around 30%. To summarize, the presented approach can be used for designing ejectors of high-temperature heat pumps, although the numerical modeling has to be further developed by validation with experiments to improve the prediction of the motive mass flow. Full article

The rotational spectrum of $2^{\prime }$-hydroxyacetophenone has been recorded and assigned for the first time using a Stark-modulated free-jet absorption millimeter-wave (FJ-AMMW) spectrometer in the 59.6–74.5 GHz frequency range. The most stable conformer has been detected and assigned: A = 2277.076(11), B = 1212.113(5) and C = 795.278(5) MHz. It is characterized by a $C_s$ symmetry where a strong hydrogen bond between the acetyl oxygen atom and the hydroxyl atom takes place. The transition lines show a fine structure due to the internal rotation of the methyl group, which allowed the determination of a $V_3$ = 565.1(5) ${\mathrm{cm}}^{-1}$ barrier. The corresponding tunneling splittings have been estimated to be 51 MHz. Calculations at the B3LYP-D3(BJ)/Def2-TZVP level underestimate the height of the barrier by about 156 ${\mathrm{cm}}^{-1}$. This value decreases to 25 ${\mathrm{cm}}^{-1}$ with MP2/aug-cc-pVTZ. Full article

In order to reduce the infrared radiation intensity of supersonic tail nozzles and in response to the increasingly severe battlefield infrared environment, simulations were conducted on axisymmetric expanding tail nozzles to study the effects of air, liquid nitrogen, and dry ice cold flows at different flow rates on the nozzle wall temperature. The results show that when the dry ice flow rate is increased by 1 kg/s, the maximum temperature of the wall surface in the expansion section decreases by about 40 K. At a cold flow rate of 5% in the 0° detection direction, the intensity of infrared radiation was reduced by 20.8% for the liquid nitrogen cold flow and 26.3% for the dry ice cold flow, compared to the cold flow of injected air. The IR suppression of the tail nozzle was significant in the range from α = 0 to 50°. Compared to cooling air, the maximum IR radiation intensity was reduced by 26.5% for dry ice and 20.4% for liquid nitrogen. When the flow rate of the injected cold stream was increased by 4%, the intensity of the infrared radiation from the nozzle was reduced by 52.6%, 55.8%, and 66.2% for the injected air, liquid nitrogen, and dry ice cold streams, respectively. Full article

The stability of a nonlinear aero-thermo-elastic panel in supersonic flow is analyzed numerically. In light of Hamilton’s principle, the governing equation of motion for a two-dimensional aero-thermo-elastic panel is established taking geometric nonlinearity and curvature effect into account. Coupling with the panel vibration, aerodynamic pressure is evaluated by first order supersonic piston theory and aerothermal load is approximated by the quasi-steady theory of thermal stress. A Galerkin method based on approximate inertial manifolds is deduced for low-dimensional dynamic modeling. The efficiency of the method is discussed. Finally, the complex stability regions of the system are presented within the parametric space. The Hopf bifurcation is found during the onset of flutter as the dynamic pressure increases. The temperature rise imposes a significant effect on the stability region of the panel. Since the material parameters of the panel (elastic modulus and thermal expansion coefficient in this case) are the function of temperature, the panel tends to lose its stability as the temperature gets higher. Full article

Atmospheric air, being also a moist gas, is present as a working medium in various areas of technology, including the areas of airframe aerodynamics and turbomachinery. Issues related to the condensation of water vapor contained in atmospheric air have been intensively studied analytically, experimentally and numerically since the 1950s. An effort is made in this paper to present new, unique and complementary results of the experimental testing of moist air expansion in the de Laval nozzle. The results of the measurements, apart from the static pressure distribution on the nozzle wall and the images obtained using the Schlieren technique, additionally contain information regarding the quantity and quality of the condensate formed due to spontaneous condensation at the transition from the subsonic to the supersonic flow in the nozzle. The liquid phase was identified using the light extinction method (LEM). The experiments were performed for three geometries of convergent–divergent nozzles with different expansion rates of 3000, 2500 and 2000 s⁻¹. It is shown that as the expansion rate increases, the phenomenon of water vapor spontaneous condensation appears closer to the critical cross-section of the nozzle. A study was performed of the impact of the air relative humidity and pollution on the process of condensation of the water vapor contained in the air. As indicated by the results, both these parameters have a significant effect on the flow field and the pressure distribution in the nozzle. The results of the experimental analyses show that in the case of the atmospheric air flow, in addition to the pressure, temperature and velocity, other parameters must also be taken into account as boundary parameters for possible numerical analyses. Omitting information about the air humidity and pollution can lead to incorrect results in numerical simulations of transonic flows of atmospheric air. The presented results of the measurements of the moist air transonic flow field are original and fill the research gap in the field of experimental studies on the phenomenon of water vapor spontaneous condensation. Full article

The nozzle, as a critical jet component in dry powder fire extinguishing systems, significantly affects jet characteristics through its geometric configuration. To explore the influence of structural parameters on ultrafine dry powder gas-solid two-phase jet characteristics, a bidirectional coupled numerical model based on the SST k-ω turbulence model and the Discrete Phase Model is employed. This study examines how variations in the semi-expansion angle (α) and semi-contraction angle (β) of the nozzle affect compressible gas flow behavior and particle distribution trajectories through a combination of simulations and experiments. The results indicate that when α = 2°, the gas jet is in an under-expanded state, leading to increased particle dispersion due to the stripping effect of the surrounding high-speed airflow. Within the range of x = 0–180 mm, the dry powder exhibits a diffusion trend. When α = 4.5°, the gas jet core region is the longest, providing optimal particle acceleration. Under constant inlet pressure, reducing α enhances particle collimation. The reduction of α alters the gas jet state, with α = 2° showing better powder diffusion compared to α = 6°. However, an excessively small α is detrimental to increasing the range of dry powder. With consistent structural parameters, the diffusion and range of dry powder remain the same across different β values, and variations in β have a relatively minor impact on supersonic jet characteristics. These findings offer theoretical guidance for optimizing and improving nozzles in ultrafine dry powder fire extinguishing systems. Full article

Creating a high-quality aircraft engine is closely connected to the problem of obtaining the jet flow characteristics that appear while an aircraft’s engine is in operation. As natural experiments are costly, studying turbulent jets by numerical simulation appears practical and acute. Biconic nozzle supersonic jet flow is the research subject of this article. A compression and expansion train of waves called barrels were formed in the jet flow at preset conditions. The simulation was performed on an unstructured numerical grid. In order to enhance the calculation accuracy in the shock-wave domain, a hybrid gradient computation scheme and numerical grid static adaptation method were applied in the regions of gas-dynamic values’ significant differential. This approach resulted in a description of nozzle supersonic gas flow structure. It was shown that building local refinement when using a static adaptation numerical grid contributed to improving the accuracy of determining shock waves’ fronts. In addition, this approach facilitated the identification of the Mach disk in the flow when using an unstructured grid, allowing for calculation schemes not higher than a second-order of accuracy. Full article

An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and turbulence–combustion interaction. The comparisons of the simulation results with experimental and computational data confirm the fidelity of this solver for problems involving multicomponent high-speed reactive flows. The gas dynamics of turbulence–chemistry interaction are modeled using a partially stirred reactor formulation and provide promising results to better understand the complex physics involved in supersonic combustors. A time-scale analysis based on local Damköhler numbers reveals different regimes of turbulent combustion. In the core of the jet flow, the Damköhler number is relatively high, indicating that the reaction time scale is smaller than the turbulent mixing time scale. This means that the combustion is controlled by turbulent mixing. In the shear layer, where the heat release rate and the scalar dissipation rate have the highest value, the flame is stabilized due to finite rate chemistry with small Damköhler numbers and a limited fraction of fine structure. This solver allows three-dimensional gas dynamic simulation of high-speed multicomponent reactive flows relevant to practical combustion applications. Full article

The goal of this paper is to investigate the aerodynamic and aerothermodynamic behavior of the Schiaparelli capsule after the deployment of a supersonic disk-gap-band (DGB) parachute during its re-entry phase into the Martian atmosphere. The novelty of this work lies in the investigation by LES (large-eddy simulations) of the coupled interaction of the flow field generated behind the capsule and that in front of the flexible DGB parachute. These simulations are performed at an altitude of 10 km and a Mach number around 2, i.e., a regime in which large canopy-area oscillations are observed. LES results have shown a strong interaction between the bow shock, the recompression and expansion waves, high pressure, density and temperature gradients, heat flux towards the airstream and the body implying turbulence generation, ingestion, and amplification through the shock waves. Vortices released from the capsule at a frequency of about 52 Hz and 159 Hz, corresponding to Strouhal numbers of ~0.2 and 0.75, respectively, are the main factors responsible for the instabilities of the hypersonic re-entry capsule and the disk-gap-band parachute coupled system. The nonlinear turbulence flow field generated at the capsule back is amplified when passing the parachute bow shock, and this is responsible for the non-axisymmetric behavior around and behind the parachute that caused the uncontrolled capsule oscillations and the Schiaparelli mission failure. In fact, an LES of the parachute without the capsule, for the same conditions, show a completely axisymmetric field, varying in time, but axisymmetric. In order to avoid this turbulence amplification, dampening of the vortex shedding is critical. Different techniques have been already proposed for other applications. In the case of capsule re-entry, due to the high temperatures in front of the capsule behind the bow shock since air plasma is generated, damping of the vortex shedding could be achieved by means of magnetohydrodynamic (MHD) control. Full article

Uncertainties in the atmosphere and flight conditions can drastically impact the performance of an aircraft and result in certification delays. However, uncertainty propagation in high-fidelity simulations, which have become integral to the design process, can pose intractably high computational costs. This study presents a non-intrusive, parametric reduced order modeling (ROM) method to enable the prediction of uncertain fields with thousands of random variables and nonlinear features under limited sampling budgets. The methodology combines linear dimensionality reduction with sparse polynomial chaos expansions and is assessed in a variety of CFD-based test cases, including 3D supersonic flow over a passenger aircraft with uncertain flight conditions. Each problem has strong nonlinearities, such as shocks, to investigate the effectiveness of models in real-world aerodynamic simulations that may arise during conceptual or preliminary design. The performance is assessed by comparing the uncertain mean, variance, point predictions, and integrated quantities of interest obtained using the ROMs to Monte Carlo simulations. It is observed that if the flow is entirely supersonic or subsonic, then the method can predict the pressure field accurately and rapidly. Moreover, it is also seen that statistical moments can be efficiently obtained using closed-form analytical expressions and closely match Monte Carlo results. Full article

Landing of supersonic transport (SST) suffers from a large uncertainty due to its highly sensitive aerodynamic properties in the subsonic domain, as well as the wind gusts around runways. At the vehicle design stage, a landing trajectory optimization under wind uncertainty in a multi-objective solution space is desired to explore the possible trade-off in its key flight performance metrics. The proposed algorithm solves this robust constrained multi-objective optimal control problem by integrating non-intrusive polynomial chaos expansion into a constrained evolutionary algorithm. The computationally tractable optimization is made possible through the conversion of a probabilistic problem into an equivalent deterministic representation while maintaining a form of the multi-objective problem. The generated guidance trajectories achieve a significant reduction of the uncertainty in their terminal states with a marginal modification in the control history of the deterministic solutions, validating the importance of the consideration of robustness in trajectory optimization. Full article

Base drag has a significant effect on the overall drag of a projectile in a supersonic flow. Herein, the base drag and flow characteristics of cold and hot gas flow in a supersonic flow are analyzed via numerical simulations. The hot gas flow is simulated using a chemical equilibrium application code based on hydrogen combustion. Two types of nozzle configurations, namely conical and contoured, are chosen for the simulation. The simulation results reveal that the change in base drag is 5–85% according to the injection gases. In the over-expanded and slightly under-expanded conditions, the base drag decreases in the hot gas flow, owing to the weak expansion fan caused by the high-temperature nozzle flow expansion, whereas in the highly under-expanded condition, the base drag decreases, owing to the strong shock wave near the base caused by the deflection of the recirculation region toward the body wall. In addition, the variations in base flow structures are observed differently compared with the cold flow; for example, a weak oblique shock wave at the nozzle exit, an increase in the distance between the shock wave and base, and deflection of the recirculation region based on the body wall are observed. Full article

At present, as a new separation technology, supersonic separators have great potential in the separation of natural gases. However, their system performance is still low. In this paper, a supersonic swirl separator design is proposed with an integration approach of the discrete phase model (DPM), bi-coupling, and the random walk model, and it is used to predict the flow process of liquid droplets within the device. Such a numerical method is further employed to study the influence of key parameters on system performance. The results show that with an increase in the inlet port number and the ratio of the gas-liquid area, the separation performance decreases. As a result, the expansion, condensation effect, and economy of the separation system are greatly improved. When the deflection angle exceeds 20°, the separation temperature increases greatly. Consequently, this may ruin the condensing environment. The working pressure ranges are: (1) the boost ratio (the dry outlet pressure/total inlet pressure) is less than 0.76; (2) the wet pressure ratio (the wet outlet pressure/total inlet pressure)is less than 0.46. The increase in droplet diameter can improve the separation performance, and the droplets are completely separated as the diameter reaches 1.75 μm. Full article