Reflected Expansion Wave Research Articles

Exploration of shock–droplet interaction based on high-fidelity simulation and improved theoretical model

Shock–droplet interaction in the early stage involves intricate wave structures. Investigating this phenomenon is inherently challenging due to the fine spatial and temporal scales involved. Past research has suggested that the occurrence of cavitation, marked by a negative peak pressure, is linked to the focus of the reflected expansion wave. In this study, a high-fidelity compressible numerical approach is utilized to replicate the initial phase of shock–droplet interactions. The location of the negative peak pressure is meticulously documented and compared with experimental measurement and numerical results. Results indicate a strong alignment between the negative peak pressure positions identified through numerical simulations and the focal points identified in theoretical models for low gas–liquid wave velocity ratios. However, this alignment is notably disrupted when dealing with higher gas–liquid wave velocity ratios. Further enhancements are made to the theoretical model, enabling a more precise depiction of internal wave structures and focus points, particularly under conditions of high gas–liquid wave velocity ratios. The study delves into the various factors influencing internal pressure fluctuations within the liquid droplet, categorizing them into four phases: the shock wave effect, relaxation effect, fluctuation effect, and expansion wave effect. Analysing the pressure decrease portion reveals that while the converging of the reflected expansion wave leads to a substantial pressure drop, it accounts for only a fraction of the total pressure variation. Consequently, any model predicting negative peak pressure positions must comprehensively consider all contributing factors.

Analysis of the dehydration performance in a two-phase variable-section gas wave oscillation tube

The two-phase gas wave oscillation tube (TPGWOT) is subjected to several problems in the application of moisture-containing gas dehydration (e.g., less accurate prediction of the results of phase transition in the tube, and strong interference effect of reverse compression waves in the tube). The predicted phase transition results approach the experimental values by coupling the CPA real gas model and the non-equilibrium phase transition model. The performance of the proposed variable-section TPGWOT is investigated using numerical and experimental methods, and the following results are achieved. The variable-section structure is capable of optimizing the wave system in the tube, as manifested by the ability to strengthen the reflected expansion wave and weaken the reverse compression waves. As a result, the maximum condensation rate of condensate droplets is increased by 2 % to 5 %, and the proportion of evaporation capacity of condensate droplets is reduced by 3 % to 7 %. The variable-section structure is capable of enhancing the performance of the GWOTs, as manifested by the ability to improve the gas temperature drop (ΔT) of nearly 20 % and increase the dehydration rate by 2.6 % to 5 %. This study is no longer limited to optimizing the wave system in the tube by changing the ports at both ends of TPGWOTs, and it provides a favorable reference for other wave rotor application research.

Theoretical and numerical analysis of effects of sudden expansion and contraction on compressible flow phenomena in Hyperloop system

With rapid changes in lifestyle patterns and recent technological advancements, there is an increasing demand for efficient, convenient, and eco-friendly transportation systems. The Hyperloop system, which is a tube–train system, was introduced with the aim of catering to the demand for improved transportation facilities. The primary factors of the Hyperloop system such as the point of departure (pod), standstill, and transfer are directly dependent on the change in the cross-sectional area of the tube such as stations. In this study, the effects of sudden expansion and contraction were analyzed though numerical simulations with respect to the blockage ratio (BR), expansion ratio (ER), and contraction ratios (CR). Furthermore, the propagation Mach number and magnitude of pressure waves were predicted through theoretical consideration. Under sudden expansion and contraction of tube, the first leading shock wave (LSW1), reflected expansion wave (REW), second leading shock wave (LSW2), reflected shock wave (RSW), and third leading shock wave (LSW3) are generated in this system. The propagation Mach number and pressure magnitude of LSW1 increase with an increase in the BR. The Mach number of REW decreases with an increase in the BR. The propagation Mach number of LSW2 increases with the BR and with a decrease in the ER owing to the pressure behind the shock wave. The propagation Mach number of RSW decreases with an increase in the BR and with a decrease in the CR, and that of LSW3 increases with an increase in the BR and with a decrease in the CR. The drag coefficient decreases when REW reaches the pod because the expansion wave decreases the pressure of flow field. Owing to the similar minimum drag coefficient, the difference of drag coefficient increases with an increase in the BR. In this study, the predicted Mach number and pressure magnitude under quasi-one-dimensional assumption are in good agreement with the simulation results. Therefore, this study can aid the design of expanded and contracted zones considering the formation of the shock wave.

Numerical investigation of shock-turbulent mixing layer interaction and shock-associated noise

Direct numerical simulation of shock-turbulent mixing layer interaction (STMLI) is conducted in this paper to study the influence of shock-turbulent interaction (STI) on the turbulence evolution and shock-associated noise. The results show that turbulent kinetic energy and pressure fluctuation around the interaction point of STI are both first increased and then reduced to a smaller value than that in the fully developed region of the turbulent mixing layer, while the Reynolds-stress anisotropy at the upper edge of STMLI is changed under the compression–expansion effect induced by the distorted shock tip and the reflected expansion wave. Additionally, it is found that shock-associated noise would increase the overall sound pressure level (OASPL) and amplify the high-frequency noise at the upstream observers. By applying the shock-leakage theory, the turbulence scale analysis, and the spectrum analysis, two generation mechanisms of shock-associated noise are identified: first, the influence of turbulence on the shock wave results in the shock unsteady movement, which generates a sound wave with cylindrical wave front; second, STI decreases the turbulence scale and increases the pressure fluctuation in the high-frequency band so as to strengthen the small-scale turbulence to radiate out more high-frequency noise. Finally, the shock strength effect on shock-associated noise is explored, and the shock-associated noise reduction is observed when decreasing the shock strength. By converting the OASPL difference to the equivalent acoustic pressure difference, a linear correlation between the shock-associated noise source strength and the shock strength is found.

The Complete Performance Map of Gas Wave Ejector and Analysis on the Variation Laws and Limitation of Performance

Abstract The gas wave ejector (GWE) is an efficient gas wave equipment using pressure waves to realize energy exchange. In this paper, a theoretical analysis of the limitation of application range and the factors affecting the performance of GWE was carried out by numerical simulation. And a complete experimental system including an adjustable GWE was employed to obtain the specific performance values in various working conditions. Such theoretical analysis showed that the device became inapplicable with a relatively high driving pressure ratio, resulting from the generation of supersonic flow at the outlet end of the passages. A relatively high supercharging ratio also limited the equipment application because of the weakening of the reflected expansion waves and the enhancement of the reversed compression wave. Furthermore, the mixing, vortex, viscosity, and other flow losses could also affect the equipment performance. Then, a complete performance map indicating the specific performance values in the application range was obtained by plenty of experiments. The performance map proved that GWE had excellent efficiency and broad applicability especially as the driving pressure ratio was lower than 2.6. The results are significant for practical application and performance improvement of GWE.

Transmission of a detonation across a density interface

The present study investigates the transmission of a detonation wave across a density interface. The problem is first studied theoretically considering an incident Chapman–Jouguet (CJ) detonation wave, neglecting its detailed reaction-zone structure. It is found that, if there is a density decrease at the interface, a transmitted strong detonation wave and a reflected expansion wave would be formed; if there is a density increase, one would obtain a transmitted CJ detonation wave followed by an expansion wave and a reflected shock wave. Numerical simulations are then performed considering that the incident detonation has the Zel’dovich–von Neumann–Doring reaction-zone structure. The transient process that occurs subsequently to the detonation-interface interaction has been captured by the simulations. The effects of the magnitude of density change across the interface and different reaction kinetics (i.e., single-step Arrhenius kinetics vs. two-step induction–reaction kinetics) on the dynamics of the transmission process are explored. After the transient relaxation process, the transmitted wave reaches the final state in the new medium. For the cases with two-step induction–reaction kinetics, the transmitted wave fails to evolve to a steady detonation wave if the magnitude of density increase is greater than a critical value. For the cases wherein the transmitted wave can evolve to a steady detonation, the numerical results for both reaction models give final propagation states that agree with the theoretical solutions.

A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970), pp. 294–417; Menikoff and Plohr, Rev. Mod. Phys. 61(1), 75 1989) are compared to those from perfect gases under nondimensionally matched initial conditions at room temperature and pressure. The study was performed using Caltech’s Adaptive Mesh Refinement, Object-oriented C++ (AMROC) (Deiterding, Adaptive Mesh Refinement: Theory and Applications (2005), Vol. 41, pp. 361–372; Deiterding, “Parallel adaptive simulation of multi-dimensional detonation structures,” Ph.D. thesis (Brandenburgische Technische Universität Cottbus, September 2003)) framework with a low-dissipation, hybrid, center-difference, limiter patch solver (Ward and Pullin, J. Comput. Phys. 229, 2999 (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related by k1=k2+k3. Comparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer’s linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected.

Mechanical Changes in Materials Caused by Explosive Precompression Shock Waves and the Effects on Fragmentation of Exploding Cylinders

Explosive driven rapid fracture in a structural body will be preceded by a compression process, and the compression effects on mechanical properties of the materials are clearly important to understand shock-induced failure such as spall or fragmentation phenomena. In this study, incident shock waves in plate specimens of aluminum A2017-T4 and 304 stainless steel are generated by plane detonation waves in the high explosive PETN initiated using wire-row explosion techniques, and the compressed specimens are successfully recovered without severe damages due to the reflected expansion waves with use of momentum trap method. A hydro code, Autodyn-2D is applied to determine test conditions: thicknesses of explosives, attenuators, specimens and momentum traps and to evaluate experimental results, simulating time-histories of stress waves in the layers of the test assembly. Microhardness distributions in cross-sections, tensile strength, fracture ductility and yield stress are measured for the recovered specimens, using miniature tensile and compression test pieces machined from them. They are compared with those of virgin specimens, showing significant increase of hardness, tensile and yield strength and remarkable reduction of elongation and ductility for shocked specimens. The results are taken into consideration for evaluation of experimental fragmentation energy in cylinder explosion tests.

Scaling Properties and Wave Interactions in Confined Supersonic Turbulent Bluff-Body Wakes

Results are presented from an experimental study that compares the large-scale structure, mean velocities, and scaling properties of confined, supersonic, planar, turbulent, bluff-body wakes at M∞ ≈ 2 and 3 with corresponding results from incompressible wakes. The large-scale structure of incompressible planar turbulent wakes is recovered at downstream locations x where the local relative Mach number Mr(x) has decreased to about 0.4. Interactions between these large-scale structures and reflected expansion waves from the near-field recompression region lead to substantial changes in the scaling properties of the flow. Wave interactions with the flow create local self-induced forcing as the large-scale structures pass through the reflected expansion waves. In the M∞ ≈ 2 wake, a subsonic upstream path exists from the first wave interaction point that allows upstream propagation of the wave-induced forcing, and consequently the measured wake scaling constants match values reported from forced incompressible wakes. In the M∞ ≈ 3 wake, no subsonic upstream path exists from the first interaction point, and as a consequence the measured scaling constants match values reported from unforced incompressible wakes. Downstream of each wave interaction point, the self-induced forcing leads to an increase in the wake growth rate and in the entrainment of free-stream fluid. The wake subsequently detrains this fluid and returns to its original growth rate. This local forcing mechanism and its effects on the wake scaling properties repeat at each downstream location where the reflected expansion waves intersect the wake.

Reflection and transmission of a compression wave at a tunnel portal

Analyses are made of the interaction of the nonlinearly steepened, compression wavefront generated by a high-speed train in a tunnel with the tunnel portal ahead of the train. The ‘micro-pressure’ pulse emitted from the portal can rattle structures in nearby buildings, and the expansion wave reflected back towards the train can cause discomfort to passengers. It is concluded that the usual simplified approximation of one-dimensional propagation within the tunnel provides an adequate representation of interactions of the wave with the portal, and also with ‘windows’ in the tunnel wall near the portal. It is shown how a discrete distribution of windows can be used to produce a reflected expansion wave that varies linearly across the wavefront, and how the thickness of that wavefront can be made many times larger than the thickness of the incident compression wave profile. A detailed analysis of the wave radiated from the portal reveals that cumulative nonlinear effects of propagation over long distances make little or no contribution to the free-space radiation of the micro-pressure wave.

A Study on Expansion Wave Formed by Reflection of Shock Wave at the Open-End of Tube.

When the propagating shock wave reaches at the exit portal of a tube, the impulsive wave discharges to surrounding area and the expansion wave occurs from an open-end of a tube in the condition of subsonic flow behind the shock wave. The problem related to the reflection of propagating shock wave at the open-end has become more important subject associated with pulse combus-tors, pressure exchangers and high-speed railway train/tunnel systems. For the case of shock Mach number Ms less than 1.34, the reflected expansion wave generated at the open-end propagates toward upstream of a tube against the direction of the incident shock wave. For the cases of reflection at an open-end with no-baffled tube, Rudinger suggested the empirical equation concerning the imaginary center of reflected expansion wave. In this paper, the improved empirical equation considering the influence of the diameter of a baffle plate at the open-end was proposed. The experiment study using the simple shock tube and the numerical calculatdon using the TVD method were carried out.

On the tuning pipe of a two-stroke engine for scooter-type motorcycles

Engine performance and simultaneous pressure wave histograms in the cylinder and exhaust port were studied in this experiment. The performance of two-stroke engines for scooter-type motorcycles depended greatly on the length and expansion angle of the tuning pipe. The length of the lead-in pipe dominated the phase of the starting point of reflected expansion waves. The full length determined the timing of reflected expansion waves. The first expansion angle of the exhaust pipe must be limited to a small value and then expanded gradually to give the desired diameter. The effect of the muffler was also discussed. There was an optimal distance between the end of the tuning pipe and the spacer of the muffler to obtain a maximum power output.

Oblique-shock/expansion-fan interaction - Analytical solution

We consider the supersonic flow inside a channel that suddenly turns. For the flow to negociate this sudden turn, a centered expansion wave and an oblique shock wave are generated at the expansive and compressive corners. We study the interaction between an oblique shock and a centered fan, the subsequent interactions of the reflected shock and reflected expansion waves are not considered here

Nucleation and growth rates of homogeneously condensing water vapor in argon from shock tube experiments

A special shock tube process combining a reflected expansion wave with a weak shock wave is analyzed and calibrated. The process is employed to transfer water vapor carried in argon into a known supersaturated state for a short period of time (0.5 ms). During that period steady state homogeneous nucleation takes place followed by condensational growth. Nucleation and growth rates are measured by a 90° Mie-light scattering technique in the temperature range 200–260 K. The results are compared with existing theoretical models.

An Investigation of the Motion of a Bubble near a Free Surface.

An investigation was made of the motion of a cavitation bubble in the vicinity of a free surface experimentally as well as theoretically. A bubble was produced by focusing a ruby laser into water, and subsequent behavior was observed with a high speed camera. The deformable nature of both a bubble and a free surface becomes significant when a bubble behaves relatively close to the surface. Immediately after the bubble rebound a secondary cavitation occurs, at around zero dynamic pressure region, which was developed in water between a rising free surface and a re-expanding bubble due to lower pressure caused by the interaction of reflected expansion waves from the surface. Some aspects of the bubble motion were compared with image theory with good agreement.

Nucleation and growth rates of homogeneously condensing water vapor in argon from shock tube experiments

A special shock tube process combining a reflected expansion wave with a weak shock wave is analyzed and calibrated. The process is employed to transfer water vapor carried in argon into a known supersaturated state for a short period of time (0.5 ms). During that period steady state homogeneous nucleation takes place followed by condensational growth. Nucleation and growth rates are measured by a 90° Mie-light scattering technique in the temperature range 200–260 K. The results are compared with existing theoretical models.

The formation of an aqueous fog in a shock tube

The extent to which a shock tube could be used for laboratory experiments on the fluid mechanics of two-phase mixtures of droplets in an inert carrier gas was determined. A shock tube high pressure section was charged with moist carrier gas and the flow produced a stationary cloud of water droplets behind the reflected expansion wave. The droplets were formed by homogeneous nucleation and preliminary experiments showed that their diameters were of the same order as the wavelength of light. Subsequently, two-colour light transmission measurements were made and the droplet diameter was determined by using the Mie scattering theory. Attempts to measure the size distribution indicated that the droplets had a narrow range of sizes. Depending on the initial conditions, diameters were in the range 0.3 mu m to 0.9 mu m. The fog persisted for several milliseconds before the arrival of the reflected shock wave from the opposite end of the shock tube. Preliminary observations indicate that the droplets cause considerable dispersion of the shock.

Paper 14: On the Reflection of Shock Waves from Deflector Plates

The paper first explains the importance of the reflection of shock waves in the design of certain chemical plant. The theory of the reflection of shock waves is also discussed in the first part of the paper. It is shown that when a shock wave travelling along a pipe containing stationary gas reaches the outlet end of the pipe there may be ( a) a reflected expansion wave, ( b) a reflected shock wave, ( c) a reflected sound wave, ( d) no reflected wave at all, ( e) a standing shock wave situated at the end of the pipe, depending upon the strength of the incident shock wave and the amount of blockage present at the outlet end of the pipe. The conditions for each kind of reflection are determined, and in the case of the reflected shock wave region the strengths and speeds of the reflected shock waves are established throughout the region and the results are presented graphically. In the second part of the paper the results are given of experiments carried out on a shock tube fitted with various kinds of deflector plates. The experiments were performed to study the reflection of shock waves from the deflector plates by measuring pressure/time indicator diagrams near the outlet end of the pipe. The indicator diagrams revealed the approximate pressure amplitudes of the incident and reflected shock waves and also the wave travel times for the shock waves. This information was used in conjunction with the charts given in the first part of the paper to establish the deflector geometry and spacing needed in order to avoid the occurrence of a reflected shock wave.

On the Reflection of Shock Waves from an Open End of a Duct

The readjustment of the mean exit pressure to its steady-flow equilibrium level, following the arrival of a shock wave at an open end of a duct, has been investigated. For a cylindrical duct in which the gas is initially at rest, a solution based on acoustic theory was obtained in the form of a Fourier integral. The nature of this solution was established as a series of damped harmonic oscillations superposed on an exponential pressure decay. The actual pressure decay curve was obtained by numerical integrations. The same problem was also attacked experimentally using a shock tube of 3.23 inches i.d. From pressure records taken some distance from the open end, the ``effective'' exit pressure was derived. It was found that the exit pressure deviates appreciably from its steady-flow equilibrium value during a time in which a sound wave could travel about three duct diameters. Satisfactory agreement between theory and experiment was observed for shock pressure ratios up to about 1.9 (in air) although, near this limit, significant deviations owing to wall friction were observed toward the end of the pressure decay region. For still stronger shocks, the influence of the decay time on the phenomena inside the duct becomes unimportant while friction effects dominate. The possible significance of the lag in the establishment of steady-flow boundary conditions in practical applications is discussed, in particular, for cases where the acceleration of the gas by the reflected expansion wave may be of importance.