Location Of Shock Wave Research Articles

CFD study on inlet unstart prediction of dual-mode scramjet

Dual-mode scramjet has become a viewpoint in the research fields of propulsion systems of aeronautics and astronautics. The key operating process of the dual-mode scramjet is from a started situation to an unstarted situation. The operating process composes of three phases. The first phase is when the pseudo shock wave is in the combustor. The second phase is when the pseudo shock wave is in the isolator. The last phase is when inlet unstart happens. In this study, two-dimensional numerical model has been made to replicate the process before inlet unstart. The location of pseudo shock wave has been determined in according to the location of the plug. As the throat area of the plug is decreasing, pseudo shock wave goes upstream. The prediction of inlet unstart has been focused in terms of the throat area ratio. The transition point of throat area ratio just before inlet unstart has been indicated. The transition points of throat area ratio in steady simulation and unsteady simulation are different. This is because the transition information needs time to spread from the plug to upstream location. The difference could be used for predicting the inlet unstart.

Variable Turbulent Prandtl Number Model for Shock/Boundary-Layer Interaction

Interaction of shock waves with turbulent boundary layers can enhance the surface heat flux dramatically. Reynolds-averaged Navier–Stokes simulations based on a constant turbulent Prandtl number often give grossly erroneous heat transfer predictions in shock/boundary-layer interaction flows. This is due to the fact that the underlying Morkovin’s hypothesis breaks down in the presence of shock waves; thus, the turbulent Prandtl number cannot be assumed to be a constant. In this paper, a new variable turbulent Prandtl number model based on linearized Rankine–Hugoniot conditions applied to shock–turbulence interaction is developed. The turbulent Prandtl number is a function of the shock strength, and a shock function is proposed to identify the location and strength of shock waves. The shock function also simulates the postshock relaxation of the turbulent heat flux, which is akin to that observed in canonical shock–turbulence interaction. The model is combined with the well-validated shock-unsteadiness model and is applied to the complex shock topology observed in oblique shock/turbulent boundary-layer interactions. Comparison with experimental data shows significant improvement in the surface heat transfer rate in the interaction region, both for attached and separated shock/boundary-layer interaction cases. The shock function is also used to propose a robust form of the existing shock-unsteadiness model that simplifies the numerical implementation enormously.

Solutions of supercritical CO2 flow through a convergent-divergent nozzle with real gas effects

Supercritical CO2 (S-CO2) has a density as high as that of its liquid phase while the viscosity remains closer to its gaseous phase. S-CO2 has the potential to be used as a working fluid in compressor as it requires much less work due to its low compressibility as well as relatively small flow resistance. Besides the material properties and design calculations, the thermodynamic properties of working gases play a vital role in the design and efficiency of various machinery such as compressors, turbines, etc. Equation of state (EOS) which accounts the real gas effects is used in computational analysis to estimates the thermodynamic properties of the working fluid. Each EOS gives priority to real gas effects phenomena differently and for the analysis of the fluid dynamic machinery, as of today, there is no standard procedure for selecting a suitable equation of state (EOS). To understand the influence of real gas effects on the formation of a shock wave, S-CO2 flow through a convergent-divergent nozzle, is theoretically analyzed. The thermophysical and transport properties calculated with the six different equation of state (EOS) are used to estimate the flow characteristics.An in-house code based on the real gas approach which solves gas dynamics equations with variable gas properties is used to analytically analyze the compressible flow of S-CO2 through nozzle. The solution for the shock strength, total pressure loss, and location of the normal shock wave at different back pressure conditions is obtained. Using Becker’s solutions with varying viscosity and thermal conductivity estimated from each EOS, the properties inside the normal shock wave are calculated. Numerical results of supersonic S-CO2 flow varies with different EOS candidates and the formation of shock wave is found to be significantly influenced by the real gas effects.

Numerical Study on Skin Friction and Shock Inception in Various Geometries of Supersonic Nozzle

In the present study, a numerical simulation is conducted to predict the influence of convergent-divergent nozzle geometry and NPR on the skin friction and shockwave location. Various shapes of nozzles are numerically simulated using the Computational Fluid Dynamics code. The shock position is examined to demonstrate the impact of nozzle shape on its location. Skin friction is shown to be smoothly decreasing at the divergent part of the nozzle for all NPRs lower than 2.0. However, an inverse behavioural trend was observed at NPR equal to 2. This could be attributed to the fact that the large disturbance of fluid near the wall is the major factor behind such an oddity. The results also show that the shock position is reliant on the nozzle geometry at certain NPR.

Impacts of Laser Energy Deposition on Flow Instability over Double-Cone Model

In this study, the effectiveness of repetitive laser pulse energy deposition over a double-cone model in a Mach 1.92 flow (half-apex angles of 22 and 40 deg) was investigated experimentally. The Reynolds number, based on the model’s outer diameter, was . Because of the shock wave/boundary-layer interaction, the shock wave over the cone’s transition corner exhibited an inherent low-frequency oscillation with a characteristic frequency of 6.3 kHz. Using high-frequency laser deposition of up to 80 kHz, the oscillation of the shock system was suppressed. Although the boundary layer experienced “sweeping” by laser-heated rings with a primary frequency equal to that of the energy deposition, the shock system above the bubble passage experienced frequency modulation to a much lower frequency range, and the shock wave location was stabilized.

Optimization of screw fixation in rat bone with extracorporeal shock waves.

Screw fixation in osteoporotic patients is becoming an increasing problem in orthopaedic surgery as deterioration of cortical and cancellous bone hamper biomechanical stability and screw fixation. This might result in delayed weight-bearing or failure of instrumentation. We hypothesized that local peri-operative shock wave treatment can optimize osseointegration and subsequent screw fixation. In eight female Wistar rats, two cancellous and two cortical bone screws were implanted in both femora and tibiae. Immediately after implantation, 3.000 unfocused extracorporeal shock waves (energy flux density 0.3 mJ/mm2 ) were applied to one side. The other side served as non-treated internal control. Evaluation of osseointegration was performed after 4 weeks with the use of microCT scanning, histology with fluorochrome labeling, and pull-out tests of the screws. Four weeks after extracorporeal shock wave treatment, treated legs exhibited increased bone formation and screw fixation around cortical screws as compared to the control legs. This was corroborated by an increased pull-out of the shock wave treated cortical screws. The cancellous bone screws appeared not to be sensitive for shock wave treatment. Formation of neocortices after shock wave therapy was observed in three of eight animals. Furthermore, de novo bone formation in the bone marrow was observed in some animals. The current study showed bone formation and improved screw fixation as a result of shock wave therapy. New bone was also formed at locations remote from the screws, hence, not contributing to screw fixation. Further, research is warranted to make shock wave therapy tailor-made for fracture fixation. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:76-84, 2018.

Activation of peroxydisulfate by gas–liquid pulsed discharge plasma to enhance the degradation of p-nitrophenol

Pulsed discharge in water and over water surfaces generates ultraviolet radiation, local high temperature, shock waves, and chemical reactive species, including hydroxyl radicals, hydrogen peroxide, and ozone. Pulsed discharge plasma (PDP) can oxidize and mineralize pollutants very efficiently, but high energy consumption restricts its application for industrial wastewater treatment. A novel method for improving the energy efficiency of wastewater treatment by PDP was proposed, in which peroxydisulfate (PDS) was added to wastewater and PDS was activated by PDP to produce more strong oxidizing radicals, including sulfate radicals and hydroxyl radicals, leading to a higher oxidation capacity for the PDP system. The experimental results show that the increase in solution conductivity slightly decreased the discharge power of the pulse discharge over the water surface. An increase in the discharge intensity improved the activation of PDS and therefore the degradation efficiency and energy efficiency of p-nitrophenol (PNP). An increase in the addition dosage of PDS greatly facilitated the degradation of PNP at a molar ratio of PDS to PNP of lower than 80:1, but the performance enhancement was no longer obvious at a dosage of more than 80:1. Under an applied voltage of 20 kV and a gas discharge gap of 2 mm, the degradation efficiency and energy efficiency of the PNP reached 90.7% and 45.0 mg kWh−1 for the plasma/PDS system, respectively, which was 34% and 18.0 mg kWh−1 higher than for the discharge plasma treatment alone. Analysis of the physical and chemical effects indicated that ozone and hydrogen peroxide were important for PNP degradation and UV irradiation and heat from the discharge plasma might be the main physical effects for the activation of PDS.

Optimization of dehydration process to improve stability and efficiency of supersonic separation

Supersonic gas-liquid separation is considered as one of the novel methods for natural gas conditioning that removes either water or heavy hydrocarbons from the natural gas without using chemical ingredients. The expansion of natural gas stream in a supersonic nozzle increases the fluid velocity to supersonic level and makes low pressure and temperature conditions in which nucleation of the liquid phase and condensation initiate. The process includes two isentropic processes with an intermediate shockwave. This research is the first serious attempt for controlling the supersonic separation units and applies the stability concept for actual conditions and disturbances in the gas pressure and composition during the lifecycle of a gas well. The article explores how the optimal performance of a supersonic nozzle can be saved with variations in the nozzle input gas pressure or composition. As the phase change and condensation are mainly occur at the shockwave position, the geometry configuration of supersonic nozzle is of high importance so that the drain location should be aligned with the shockwave location. An algorithm is employed to find a control function to compensate the backpressure of the nozzle within the feed pressure variation. It guarantees the equipment to be kept effectively in the optimal operating condition. In a case study, it is explained how the proposed solution enables the system to keep the dew point within ±2.5 °C drift from the desired criteria following a ±18% disturbance in the inlet pressure. Moreover, investigation on the effect of natural gas composition shows that the separation system is intrinsically robust to variations in the main natural gas composition.

Nonlinear propagation of ion-acoustic waves through the Burgers equation in weakly relativistic plasmas

The Burgers equation is obtained to study the characteristics of nonlinear propagation of ionacoustic shock, singular kink, and periodic waves in weakly relativistic plasmas containing relativistic thermal ions, nonextensive distributed electrons, Boltzmann distributed positrons, and kinematic viscosity of ions using the well-known reductive perturbation technique. This equation is solved by employing the (G'/G)-expansion method taking unperturbed positron-to-electron concentration ratio, electron-to-positron temperature ratio, strength of electrons nonextensivity, ion kinematic viscosity, and weakly relativistic streaming factor. The influences of plasma parameters on nonlinear propagation of ion-acoustic shock, periodic, and singular kink waves are displayed graphically and the relevant physical explanations are described. It is found that these parameters extensively modify the shock structures excitation. The obtained results may be useful in understanding the features of small but finite amplitude localized relativistic ion-acoustic shock waves in an unmagnetized plasma system for some astrophysical compact objects and space plasmas.

Robust control design of an air‐breathing engine for a supersonic vehicle using backstepping and UKF

AbstractThis paper presents an efficient robust control design approach for an air‐breathing engine for a supersonic vehicle using the Lyapunov stability theory based nonlinear backstepping control, augmented with unscented Kalman filter (UKF). The primary objective of the control design is to ensure that the thrust produced by the engine tracks the commanded thrust by regulating the fuel flow to the combustion chamber. Moreover, as the engine operates in a supersonic range, an important secondary objective is to manage the shock wave location in the intake for maximum pressure recovery with adequate safety margin by varying the throat area of the nozzle simultaneously. To estimate the states and parameters as well as to filter out the process and sensor noises, a UKF has been incorporated for robust output feedback control computation. Furthermore, independent control designs for the actuators have been carried out to assure satisfactory performance of the engine. Additionally, a guidance loop is designed to generate a typical flight trajectory of the representative vehicle using a nonlinear suboptimal input constrained model predictive static programming formulation for testing the performance of the engine. Simulation results clearly indicate quite successful robust performance of the engine during both climb and cruise phases.

Maximization of energy recovery inside supersonic separator in the presence of condensation and normal shock wave

Natural gases provide around a quarter of energy consumptions around the globe. Supersonic separators (3S) play multifaceted role in natural gas industry processing, especially for water and hydrocarbon dew point corrections. These states of the art devices have minimum energy requirement and favorable process economy compared to conventional facilities. Their relatively large pressure drops may limit their application in some situations. To maximize the energy recovery of the dew point correction facility, the pressure loss across the 3S unit should be minimized. The optimal structure of 3s unit (including shock wave location and diffuser angle) is selected using simultaneous combination of normal shock occurrence and condensation in the presence of nucleation and growth processes. The condense-free gas enters the non-isentropic normal shock wave. The simulation results indicate that the normal shock location, pressure recovery coefficient and onset position strongly vary up to a certain diffuser angle (β = 8°) with the maximum pressure recovery of 0.88 which leads to minimum potential energy loss. Computational fluid dynamic simulations show that separation of boundary layer does not happen for the computed optimal value of β and it is essentially constant when the inlet gas temperatures and pressures vary over a relatively broad range.

A RANS model correction on unphysical over-prediction of turbulent quantities across shock wave

The unphysical increase of turbulent quantities in turbulence model induced by shock wave in simulations of hypersonic flows and its influence on the aerothermal prediction are studied. Using k-ω SST model, numerical experiments on the hypersonic flow over a blunt body indicate that the strong detached shock wave will result in serious unphysical increase of turbulent quantities and the increase magnitudes are closely related to the mesh scales near the shock wave. This phenomenon could generally cause an over-prediction of the aerothermal prediction. To eliminate this unphysical phenomenon and enhance the accuracy of aerothermal prediction, a new correction model for current k-ω SST model is established, which includes two parts: a shock wave detector to identify the location of shock wave and a damping function for the production terms in turbulent transport equations. Finally, the modified k-ω SST model using the correction model is applied to two types of hypersonic flows. Numerical results prove that the correction model can effectively eliminate the unphysical increase of turbulent quantities around the shock wave and meanwhile does not affect the normal development of turbulent quantities inside boundary layer. Through the correction model, the accuracy of aerothermal prediction is remarkably improved.

A Riemann problem based method for solving compressible and incompressible flows

A Riemann problem based method for solving two-medium flow including compressible and incompressible regions is presented. The material interface is advanced by front tracking method and the material interface boundary conditions are defined by modified ghost fluid method. A coupled compressible and incompressible Riemann problem constructed in the normal direction of the material interface is proposed to predict the interfacial states. With the ghost fluid states, the compressible and incompressible flows are solved by discontinuous Galerkin method. An incompressible discontinuous Galerkin method with nonuniform time step is also deduced. For shock wave formed in compressible flow, the numerical errors for the ghost fluid method in earlier works are analyzed and discussed in the numerical examples. It shows that the proposed method can provide reasonable results including shock wave location.

Flow visualisation of a normal shock impinging over a rounded contour bump in a Mach 1.3 free-stream

An experimental study has been conducted to visualise the instantaneous streamwise and spanwise flow patterns of a normal shock wave impinging over a rounded contour bump in a Mach 1.3 free-stream. A quartz-made transparent shock generator was used, so that instantaneous images could be captured during the oil-flow visualisation experiments. Fluorescent oil with three different colours was used in the surface oil-flow visualisation experiment to enhance the visualisation of flow mixing and complicated flow features that present in the flow field. Experimental data showed that the rounded contour bump could split the impinging normal shock wave into a or a series of lambda-shaped shock wave structure(s). In addition, it was found that the flow pattern and the shock wave structures that appeared over the rounded contour bump depended highly on the impinging location of the normal shock wave. The flow pattern shown in this study agreed with the findings documented in literature. Moreover, it was observed from the instantaneous oil streaks that the normal shock impinging location also affected the size and the formation location of the spanwise counter-rotating vortices downstream of the bump crest. Finally, it was concluded that the terminating shock could distort the oil streaks that left over the surface of the contour bump. Therefore, the use of the transparent normal shock wave generator is recommended when conducting experiments with normal shock wave impingement involved.Graphical abstract

Prediction of shockwave location in supersonic nozzle separation using self-organizing map classification and artificial neural network modeling

One of the novel technologies for natural gas dehydration and natural gas dew-point conditioning is supersonic separation, which has remarkable features, including compact and maintenance-free design. Due to its complex design and the difficulty of experimental analysis, researchers tend to conduct numerical modeling for behavior investigation of the nozzle focusing on shockwave which is the main phenomena inside the nozzle. The present NN-model outperforms a selection of data and proposes an efficient NN-based algorithm for shockwave position estimation as the key nozzle geometry parameter. Data for the shockwave location was collected from a wide range of results from the literature and then a neural network based self-organizing map was adapted to the dataset. This created a classified dataset and the use of unreal weight and repeated experimental results from different research were avoided. A neural network was employed for modeling the shockwave location through the nozzle using a better quality dataset. Additionally, the one-dimensional inviscid theory was utilized in the recursive approach for comparison to the main proposed model. Simulation results presented in this research reveal the effectiveness of the proposed neural network technique for supersonic nozzle modeling and make it possible to determine the shockwave location from the nozzle pressure boundary conditions. The results showed that the supersonic nozzle separation have capability to be used in both low-pressure applications and high pressure ones. The dimensionless length for shockwave location is predicted in the range of 0.82–0.92 for the former and 0.72 to 0.95 for the later, depending on pressure recovery ratio.

Effect of nose shape on the shock standoff distance at nearsonic flows

This paper describes a numerical solution of the bow shock shape ahead of some blunt and sharp axisymmetric noses containing sphere, blunt cone, and sharp cone at steady transonic flow in the Mach number range of 1.01 to 1.2. For validating the results, one sphere and three blunt cones are modeled, and their shock standoff distance is compared with other experimental and numerical studies. The flow over other noses with similar geometric parameters is then solved and compared with each other. In this study, the Reynolds-averaged Navier—Stokes equations are solved using the Spalart—Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for some blunt and sharp noses at low supersonic free flight speed. The shock standoff distance is determined from the Mach number curve on the symmetry line. The present numerical simulations reach down to M8=1.01 a range where it is almost very difficult to set in experimental studies. The shock wave locations were found to agree well with previous numerical and experimental studies. Our results are closer to the experimental results compared to other numerical studies. In addition, the results for shock standoff distances over paraboloids in these speed ranges have not been previously published as far as we know.

Scalar Green function bounds for instantaneous shock location and one-dimensional stability of viscous shock waves

In this paper, we investigate and prove the nonlinear stability of viscous shock wave solutions of a scalar viscous conservation law, using the methods developed for general systems of conservation laws by Howard, Mascia, Zumbrun and others, based on instantaneous tracking of the location of the perturbed viscous shock wave. In some sense, this paper extends the treatment in a previous expository work of Zumbrun [Instantaneous shock location ...] on Burgers equation to the general case, giving an exposition of these methods in the simplest setting of scalar equations. In particular we give by a rescaling argument a simple treatment of nonlinear stability in the small-amplitude case.

Free-stream static pressure measurements in the Longshot hypersonic wind tunnel and sensitivity analysis

The performance of fast-response slender static pressure probes is evaluated in the short-duration, cold-gas, VKI Longshot hypersonic wind tunnel. Free-stream Mach numbers range between 9.5 and 12, and unit Reynolds numbers are within 3–10 × 106/m. Absolute pressure sensors are fitted within the probes, and an inexpensive calibration method, suited to low static pressure environments (200–1000 Pa), is described. Transfer functions relating the probe measurements pw to the free-stream static pressure p∞ are established for the Longshot flow conditions based on numerical simulations. The pressure ratios pw/p∞ are found to be close to unity for both laminar and turbulent boundary layers. Weak viscous effects characterized by small viscous interaction parameters \({\bar{\chi }} 16.5 by installing multiple pressure sensors in a single probe. The effect of pressure orifice geometry is also evaluated experimentally and found to be negligible for either straight or chamfered holes, 0.6–1 mm in diameter. No sensitivity to probe angle of attack could be evidenced for α < 0.33°. Pressure measurements are compared to theoretical predictions assuming an isentropic nozzle flow expansion. Significant deviations from this ideal case and the Mach 14 contoured nozzle design are uncovered. Validation of the static pressure measurements is obtained by comparing shock wave locations on Schlieren photographs to numerical predictions using free-stream properties derived from the static pressure probes. While these results apply to the Longshot wind tunnel, the present methodology and sensitivity analysis can guide similar investigations for other hypersonic test facilities.

Increasing the HIFU ablation rate through an MRI-guided sonication strategy using shock waves: feasibility in the in vivo porcine liver

This study investigated whether an MR-guided pulsed HIFU ablation strategy could be implemented under clinical conditions, using a transducer designed for uterine fibroid ablation, to obtain an ablation rate that is sufficiently high for clinical abdominal HIFU therapy in highly perfused organs. A pulsed HIFU ablation strategy, aimed at increasing the energy absorption in the HIFU focal area by local shock wave formation in the non-linear pressure regime, was compared to an energy-equivalent continuous wave sonication strategy in the linear pressure regime. Both ablation strategies were used for transcutaneous sonication of pre-defined treatment cells in the livers of 5 pigs in vivo. Temperature evolution in both the target area as well as the pre-focal muscle layer was monitored simultaneously using MR thermometry. Local energy absorption and thermal dose volumes were shown to be increased using the pulsed ablation strategy, while preserving healthy tissue in the near field of the acoustic beam. Respiratory motion compensation of both acoustic energy delivery and MR thermometry was applied through gating based on MR navigator echoes. Histopathology showed that confluent vacuolated thermal lesions were created when the pulsed ablation strategy was used. Additionally, it was shown that the heat sink effect caused by the presence of larger vessels could be overcome. The pulsed HIFU ablation strategy achieved an ablation rate of approximately 4 ml per hour in the in vivo porcine liver, without causing undesired damage to healthy tissues in the near field.

Electro Conductive Alumina Nanocomposites From Different Alumina-Carbides Mixtures

This work presents the results of an electro-discharge machined ceramic composites consisting of a base non-conductive ceramic component such Al 2 O 3 , to which is added sufficient amounts of an electro-conductive ceramic nanoparticles such as TiC, TiNC, NbNC, TaNC, and SiC (whiskers) to achieve an electrical resistance of less than about 100W.cm. With these compositions intricate geometries and features as holes, chamfers, slots, angles, changing radii and complex curves can be electro-discharge machined (EDM) into the ceramic body after Pulsed Electrical Current Sintering (PECS) to achieve maximum density and mechanical properties. In EDM, the electrically conductive workpiece or ceramic blank is eroded by electric discharges or sparks which on a small scale generate localized shock waves and intense heat.The four compositions studied were in the same proportion for all raw materials: alumina 42 (vol %) + conductive material (TiC, TiNC, NbNC, and TaNC) 22 (vol %) + SiC w 36 (vol %). Processing was carried out mixing raw materials in the suitable proportions in a polypropylene container with zirconia balls and isopropanol media for 72 hours in order to guarantee the homogeneity of the final compositions. The powders were dried and introduced into a PECS furnace for sintering to 1650°C (100 MPa/2 min). The diameters of the pieces obtained were 20 and about 40 mm and 7 mm thickness.SiC whiskers reinforced electrically conductive ceramic compositions provide a fully dense material with optimal mechanical properties. The capability of electro-discharge machining obtains good surface quality, chip-free edges, dimensional accuracy and complex shapes. The fracture toughness is improved two to three fold over individual ceramic components. Strength and hardness is also increased. Some composites were tested as a cutting tool to machine IN-718 nickel-base superalloy industrial laminating cylinders. The composites were formed and electro-discharge machined to a standard size cutting insert.