Position Of Shock Wave Research Articles

Uncertainty quantification based on active subspace dimensionality-reduction method for high-dimensional geometric deviations of compressors

Compressors are inevitably exposed to diverse geometric deviations from manufacturing errors and in-service degradation. Consequently, the evaluation of performance uncertainties becomes of utmost importance for compressors in engineering application. However, the presence of high-dimensional and strongly nonlinear geometric deviations poses significant challenges in efficiently and accurately assessing the performance uncertainties of compressors. This study proposes an active subspace-based dimensionality-reduction method for high-dimensional uncertainty quantification (UQ) of compressors. Based on the active subspace (AS) method, a dimensionality-reduction high-precision artificial neural network is raised to solve the dimension disaster problem for high-dimensional UQ. Additionally, a data-driven approach is used to calculate the gradient of the quantity of interest, addressing the issue of high computational cost during the AS dimensionality reduction process. Furthermore, the Shapley method is applied to explore the influence mechanism of geometric uncertainties on performance deviations of compressors. The UQ of one transonic compressor stage at design point and near stall point is conducted by the proposed method. The findings show that the original 24-dimensional uncertainties are reduced to three-dimensional uncertainties by using this method. Consequently, the required sample size is reduced by 75% while maintaining almost unchanged model accuracy. The findings reveal that the sweep and stagger deviation of the rotor are key uncertainties on the performance of the compressor. The dispersion in efficiency is attributed to variations in shock wave position and intensity, while the dispersion in total pressure ratio is primarily affected by changes in rotor work capacity. Moreover, the dispersion at near stall is 50% higher than that at design point. Therefore, when studying UQ, it is important to pay closer attention to the performance dispersion at near stall conditions.

Design, Fabrication, and Commissioning of Transonic Linear Cascade for Micro-Shock Wave Analysis

Understanding shock wave behavior in supersonic flow environments is critical for optimizing the aerodynamic performance of turbomachinery components. This study introduces a novel transonic linear cascade design, focusing on advanced blade manufacturing and experimental validation. Blades were 3D-printed using Inconel 625, enabling tight control over the geometry and surface quality, which were verified through extensive dimensional accuracy assessments and surface finish quality checks using coordinate measuring machines (CMMs). Numerical simulations were performed using Ansys CFX with an implicit pressure-based solver and high-order numerical schemes to accurately model the shock wave phenomena. To validate the simulations, experimental tests were conducted using Schlieren visualization, ensuring high fidelity in capturing the shock wave dynamics. A custom-designed test rig was commissioned to replicate the specific requirements of the cascade, enabling stable and repeatable testing conditions. Experiments were conducted at three different inlet pressures (0.7-bar, 0.8-bar, and 0.9-bar gauges) at a constant temperature of 21 °C. Results indicated that the shock wave intensity and position are highly sensitive to the inlet pressure, with higher pressures producing more intense and extensive shock waves. While the numerical simulations aligned broadly with the experimental observations, discrepancies at finer flow scales suggest the need for the further refinement of the computational models to capture detailed flow phenomena accurately.

Impact of non-axisymmetric tip clearance on the aerodynamic and aeroelastic stabilities of a transonic compressor

The aerodynamic and flutter effects caused by the circumferential non-uniform tip clearances from the non-axisymmetric casing geometry, which are more representative of real operational conditions, should receive more attention. In this paper, sensitivity analyses on clearance and non-uniformity regarding rotor performance are conducted. The isentropic efficiency, total pressure ratio and stability margin of the rotor are reduced by 1.96%, 1.06% and 6.76% for an increase of tip clearance by 1% tip chord, respectively. The non-axisymmetric configuration reconfigures the interaction between leakage flow and mainstream in each rotor passage and alters the strength and influence range of the low-speed separation region generated by shock wave. The phase lag phenomenon observed in the aerodynamics of the non-axisymmetric layout also manifests in the aeroelastic effects but requires a larger phase shift at the maximum clearance sector, owing to the longer timescales for flow adjustment relative to the local tip gap considering the flow-induced vibration. Clearance sensitivity on flutter stability varies with the direction of the traveling wave: under forward traveling conditions, damping values initially decrease and then increase with increasing rotor tip clearance; while under backward traveling condition, blade damping linearly decreases with increasing rotor tip clearance. Additionally, variations in flow conditions and nodal diameters affect flutter stability by altering the position of shock waves and their work on the suction surface of the rotors. The mechanism responsible for unsteady flows induced by non-axisymmetric clearances from the casing ovalization on flutter stability is discussed for the first time in this paper, which can guide the industry to evaluate its impact.

Unsteady measurement in a transonic axial compressor with optimized axial slot casing treatment

Casing treatment has been widely adopted to enhance the operating range of compressors by extending the stall margin. In this article, a high-precision experimental investigation was conducted in a transonic compressor. Unsteady pressure is measured in the casing wall using a cluster of time-resolved transducers with axial and circumferential spatial resolution. The experimental data show that the optimized axial slot casing treatment improves the stall margin without peak efficiency penalty for all measured speedlines. A comprehensive flow field analysis indicates that the surge boundary of transonic compressor is sensitive to the position of shock wave and tip leakage flow. After the application of optimized axial slot casing treatment, the flow structure can be significantly modified, which specifically manifests as both the mitigation in shock wave detachment and redistribution of tip leakage flow trajectory toward the trailing edge of the blade. Furthermore, power spectral density analysis is conducted to examine the unsteady effect. The amplitude of characteristic frequency band induced by the unsteady fluctuation of tip leakage flow and shock wave is considerably suppressed, which can also be regard as the stability enhancement mechanism of casing treatment.

Experimental study on the evolution of shock waves in the near field of cylindrical charge explosion

Cylindrical charges are frequently used in blasting engineering and military operations, often detonated very close to target structures. Obtaining the characteristics of the flow field distribution in the near field of explosions through experimentation consistently poses challenges. These challenges constrain efforts to elucidate the evolutionary processes of explosive shock waves. Employing the explosive schlieren experimental system yields a clearer depiction of the near field flow than previous studies, thereby facilitating a more comprehensive understanding of the characteristics of cylindrical charge explosions. The overall flow field adopts a droplet shape, with the interface of the detonation products and the shock wave front forming continuous concave shapes. The detonation process in cylindrical charges can be conceptualized as the detonation wave propelling the detonation products at supersonic speeds. The formation of explosive shock waves can be elucidated through the dynamics of oblique shock waves generated by two-dimensional curved surfaces. This mechanism influences the relationship between the deflection angles of detonation products and the shock wave angles resulting from different detonation velocities. Theoretical calculations of shock wave positions align with experimental images. Significant variations in shock wave velocities at different positions within cylindrical charges are observed, identifying patterns of these variations. The research findings clarify the formation mechanisms of explosive shock waves in cylindrical charges and deepen the understanding of shock wave evolution in the near field.

Twist Angle Error Statistical Analysis and Uncertain Influence on Aerodynamic Performance of Three-Dimensional Compressor Rotor

Twist angle errors along the blade radial direction are uncertain and affected by cutting force, tool wear, and other factors. In this paper, the measured twist angle errors of 13 sections of 72 rotor blades were innovatively analyzed to obtain the rational statistical distribution. It is surprisingly found that the under-deflection systematic deviation of twist angle errors shows a gradually increasing W-shaped distribution along the radial direction, while the scatter is nearly linear. Logically, the statistical model is established based on the linear correlation of the scatter by regression analysis to reduce variable dimension from 13 to 1. The influence of the radial non-uniform twist angle errors’ uncertainty on the aerodynamic performance of the three-dimensional compressor rotor is efficiently quantified combining the non-intrusive polynomial chaos method. The results show that the mean values of mass flow rate, total pressure ratio, and isentropic efficiency at the typical operating conditions are lower than the nominal values due to the systematic deviation, indicating that the under-deflection twist angle errors lead to the decrease in compressor thrust. The compressor’s stable operating range is more sensitive to the scatter of twist angle errors, which is up to an order of magnitude greater than that of the total pressure ratio and isentropic efficiency, indicating the compressor’s safe and stable operation risk increases. Additionally, the flow field at the tip region is significantly affected by twist angle errors, especially at the shock wave position of the near-stall condition.

A computational investigation of shock wave train in diverse duct geometries using machine learning-adopted k-ω turbulence model

This research paper presents a thorough examination of shock wave train phenomena in various duct structures, utilizing a machine learning-optimized k-ω model. The focus of the study is to apply machine learning techniques to adapt the constant coefficients of the k-ω turbulence model, improving its accuracy and computational efficiency in capturing the dynamics of shock waves. An important aspect of this investigation is the impact of diverging sections within the duct, specifically how changes in the divergence angle, while maintaining a constant ratio of the exit area to the throat area, affect compressible flow parameters, shock wave positions, and other related characteristics of shock trains. The study systematically explores these effects and provides fresh insights into the behavior of shock wave trains under different divergence conditions. In a departure from the usual practices in supersonic research, this study compares the phenomena of shock wave trains in rectangular and circular duct geometries. The findings contribute valuable data and analyses to a field that has traditionally focused on rectangular configurations. The results indicate that the shape of the duct has a significant influence on the shock wave train, emphasizing the importance of considering geometric diversity in the study of supersonic flows and shock wave phenomena. This research sets the stage for further investigations into the interaction between duct geometry, shock wave propagation, and the dynamics of compressible flows.

Shunt capacitor array shock wave position sensor

The position of the shock wave front under an impact load can reveal many material properties. A design of a shunt capacitive shock wave position sensor has been investigated in this work, utilizing a series of electric probes connected to the shunt capacitor array to measure the moment when the shock wave front reaches a specific point on the sample, which can be used to determine the shock wave front's evolution law. Using the Simulink module in MATLAB software, a sensor circuit model was designed and simulated, and the influence of various conditions on the output signal's falling edge relaxation times were investigated. The results indicate that the relaxation times initially increase, then gradually flatten out, after that, when electrical probes are progressively triggered, the relaxation times will increase again. The relaxation time increase with the rising capacitance, self-inductance coefficient, and voltage drop, and it decrease with increasing coupling coefficient. In addition, it initially decreases and then increase as the initial output voltage increases. Comparing the output signals of the traditional series resistance shock wave position sensor under the same general parameters, it reveals that the voltage falling edge relaxation times for each stage of the sensor are in the order of 10−10 s magnitude, much smaller than the 10−8 s magnitude of the latter, indicating higher measurement accuracy for the sensor. In this work, it also provides a reliable theoretical basis for selecting circuit parameters of the shunt capacitor shock position sensor in experiments by simulation.

From shockwaves to the gravitational memory effect

We study the relationship between shockwave geometries and the gravitational memory effect in four-dimensional asymptotically flat spacetime. In particular, we show the ’t Hooft commutation relations of shockwave operators are equivalent to the commutation relation between soft and Goldstone modes parametrizing a sector of the gravitational phase space. We demonstrate this equivalence via a diffeomorphism that takes a shockwave metric to a metric whose transverse traceless component is the gravitational memory. The shockwave momentum in ’t Hooft’s analysis is related to the soft graviton mode, which is responsible for the memory effect, while the shift in the shockwave position is related to the Goldstone mode. This equivalence opens new directions to utilize the gravitational memory effect to explore the observational implications of shockwave geometries in flat space.

Influence of inner wall roughness of supersonic separator on non-equilibrium condensation of CO2 benefiting flue gas decarbonization

Supersonic separators are energy efficient and environmental separation device. Recent work has demonstrated the potential of supersonic separators to separate CO2 from flue gas. Because the supersonic flows in the separator is accompanied by shock waves and non-equilibrium condensation, the current cognition level on flow behavior in the separator is low. This work establishes a numerical model to describe the high-speed two-phase flows in the separator and the non-equilibrium condensation of CO2 during carbon capture process, and clarify the influence of inner wall roughness on carbon capture process. The results show that the rapid expansion of gas pushes the thermodynamic system to non-equilibrium state and promotes the spontaneous condensation of CO2. Wall roughness has obvious influence on normal shock wave position, non-equilibrium condensation and normal shock wave intensity. When the roughness height increases by 0.1 mm, the maximum droplet radius in the separator decreases by 17.4%, liquid CO2 fraction decreases by 49.1%, and radial range of liquid phase decreases by 46.3%.

GAN-based generation of realistic compressible-flow samples from incomplete data

Predictive sampling of compressible flows is an important aspect of aerodynamic design, analysis, and optimization. The process is usually done by generating flow fields from computational fluid dynamics (CFD) simulations and solving governing evolution equations, from which quantities of interest (QoI) are obtained by post-processing. With this study, we propose a data-driven approach for the predictive sampling of compressible flows around airfoils. This paper demonstrates the potential of generative adverserial networks (GANs), particularly the Pix2Pix model, to predict supersonic flow fields around airfoils. Building upon the similarities between our generator architecture and FlowGAN, which also employs the Pix2Pix model, our work extends the capabilities of FlowGAN to encompass supersonic flows and higher-resolution predictions. Our methodology introduces a multi-variable prediction framework, enabling the simultaneous prediction of various flow variables, including pressure, velocity, and density. We achieve the generation of flow fields with a relative error of less than 1.5%. We utilize the same framework to train a model capable of generating synthetic schlieren images, exhibiting a similarity structure index greater than 0.97, underscoring the high-fidelity generation capacity of our model. Addressing the challenges of generalization to unseen Mach numbers and angles of attack, we adopt transfer learning. By fine-tuning a pre-trained model on a limited number of examples from the unseen parameters, we obtain an improved prediction of shock wave positions. Furthermore, we present a practical application of our methodology by reconstructing flow fields from schlieren images. This application could prove valuable in real-world scenarios, providing a useful tool for studying and comprehending complex flow phenomena.

Numerical Simulation of Constrained Flows through Porous Media Employing Glimm’s Scheme

This work uses a mixture theory approach to describe kinematically constrained flows through porous media using an adequate constitutive relation for pressure that preserves the problem hyperbolicity even when the flow becomes saturated. This feature allows using the same mathematical tool for handling unsaturated and saturated flows. The mechanical model can represent the saturated–unsaturated transition and vice-versa. The constitutive relation for pressure is a continuous and differentiable function of saturation: an increasing function with a strictly convex, increasing, and positive first derivative. This significant characteristic permits the fluid to establish a tiny controlled supersaturation of the porous matrix. The associated Riemann problem’s complete solution is addressed in detail, with explicit expressions for the Riemann invariants. Glimm’s semi-analytical scheme advances from a given instant to a subsequent one, employing the associated Riemann problem solution for each two consecutive time steps. The simulations employ a variation in Glimm’s scheme, which uses the mean of four independent sequences for each considered time, ensuring computational solutions with reliable positions of rarefaction and shock waves. The results permit verifying this significant characteristic.

The perturbed Riemann problem for the Chaplygin pressure Aw–Rascle model with Coulomb-like friction

In this paper, we are concerned with the Riemann problem and the perturbed Riemann problem for the Chaplygin pressure Aw–Rascle model with Coulomb-like friction, which can also be seen as the nonsymmetric Keyfitz–Kranzer system with Chaplygin pressure and Coulomb-like friction. For the Riemann problem, we show that it explicitly exhibits two kinds of different structures and the delta shock wave appears in some certain situations. The generalized Rankine–Hugoniot conditions of the delta shock wave are established and the exact position, propagation speed and strength of the delta shock wave are given explicitly. Unlike the homogeneous case, it is shown that the Coulomb-like friction term makes contact discontinuities and the delta shock wave bend into parabolic shapes and the Riemann solutions are not self-similar anymore. For the perturbed Riemann problem with delta initial data, not only the delta shock wave but also the delta contact discontinuity are found in solutions and the friction term makes them bent. Under the generalized Rankine–Hugoniot conditions and the entropy condition, by taking variable substitution, we constructively obtain the global existence of generalized solutions which explicitly exhibit four kinds of different structures. The results in this paper yield a way of studying the wave interaction involving the delta shock wave for conservation laws with source terms and will give us some insights into the research on the Chaplygin pressure Aw–Rascle model, the pressureless Euler equations and the Chaplygin Euler equations with various kinds of source terms.

Multidisciplinary Design Optimization of Transonic Wings with Boundary-Layer Suction

A quasi-three-dimensional aerodynamic solver is developed for the aerodynamic analysis of wings in a transonic regime that is able to capture the effect of BLS in hybrid laminar flow control (HLFC) application or transition to turbulent flow for natural laminar flow (NLF). The tool provides accurate results, but without the high computational cost of high-fidelity tools. The solver combines the use of an Euler flow solver characterized by an integral boundary-layer method and linear stability analysis using a approximation for transition prediction. In particular, a conical transformation is adopted, including the determination of the shock-wave position. The solver is implemented in a multidisciplinary design optimization (MDO) framework, including wing weight estimation and aircraft performance analysis. The framework consists of different modules: aerodynamics, structure, suction system analysis, and performance evaluation. Using a genetic algorithm and considering HLFC technology, wing MDO has been performed to find the optimum wing planform and airfoil shape. A backward-swept wing (BSW) aircraft, developed inside the Cluster of Excellence–Sustainable and Energy Efficient Aviation (A) is studied. Novel technologies such as active flow control, limited maximum load factors due to load alleviation, and novel materials allow a fuel weight reduction of 6%.

Experimental investigation of the combined impact of backpressure with the pintle dynamic on the hydrogen spray exiting a medium pressure DI outward-opening injector

A vast scientific literature has shed light on hydrogen as a promising vector for carbon-free mobility. Within this scope, over the last few decades several efforts were directed towards the characterization of hydrogen spray, given its significant influence on the combustion efficiency. Nevertheless, several aspects underlying the hydrogen spray development are still far from being fully understood. This framework prompted the authors to undertake a robust experimental campaign, performing hydrogen injections over a wide range of injection settings. In this study, the schlieren method was utilized to capture the image of jets performed at injection pressure of 3.6 MPa and exiting an outward-opening injector. Afterwards, the spray images were processed by means of an in-home developed Matlab script. In order to assess the spray characteristics, such as the penetration length, area and volume, the analysis of the results was focused on the combined impact of backpressure, ranging from 0.12 to 1.5 MPa, with current profile determining the pintle dynamic. Besides, a qualitative analysis of the injection setting impact on the shock wave position was carried out. In the light of emerged findings, the research serves as a further baseline for forthcoming research activities dealing with hydrogen spray.

Effects of influencing factors on the performance and morphology of shock waves in ejectors: A review

This paper presents a detailed literature review on the studies carried out in the last three decades, for understanding the factors affecting the performance of the ejector. An ejector is one of the important components in many industrial applications in the field of refrigerant expansion, circulation of fluids, vacuum creation, etc. From the analysis of the reported works of the ejector, the CFD modeling has proved to be a convenient method for analyzing the complex phenomenon in the ejector like mixing process, turbulence characteristics, shock interactions, and condensation process. The first part of this paper discusses the operation of ejector, flow structure, parameters required for the computational modeling, governing equations, etc. The second part discusses the influence of geometrical parameters and various operating conditions on the ejector performance. The shape and position of shock waves in the ejector for various operating conditions are also narrated under the same section. Third part of this paper is devoted to discussions on advances in modeling to be considered for the performance improvement of ejectors. Finally, the paper concludes with clear guidelines for the effective ejector modeling. Future scope of ejector research, pathways to progress, etc., mentioned in the conclusion section should help researchers and designers in this field.

Effects of expansion waves on incident shock-wave/boundary-layer interactions in hypersonic flows

The effects of expansion waves on incident shock-wave/boundary-layer interactions (SWBLIs) at a Mach number of 4.96 are experimentally studied. The flow characteristics of the interaction zone under various intensities and positions of the incident shock wave and expansion waves are quantitatively analyzed. The expansion waves weaken the intensity of the shock waves encountered, thereby weakening the intensity of the SWBLIs. With an increasing distance between the expansion waves and the interaction zone, the total wall pressure jump and the interference length show a linear growth trend. However, the expansion waves do not affect the initial pressure jump of the separation, which is consistent with free-interaction theory. Finally, the scaling model proposed by Souverein et al. [“A scaling analysis for turbulent shock-wave/boundary-layer interactions,” J. Fluid Mech. 714, 505 (2013)] is simply modified using the measured value of the pressure jump. This correction provides a better approximate result for SWBLIs under the impact of expansion waves.

Bayesian uncertainty quantification analysis of the SST model for transonic flow around airfoils simulation

Transonic flow simulation is a common but complex task in engineering, and poses a great challenge to computational fluid dynamics using the Reynolds-averaged Navier–Stokes approach. One of the important factors influencing the complexity of this task is the uncertainty introduced by turbulence models. In this paper, to improve the performance of the shear stress transport model, a Bayesian uncertainty quantification analysis of turbulence model parameters is carried out on transonic flow around the RAE2822 airfoil and the ONERA M6 wing. First, the Sobol indices are obtained for sensitivity analysis, the results of which show that the pressure coefficients are mainly sensitive to four parameters a1, κ, β⁎, and β1. A posterior uncertainty analysis is then performed based on the pressure coefficients of two-dimensional sections. The maximum a posteriori estimates from the two examples indicate opposite trends for the predicted shock wave positions. In the predictions for RAE2822, the shock wave position is advanced, while in those for ONERA M6, it is delayed. The estimates from RAE2822 enable a better prediction capability at a small angle of attack, while those from ONERA M6 enables an ability to simulate flow with separation at a large angle of attack, mainly because of the increase in a1. In practical engineering applications, the choice between the two sets of calibrated parameters to achieve the best simulation results may be facilitated by reference to experimental data.

The Riemann problem for a traffic flow model

A traffic flow model describing the formation and dynamics of traffic jams was introduced by Berthelin et al. [“A model for the formation and evolution of traffic jams,” Arch. Ration. Mech. Anal. 187, 185–220 (2008)], which consists of a pressureless gas dynamics system under a maximal constraint on the density and can be derived from the Aw–Rascle model under the constraint condition ρ≤ρ* by letting the traffic pressure vanish. In this paper, we give up this constraint condition and consider the following form: {ρt+(ρu)x=0,(ρu+εp(ρ))t+(ρu2+εup(ρ))x=0,in which p(ρ)=−1ρ. The Riemann problem for the above traffic flow model is constructively solved. The delta shock wave arises in the Riemann solutions, although the system is strictly hyperbolic, its first eigenvalue is genuinely nonlinear, and the second eigenvalue is linearly degenerate. Furthermore, we clarify the generalized Rankine–Hugoniot relations and δ-entropy condition. The position, strength, and propagation speed of the delta shock wave are obtained from the generalized Rankine–Hugoniot conditions. The delta shock may be useful for the description of the serious traffic jam. More importantly, it is proved that the limits of the Riemann solutions of the above traffic flow model are exactly those of the pressureless gas dynamics system with the same Riemann initial data as the traffic pressure vanishes.

Fast Inverse Design of Transonic Airfoils by Combining Deep Learning and Efficient Global Optimization

In this paper, a deep learning model trained to generate well-posed pressure distributions at transonic speeds is coupled by the efficient global optimization (EGO) algorithm to speed up the inverse design process for transonic airfoils. First, the Wasserstein generative adversarial network (WGAN) is trained to generate well-posed pressure distributions at transonic speeds. Then, the EGO algorithm is used to pick up a pressure distribution in WGAN by solving the associated optimization problem defined for matching the prescribed pressure features, such as the suction peak and the shock-wave position. Finally, a deep convolutional neural network (DCNN) for nonlinear mapping is adopted to obtain the corresponding airfoil shape. Several cases with prescribed pressure features were performed to verify the feasibility and efficiency of the proposed method. Test cases indicate that the airfoil shape with the desired pressure distribution can be found in around one minute using a desktop computer with an Intel i5-9300H CPU.