Position Of Shock Wave Research Articles

Hysteresis of shock wave locations in divergent bent channels

The turbulent airflow in 2D and 3D channels with bends of opposite walls is studied numerically. The channels are slightly divergent in the longitudinal direction upstream and downstream of the bends. The flow is supersonic on the inlet and outlet boundaries of the computational domain. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy. The solutions demonstrate considerable hysteresis under variations of the free-stream Mach number or angle of attack. At the ends of hysteresis bands, the flow structure changes drastically due to instability of shock wave positions. Effects of 3D phenomena, turbulent viscosity, and thickness of walls on the hysteresis are discussed.

The universal algorithm for solving the gas dynamics equations on the mesh with arbitrary number of cell faces

The paper presents methodology and algorithm for calculating the equations of gas dynamics on arbitrary computational meshes with a mixed type of cells. The calculation method is based on the method of linear reconstruction proposed by Barth and Jesperson. The algorithm for determining the geometric parameters of arbitrary computational cell is presented. To implement the calculation algorithm, a data storage system has been proposed and tested. The algorithm of the solver and the algorithm of docking the computational meshes in the case of using block-structured meshes are proposed. The efficiency of methodology and developed program of calculation are demonstrated by the calculation example of the air flow in flat air intakes. The structure of flow and position of the bow shock wave are determined. These results with the theoretical values were compared. The application of the proposed methodology and calculation algorithm to arbitrary computational meshes with a mixed cell type makes it possible to optimize the process of constructing computational mesh and conduct numerical studies of gas dynamics in regions of complex geometry.

Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term

The Riemann problems for a class of coupled hyperbolic systems of conservation laws with a source term are studied. The Riemann solutions exactly include two kinds: delta-shock solutions and vacuum solutions. In order to see more clearly the influence of the source term on Riemann solutions, the generalized Rankine-Hugoniot relations of delta shock waves are derived in detail, and the position, propagation speed and strength of delta shock wave are given. It is also shown that, as the source term vanishes, the Riemann solutions converge to the corresponding ones of the homogeneous system, which is just the generalized zero-pressure flow model and contains the one-dimensional zero-pressure flow as a prototypical example. Furthermore, the generalized balance relations associated with the generalized mass and momentum transportation are established for the delta-shock solution. Finally, two typical examples are presented to illustrate the application of our results.

Discontinuities dynamics after the interaction of a plane shock wave with pulse volume discharge

The dynamics of the nanosecond combined volume discharge radiation in the air flow with the plane shock wave was studied. Shock wave with Mach number 1.9-4.5 was passing through the discharge chamber and coming out of it while the electric pulse was switched on. The radiation spectra and the discharge currents were registered in the air pressure range 10-150 Torr, a pulsed voltage of 25 kV, and an electric current ∼1 kA. It is shown that the electric current duration depends on shock wave position relative to the discharge gap and does not exceed 500 ns at various conditions. As a result of discharge energy input, the shock breakdown occurs with the formation of shock waves and contact surfaces. The high-speed shadow imaging was used to study the flow evolution after the discharge pulse. The experimental data on shock waves and contact surfaces positions is compared with numerically calculated positions, making it possible to determine the amount of thermal energy release during the discharge electric current time.

Suppressing Numerical Oscillation for Nonlinear Hyperbolic Equations by Wavelet Analysis

In the numerical solution for nonlinear hyperbolic equations, numerical oscillation often shows and hides the real solution with the progress of computation. Using wavelet analysis, a dual wavelet shrinkage procedure is proposed, which allows one to extract the real solution hidden in the numerical solution with oscillation. The dual wavelet shrinkage procedure is introduced after applying the local differential quadrature method, which is a straightforward technique to calculate the spatial derivatives. Results free from numerical oscillation can be obtained, which can not only capture the position of shock and rarefaction waves, but also keep the sharp gradient structure within the shock wave. Three model problems—a one-dimensional dam-break flow governed by shallow water equations, and the propagation of a one-dimensional and a two-dimensional shock wave controlled by the Euler equations—are used to confirm the validity of the proposed procedure.

Real‐time detection of end‐of‐queue shockwaves on freeways using probe vehicles with spacing equipment

The identification of a traffic shockwave traditionally is conducted offline, which inhibits its implementation for active traffic management strategies. This study aims to develop an online approach to detect traffic shockwaves on freeways, particularly the end-of-queue shockwaves, using spacing-based probe vehicles (SPVs) that can obtain the trajectories of its leading and/or following vehicles. The proposed framework consists of four stages: (i) local shockwave (LSW) position detection, (ii) LSW speed estimation, (iii) grouping of LSWs into a whole shockwave (WSW) and (iv) WSW speed estimation. In particular, two alternatives, namely the line connection-based method and the Lighthill–Whitham–Richards model-based method (LWRM), are proposed for stage 2, and other two alternatives, namely the simple averaging method and the hybrid method (HM), are proposed for stage 4. A set of next generation simulation data are utilised to evaluate the performance of the proposed method. The results demonstrate that the combination of LWRM + HM outperforms among the four combined methods. A series of the analysis indicate that the proposed method is computationally efficient, accurate and more importantly, it is applicable to sensor data from SPVs with real-world noise.

Wet Steam Nonequilibrium Condensation Flow-Induced Vibrations of a Nuclear Turbine Blade

Condensing flow induced vibration (CFIV) of the rotor blade is a tough problem for designers of nuclear turbines because nonequilibrium condensing flow excitation (NECFE) is hard to be directly modeled. Generally, in design, NECFE is assumed as equilibrium condensing flow excitation (ECFE), of which the pressure fluctuations caused by phase temperature difference (PTD) between gaseous and liquid are ignored. In this paper, a novel method to calculate the equivalent load of NECFE based on the principle of virtual work was proposed. This method could consider the effects of PTD-induced pressure fluctuations by simulating nonequilibrium condensation with ANSYS cfx, and improve computational efficiency. Once the equivalent NECFE load is determined, CFIV of the rotor blade, which was modeled as a pretwisted asymmetric cantilever beam, can then be predicted by the finite element method (FEM). Additionally, to estimate the effects of PTD-induced pressure fluctuations, comparisons between NECFE and ECFE as well as their induced vibrations were presented. Results show that PTD in nucleation area could change the position and type of shock waves, restructure the pressure distribution, as well as enhance the pressure fluctuations. Compared with ECFE, the frequency ingredients and amplitude of the equivalent NECFE load and its induced vibrations are increased. Specifically, the amplitude of the equivalent NECFE load is increased by 9.38%, 15.34%, and 7.43% in the tangential component, axial component, and torsion moment. The blade vibration responses induced by NECFE are increased by 11.66% and 19.94% in tangential and axial.

English

The present paper presents the numerical analysis for a transonic centrifugal compressor using steady state CFD. The blade tip clearance effect over the position of shock waves, tip losses and the ...

Riemann problem for a compressible perfect fluid with a constant external force for the Chaplygin gas

The Riemann problem for a compressible perfect fluid with a constant external force for the Chaplygin gas is considered. We obtain two kinds of exact solutions. The first one consists of contact discontinuities, while the other one involves a delta shock wave in which both density and internal energy contain a Dirac delta function. The position, speed and weights of the delta shock wave are derived from both generalized Rankine–Hugoniot relation and entropy condition, which are established in detail. Moreover, the solutions are no longer self-similar due to the influence of the constant external force.

Quantitative Visualisation of Compressible Flows

Abstract The paper demonstrates the feasibility of quantitative flow visualisation methods for investigation of transonic and supersonic flows. Two methods and their application for retrieving compressible flow field properties has been described: Background Oriented Schlieren (BOS) and Particle Image Velocimetry (PIV). Recently introduced BOS technique extends the capabilities of classical Schlieren technique by use of digital image processing and allow to measure density gradients field. In the presented paper a review of applications of BOS technique has been presented. The PIV is well established technique for whole field velocity measurements. This paper presents application of PIV for determination of the shock wave position above airfoil in transonic flow regime. The study showed that application of quantitative flow visualisation techniques allows to gain new insights on the complex phenomenon of supersonic and transonic flow over airfoils like shock-boundary layer interaction and shock induced flow separation.

Effects of fluid type and pressure order on performance of convergent–divergent nozzles: An efficiency model for supersonic separation

AbstractA deep analysis on the hydrodynamics of convergent–divergent nozzles is performed by changing the working conditions and fluid type. The nozzle geometry lowers the temperature of the flowing fluid, which contributes to condensation and phase change. The focus of this paper is to evaluate the nozzle performance and cooling capacity in terms of temperature, pressure, and gas type in a fixed geometry of Sajben Laval nozzle. The analysis has been conducted via a 2‐dimensional turbulent computational fluid dynamics simulation for illustrating the behavior of the fluid. A criterion for the nozzle performance is provided by prediction of exact shock wave position. An investigation on 6 different gas types demonstrates that heat capacity and thermal conductivity are the most rolling fluid properties of the nozzle performance. Furthermore, it is found that the shock wave position is unchanged during alteration of fluid type or pressure scale.A new model is provided for prediction of convergent–divergent nozzle performance in the supersonic conditions for dehydration of natural gas as a well‐known industrial application of the nozzles. The model is developed by the genetic algorithm as a multivariable optimization method.

Modification of hypersonic waveriders by vorticity-based boundary layer displacement thickness determination method

For general hypersonic vehicles flying at high altitudes and Mach numbers, the appearance of the large boundary layer displacement thickness can change the pressure distribution and aerodynamic characteristics significantly. As for the waverider, another side effect is that the shock wave position is deflected downward evidently even at the design Mach number, which is adverse for the shock wave being attached to the leading edge and may lead to more leakage of high pressure gas from the lower surface onto the upper surface. Therefore, this paper first develops a vorticity-based method to determine the boundary layer displacement thickness, in combination with the tangent wedge/cone method. Then, trying to alleviate the high pressure gas leakage near the leading edge, modification of a viscous optimized waverider is conducted under the condition of strong viscous interaction, by deducting the corresponding boundary layer displacement thickness from the original lower surface along the normal direction. Results show that the shock wave position around the lower surface of the modified waverider under the condition of strong viscous interaction is very close to that of the inviscid basic flowfield around the original waverider, which means less leakage of high pressure gas. But it's found that such change has little influence on the aerodynamic characteristics of the upper surface. However, an interesting discovery is that due to the lower pressure near the leading edge of the modified lower surface, the wave drag is lowered for the same lift, thus the lift-to-drag ratio is improved. The modified waverider also exhibits higher lift-to-drag ratio at large angles of attack when compared to waveriders with upper expansion surfaces. Overall, a vorticity-based boundary layer displacement thickness determination method is proposed in this paper, which is then used to modify waveriders to achieve higher aerodynamic efficiency.

Dehydration of low-pressure gas using supersonic separation: Experimental investigation and CFD analysis

Supersonic nozzles are recently applied for carrying out water separation from natural gas streams and dew pointing in early stages of gas processing. This paper represents an experimentally and numerically study on a novel low-pressure two-phase driven supersonic nozzle constructed based on a new annular design. The nozzle includes a set of tilted fixed blades at the entrance and a swirling stabilizer along with a convergence-divergence nozzle. The liquid phase is separated from the primary gas phase by decompression and compression happening accompanied with the centrifugal effect induced by the swirling of the gas stream. The phase change happens by gradual drops in temperature and pressure upstream of the shockwave position, and an abrupt change at the shockwave position followed by a subsequent gradual increase in temperature and pressure. The pressure, temperature, and moisture level of the gas are measured to investigate the performance of the supersonic separation unit.The computation is carried out by a 2D approach capable of two-phase heat and mass transfer modeling. For the first time, the analysis uses high order of discretization schemes in order to well capture the shockwaves in a low-pressure supersonic nozzle and find out their effects on separation. An assessment is carried out focusing on the effect of operational conditions on the nozzle performance. The experimental data for dehydration efficiencies are in good agreement with the simulation results within 3%.The shockwave position is found in the range of 0.3–0.5 of non-dimensional nozzle length. The positions of both shockwave and initiation of condensation are shifted toward the exit side when the nozzle pressure ratio decreases. Reducing the pressure ratio from 0.8 to 0.6 will enhance the dehydration efficiency by about 5%.

Numerical simulation of unsteady tip clearance flow in a transonic compressor rotor

A three-dimensional, multi-passage unsteady numerical study was conducted to enhance the understanding of unsteady flow phenomena in the tip region of a transonic axial compressor rotor. Two different inlet conditions were applied to the transonic rotor to demonstrate the effect of the inlet condition on the unsteady flow phenomenon in the rotor tip region. The inlet conditions selected were axial inflow and 16-deg of co-swirl. The results show that different inlet conditions lead to different shock wave intensities and positions, which critically affects the unsteady flow structure in the tip region of the transonic rotor. Under the co-swirl inlet condition, the tip leakage vortex of each blade oscillates synchronously at the near stall point because of the weak interaction between the tip leakage vortex and the shock. Under the axial inlet condition, the rotating instability phenomenon appears as the “multi-passage structure,” which propagates along the circumference occurring at the tip of the rotor in the stable operating range due to the strong interaction between the tip leakage vortex and the shock wave. With the decrease of the mass flow, the mode order of the “multi-passage structure” does not change, but the fluctuation frequency decreases gradually.

Effect of nose thickness distribution on the stall characteristics of low aspect ratio flying wing configuration at transonic flow

The wing wing-body thickness of the highly swept flying wing configuration has great influence on the shock-leading edge vortex interaction at transonic speed, which would make significant effect on the stall characteristics. The effects of the nose thickness on the stall characteristics and heading characteristic of the low aspect ratio flying wing configuration are analyzed in simulated method and the flow mechanism is also studied. The results show that to decrease the nose thickness would make the position of the first shock wave and the breakdown position move back and the shock-leading edge vortex interaction will be weakened. To make the nose move back 10% c , the first shock wave in the leeward side will move back and it can delay the vortex breakdown by an angle 4°, which makes the stall angle and available lift coefficient increase. It would significantly improve the stall characteristics and the pitching moment characteristics. To decrease the thickness in nose also can make the heading static instability margin which would improve the heading performance. This study is useful reference for the layout design and flow mechanism of the low aspect flying wing configuration.

Nonstationary phenomena in the region of shock-wave interaction with a boundary layer at transonic flow velocities

Nonstationary characteristics of detached flow have been experimentally studied during interaction of the boundary layer with a shock wave that appears on a profiled bump in transonic flow. The experiments were performed with variable shock-wave intensity and position in a T-325 wind tunnel. The flow was studied using methods of schlieren imaging, measuring average pressure and its pulsations on the surface of a model, and determining velocity fields by particle image velocimetry. Analysis of the experimental data showed that the observed shock-wave oscillations and flow pulsations in the detachment zone were related to disturbances present in the oncoming boundary layer.

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.

Transonic flow instability in the entrance region of a channel with breaks of walls

We study numerically turbulent flow of the air in a channel with breaks of walls. The flow is supersonic downstream of the break section and in the free stream. Instability of shock waves formed in the channel and in front of the entrance is examined. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy. The solutions demonstrate an expulsion/swallowing of the shock waves with variation of the free-stream Mach number. Effects of the upper wall slopes on the shock wave positions and flow bifurcation are examined.

Computational fluid-dynamics modeling of supersonic ejectors: Screening of turbulence modeling approaches

Abstract Ejector refrigeration has not been able to penetrate the market because of the low coefficient of performance and because of the high influence of ejector performance on the efficiency of the refrigeration system. Improving the performance of ejector refrigeration systems relies on the understanding of the fluid dynamic phenomena, which can be obtained through computational fluid-dynamics approaches. Unfortunately, no agreement has been reached yet on the closures for the turbulence modeling in the Reynolds Averaged Navier-Stokes (RANS) approach. This paper contributes to the existing discussion by presenting a numerical study of the turbulent compressible fluid in a supersonic ejector. Seven RANS turbulence closures have been compared and, in addition, the turbulence models were tested under different near-wall modeling options in order to investigate the wall treatment effect on the numerical results. The numerical results have been validated by literature data consisting in entrainment ratio and wall static pressure measurements, for different ejector geometries and operating conditions. As a result, the k-ω SST model shows better performance in terms of global and local flow phenomena predictions for the different ejector geometries and operating conditions: (a) on the global point of view, the entrainment ratio is well predicted with a maximum relative error equal to about 10%, (b) on the local point of view, the shock wave position, the pressure recovery and the wall static pressure values are well predicted. The results, taking into account previous numerical studies, suggest the use of the k-ω SST model to simulate ejector fluid dynamics.

The effect of variations in first- and second-order derivatives on airfoil aerodynamic performance

ABSTRACTThe geometric factors which influence airfoil aerodynamic performance are attributed to variations in local first- and second-order curvature derivatives. Based on a self-developed computational fluid dynamics (CFD) program called UCFD, the influence of local profile variations on airfoil aerodynamic performance in different pressure areas is investigated. The results show that variations in first- and second-order derivatives of the airfoil profiles can cause fluctuations in airfoil aerodynamic performance. The greater the variation in local first- and second-order derivatives, the greater the fluctuation amplitude of the airfoil aerodynamic coefficients. Moreover, at the area near the leading edge and the shock-wave position, the surface pressure is more sensitive to changes in first- and second-order derivatives. These results provide a reference for airfoil aerodynamic shape design.