Laminar Shock Research Articles

Flow Response of a Laminar Shock–Boundary Layer Interaction to Prescribed Surface Motions

The response of an impinging laminar shock–boundary layer interaction (SBLI) to prescribed surface motions is investigated numerically at M∞=2, Rea=120,000, and a shock-associated pressure ratio of 1.5. Parametric sweeps over classical standing and traveling mode shapes are considered at low-, moderate-, and high-frequency conditions for fluid–structure interaction. The specific values are chosen based on compliant panel deformations and frequencies reported in the literature. At low surface oscillation frequencies, the SBLI responds to the deformations in a quasi-steady fashion, with standing wave forcing displaying both breathing and sloshing of the separated region depending on structural mode shape. As the oscillation frequency is increased, the flow transitions to an unsteady response with pronounced separation bubble undulations in time. Higher-order modes and frequencies lead to the largest reductions in the time-mean separation bubble size, more so with traveling surface waves. Modal decompositions show that pressure fluctuations, which arise due to dynamic interaction with the surface, persist downstream and increase in amplitude with the surface oscillation frequency.

Boundary layer control for low Reynolds number fan rig testing

Ultra-high bypass ratio turbofans offer significant reductions in fuel and pollution due to their higher propulsive efficiency. Short intakes might lead to a stronger fan-intake interaction, which creates uncertainty in stability at off-design conditions. Due to the prohibitive cost of full-scale experimental testing, subscale testing in wind tunnels is used to understand this behaviour. The low Reynolds number of subscale models results in unrepresentative laminar shock-boundary layer interactions. The boundary layer state thus needs to be conditioned to better represent full-scale transonic fans. This paper proposes the use of an inexpensive and robust flow control method for the suction side of a fan blade. Design guidelines are given for the location and height of the discrete roughness elements used to control the boundary layer state. This paper also presents a rapid experimental validation methodology to ensure and de-risk the application of the boundary layer trip to 3D rig blades. The experimental methodology is applied to a generic aerofoil representative of a fan tip section. The experimental method proves that it is possible to reproduce boundary layers and pressure distributions of a full-scale fan blade on a 1/10 subscale model. The results obtained confirm that the boundary layer trip method successfully promotes transition at the location representative of full-scale blades, avoiding unrepresentative laminar shock wave boundary layer interactions. This highlights the importance of conditioning boundary layers in low Reynolds number fan rig testing.

Boundary-Layer Instabilities over a Cone–Cylinder–Flare Model at Mach 6

Computations are performed to investigate the convective and global boundary-layer instabilities over a sharp cone–cylinder–flare model at zero-degree angle of attack. The model geometry and the flow conditions are selected to match the experiments conducted in the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University. The geometry consists of a nominally sharp 5 deg half-angle cone, followed by a cylindrical segment, and then a 10 deg flare. Additionally, flare half angles equal to 8 and 12 deg and nosetip radii equal to 0.1, 1, and 5 mm are studied. An axisymmetric separation bubble is generated as a result of the laminar shock–boundary-layer interaction in the cylinder–flare region. The comparison of the laminar flow solution and the schlieren images shows a remarkable agreement between the respective locations of both the boundary-layer edge and the reattachment shock. The linear amplification of first and second Mack mode instabilities that begin to amplify in the cone region are computed with a combination of the parabolized stability equations and the harmonic linearized Navier–Stokes equations. The predicted frequency spectra of the surface pressure fluctuations associated with both planar and oblique instability waves capture the distinct lobes within the disturbance amplification spectra measured with PCB® and Kulite sensors. To our knowledge, this represents the first successful comparison between convective instability analysis and measured surface pressure fluctuations for a hypersonic configuration with a separation bubble. Finally, the global instability analysis shows that the laminar flow becomes supercritical for flare half angles larger than 8 deg.

Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$ . This damping rate is found to scale as $1/L$ , leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$ , a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

Probabilities of ion scattering at the shock front

Collisionless shocks efficiently convert the energy of the directed ion flow into their thermal energy. Ion distributions change drastically at the magnetized shock crossing. Even in the absence of collisions, ion dynamics within the shock front is non-integrable and gyrophase dependent. The downstream distributions just behind the shock are not gyrotropic but become so quickly due to the kinematic gyrophase mixing even in laminar shocks. During the gyrotropization all information about gyrophases is lost. Here we develop a mapping of upstream and downstream gyrotropic distributions in terms of scattering probabilities at the shock front. An analytical expression for the probability is derived for directly transmitted ions in the narrow shock approximation. The dependence of the probability on the magnetic compression and the cross-shock potential is demonstrated.

ARTEMIS Observations of Plasma Waves in Laminar and Perturbed Interplanetary Shocks

Abstract The “Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun” mission provides a unique opportunity to study the structure of interplanetary shocks and the associated generation of plasma waves with frequencies between ∼50 and 8000 Hz due to its long duration electric and magnetic field burst waveform captures. We compare wave properties and occurrence rates at 11 quasi-perpendicular interplanetary shocks with burst data within 10 minutes (∼3200 proton gyroradii upstream, ∼1900 downstream) of the shock ramp. A perturbed shock is defined as possessing a large amplitude whistler precursor in the quasi-static magnetic field with an amplitude greater than 1/3 the difference between the upstream and downstream average magnetic field magnitudes; laminar shocks lack these large precursors and have a smooth, step function-like transition. In addition to wave modes previously observed, including ion acoustic, whistler, and electrostatic solitary waves, waves in the ion acoustic frequency range that show rapid temporal frequency change are common. Three shocks had burst captures in the ramp; of these, the two laminar shocks contained a wide range of large amplitude wave modes in the ramp whereas the one perturbed shock contained no such waves. Thus, energy dissipation through wave–particle interactions is more prominent in these two laminar shocks than in the perturbed shock. Based on observations from all 11 shocks, the wave occurrence rates for laminar shocks are higher in the transition region, especially the ramp, than downstream. In contrast, perturbed shocks have approximately 2–3 times the wave occurrence rate downstream than laminar shocks.

On the Importance of Transition Control at Transonic Compressor Blades

AbstractThe flow through a transonic compressor cascade is characterized by high unsteadiness and a high loss level. This results from the shock waves in the blade cascade and their interaction with the blade suction side boundary layer. In the case of a laminar shock wave boundary layer interaction, the loss level is higher due to the occurrence of a laminar separation bubble below the shock wave compared to the shock wave interaction with a turbulent boundary layer. In addition, the oscillation of the shock position in both cases influences the working range concerning the point of stall onset as well as leading to an unsteady interaction with the blade called buffeting. The reduction of losses and of unsteadiness in the shock wave oscillation, connected to a decrease of the blade buffeting effect, is the aim of the current investigation. Therefore, experimental investigations using a roughness patch as well as air jet vortex generators in order to control the transition in a transonic compressor cascade have been conducted at the transonic cascade wind tunnel of the German Aerospace Center (DLR) at Cologne. At an inflow Mach number of 1.21, a loss reduction for both transition control cases is achieved. In spite of a nearly uninfluenced fluctuation range of the passage shock wave compared to the reference cascade, the oscillation spectra of the transition control cases show a reduction of the shock movement amplitude at a frequency below 500 Hz and above 1 kHz. In the closing section of the paper, a detailed discussion on the reasons for the resulting flow behavior based on particle image velocimetry and high-speed shadowgraphy data is given. The resulting conclusion of the study is that the consideration of transition control at transonic compressor blades is very important in order to reduce losses and flow unsteadiness that directly influences blade buffeting and the numerical prediction quality of the stall onset.

Transition Effect on the Flow Dynamics in a Compressor Blade Passage

An experimental investigation was carried out to study the effect of the boundary layer transition on the flow dynamics in the blade passage of a compressor cascade. A model of a turbine compressor passage was designed and assembled in a transonic wind tunnel for this purpose. Two different flow control methods were used in the experiment to induce the transition upstream of the shock wave, one concerning the microstep application and the other using distributed roughness strips. Two locations of spanwise microsteps for the transition trigger were chosen, one at the leading edge and the other closer to the shock wave position. The distributed roughness in the form of standard sandpaper strips with different heights was applied in three various locations on the blade upstream of the shock. The main objective of investigations is to present the influence of the laminar and turbulent shock wave‐boundary layer interaction on the flow dynamics in a compressor fan passage, and the specific objective is to show how the parameters of particular transition control methods affect the flow dynamics in the investigated channel. The major challenge for this research was to minimize the disturbance caused by the microstep or roughness to the laminar boundary layer, while still ensuring a successful transition. Very interesting results were obtained in the flow control application for the boundary layer transition control, demonstrating a positive effect on the flow unsteadiness in changing the nature of the interaction.

Galactic Cosmic-ray Anisotropies: Electrons Observed by Voyager 1 in the Very Local Interstellar Medium

Abstract Now over seven years into its journey beyond the heliopause, Voyager 1 continues to return unprecedented observations of energetic particles, magnetic fields, and plasma emissions from the very local interstellar medium. Shortly after its heliopause crossing, Voyager 1 discovered an unusual time-varying galactic cosmic-ray anisotropy, characterized by smoothly changing intensity reductions in particles propagating nearly perpendicular to the magnetic field; outside of this isolated region, cosmic rays appear mostly unvarying, without a significant radial gradient. These small (∼15%) but lasting (∼100 to ∼630 days) anisotropic events are still not fully understood. Nevertheless, they serve as clear markers, together with shorter-lived cosmic-ray intensity enhancements, electron plasma oscillations, and weak laminar shocks, that even beyond the heliopause, the Sun’s variable output significantly influences its surroundings. So far, these unusual energetic particle occurrences have mainly been studied using integrated proton intensities of ∼20 MeV and higher. Using data from the Voyager 1 Cosmic Ray Subsystem, we extend the analysis to electrons, as well as lower energy protons, and discover the surprising new result that the ∼3 to ∼105 MeV electrons remain mostly isotropic and unchanging, in sharp contrast to their proton counterparts. We search for clues to explain this underlying species dependence and rule out potential causes related to instrumental effects, velocity and energy, trapping and energy loss, drifts, and turbulence-induced scattering. We also explore some plausible mechanisms and open the door for more detailed follow-up theories and simulations.

On the use of thermally perfect gas model for heating prediction of laminar and turbulent SWBLI

The model of thermally perfect gas has been investigated in the heating prediction of laminar and turbulent shock wave boundary layer interaction (SWBLI) flows. The method of the polynomial curve fit coupling to thermodynamics equation is examined for higher temperature range. The characteristic weighted essentially non-oscillatory (WENO) scheme is utilized to capture the complex flow details and meantime stabilize the strong shocks in the SWBLI flows. Both the laminar and turbulent, steady and unsteady test cases are carried out to assess the performance of the designed method. Numerical results have substantiated the thermally perfect gas model as an effective model in the challenging SWBLI heating predictions in comparison with the existing model of calorically perfect gas.

Reattachment streaks in hypersonic compression ramp flow: an input–output analysis

We employ global input–output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock–boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat-flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favourably with observations from two different hypersonic compression ramp experiments. Furthermore, our analysis of inviscid transport equations demonstrates that base-flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Finally, the appearance of the temperature streaks near reattachment is triggered by the growth of streamwise velocity and streamwise vorticity perturbations as well as by the amplification of upstream temperature perturbations by the reattachment shock.

Unified gas-kinetic wave-particle methods I: Continuum and rarefied gas flow

The unified gas-kinetic scheme (UGKS) provides a framework for simulating multiscale transport with the updates of both gas distribution function and macroscopic flow variables on the cell size and time step scales. The multiscale dynamics in UGKS is achieved through the coupled particle transport and collision in the particle evolution process within a time step. In this paper, under the UGKS framework, we propose an efficient multiscale unified gas-kinetic wave-particle (UGKWP) method. The gas dynamics in UGKWP method is described by the individual particle movement coupled with the evolution of the probability density function (PDF). During a time step, the trajectories of simulation particles are tracked until collision happens, and the post-collision particles are evolved collectively through the evolution of the corresponding distribution function. The evolution of simulation particles and distribution function is guided by the evolution of macroscopic variables, and guarantees the conservation of the scheme in the final wave-particle formulation. A new concept of multiscale multi-efficiency preserving (MMP) method is introduced. Multiscale preserving means UGKWP method preserves the flow regime from collisionless regime to hydrodynamic regime without requiring the cell size and time step to be less than the mean free path and collision time. Multi-efficiency preserving means the computational cost of the scheme including the computational time and memory cost is on the same level as the most efficient method in the corresponding regime, such as the particle methods in the rarefied regime and hydrodynamic solvers in continuum regime. The UGKWP method is shown to satisfy the MMP requirement. The UGKWP method is specially efficient for hypersonic flow simulation in all regimes in comparison with the discrete ordinate methods, and presents a much lower stochastic noise in the continuum flow regime in comparison with the particle-based Monte Carlo methods. Numerical tests for flows over a wide range of Mach and Knudsen numbers are presented. The examples include the hypersonic flow passing a circular cylinder at Mach numbers 20 and 30 and Knudsen numbers 1 and 10−4, low speed lid-driven cavity flow, laminar boundary layer, shock structure, and shock tube problems. These results validate the accuracy, efficiency, and multiscale and multi-efficiency property of UGKWP method.

Kinematic Collisionless Relaxation and Time Dependence of Supercritical Shocks with Alpha Particles

Abstract Upon crossing, the shock front ions begin to strongly gyrate due to the effect of the macroscopic magnetic and electric field. The strongly nongyrotropic downstream distributions gradually gyrotropize due to the gyrophase mixing. Kinematic collisionless relaxation has been successful in explaining the downstream magnetic oscillations in time-independent planar laminar shocks. Time dependence of supercritical shocks becomes more pronounced with the increase of the Mach number. While downstream gyrating distributions are still formed due to macroscopic fields, pressure balance can no longer be maintained throughout, causing time dependence. The presence of alpha particles enhances the destabilization of the shock.

Modal analysis with proper orthogonal decomposition of hypersonic separated flows over a double wedge

A study combining direct simulation Monte Carlo simulations with window proper orthogonal decomposition investigates the temporal characteristics of unsteady, laminar shock boundary-layer interactions for different gas mixtures for an Edney type-IV flow.

Expansion of a radially symmetric blast shell into a uniformly magnetized plasma

The expansion of a thermal pressure-driven radial blast shell into a dilute ambient plasma is examined with two-dimensional PIC simulations. The purpose is to determine if laminar shocks form in a collisionless plasma which resemble their magnetohydrodynamic counterparts. The ambient plasma is composed of electrons with the temperature of 2 keV and cool fully ionized nitrogen ions. It is permeated by a spatially uniform magnetic field. A forward shock forms between the shocked ambient medium and the pristine ambient medium, which changes from an ion acoustic one through a slow magnetosonic one to a fast magnetosonic shock with increasing shock propagation angles relative to the magnetic field. The slow magnetosonic shock that propagates obliquely to the magnetic field changes into a tangential discontinuity for a perpendicular propagation direction, which is in line with the magnetohydrodynamic model. The expulsion of the magnetic field by the expanding blast shell triggers an electron-cyclotron drift instability.

A parametric study of laminar and transitional oblique shock wave reflections

High-resolution particle image velocimetry measurements were performed on laminar and transitional oblique shock wave reflections for a range of Mach numbers ($M=1.6{-}2.3$), Reynolds numbers ($Re_{x_{sh}}=1.4\times 10^{6}{-}3.5\times 10^{6}$) and flow deflection angles ($\unicode[STIX]{x1D703}=1^{\circ }{-}5^{\circ }$ or $p_{3}/p_{1}=1.11{-}1.64$). The laminar interactions revealed a long, flat and triangular shaped separation bubble. For relatively strong interactions ($p_{3}/p_{1}>1.2$), the bubble grows linearly in the upstream direction with increasing shock strength. Under these conditions, the boundary layer keeps an on average laminar velocity profile up to the shock impingement location, followed by a quick transition and subsequent reattachment of the boundary layer. For weaker interactions ($p_{3}/p_{1}<1.2$), the boundary layer is able to remain laminar further downstream of the bubble, which consequently results in a later reattachment of the boundary layer. The pressure distribution at the interaction onset for all laminar cases shows excellent agreement with the free-interaction theory, therefore supporting its validity even for incipiently separated laminar oblique shock wave reflections.

Solving the Two Objective Evolutionary Shape Optimization of a Natural Laminar Airfoil and Shock Control Bump with Game Strategies

In order to improve the performances of a civil aircraft at transonic regimes, it is critical to develop new computational optimization methods reducing friction drag. Natural laminar flow (NLF) airfoil/wing design remain efficient methods to reduce the turbulence skin friction. However, the existence of wide range of favorable pressure gradient on a laminar flow airfoil/wing surface leads to strong shock waves occurring at the neighborhood of the trailing edge of the airfoil/wing. Consequently, the reduction of the friction drag due to the extension of the laminar flow surface of the airfoil is compensated with an increase of the shock wave induced drag. In this paper, an evolutionary algorithm (EAs) hybridized with different games (cooperative Pareto game, competitive Nash game and hierarchical Stackelberg game) for comparison is implemented to optimize the airfoil shape with a larger laminar flow range and a weaker shock wave drag simultaneously due to a shock control bump (SCB) active device. Numerical experiments demonstrate that each game coupled to the EAs optimizer can easily capture either a Pareto front, a Nash equilibrium or a Stackelberg equilibrium of this two-objective shape optimization problem. From the analysis/synthesis of 2D results it is concluded that a variety of laminar flow airfoils with greener aerodynamic performances can be significantly improved due to optimal SCB shape and position when compared to the baseline airfoil geometry. This methodology illustrate the potentiality of such an approach to solve the challenging shape optimization of the NLF wings in industrial design environments.

HOW BRIGHT ARE THE GAPS IN CIRCUMBINARY DISK SYSTEMS?

ABSTRACT When a circumbinary disk surrounds a binary whose secondary’s mass is at least the primary’s mass, a nearly empty cavity with radius a few times the binary separation is carved out of the disk. Narrow streams of material pass from the inner edge of the circumbinary disk into the domain of the binary itself, where they eventually join onto the small disks orbiting the members of the binary. Using data from three-dimensional magnetohydrodynamics simulations of this process, we determine the luminosity of these streams; it is mostly due to weak laminar shocks, and is in general only a few percent of the luminosity of adjacent regions of either the circumbinary disk or the “mini-disks.” This luminosity therefore hardly affects the deficit in the thermal continuum predicted on the basis of a perfectly dark gap region.

Experimental and modeling study of styrene oxidation in spherical reactor and shock tube

The oxidation of styrene, one of the main stable intermediates from the oxidation of large alkylated aromatic hydrocarbons, has been investigated in the present work both experimentally and numerically. Experiments were performed using two complementary techniques, spherical bomb for laminar flame speed studies and shock tube for ignition delay time measurements. In particular, the laminar flame speeds of styrene/air mixtures were measured at three different initial temperatures (342 K, 373 K, and 405 K), over a wide range of equivalence ratios (0.75–1.45), for an initial pressure of 100 kPa. In addition, the autoignition of styrene/O2 mixtures in argon bath gas (ϕ = 0.5, 1.0, and 1.5) was investigated over a wide range of temperatures (1390–1990 K), at highly diluted conditions (94.3%–99% argon), and for pressures between 110 and 200 kPa. A detailed chemical kinetic model, based on the toluene chemistry by Metcalfe et al. (2011), was developed and validated against the newly obtained experimental results and the flow reactor data available in the literature (Litzinger et al., 1986). Sensitivity and rate of production analyses were performed and showed that, at the conditions studied herein for the flame speed investigation, the main fuel consumption pathways include the reaction of the fuel with H atoms to form phenyl radical and ethylene or benzene and vinyl radical, with O to form benzyl radical + HCO, and the H-abstraction reactions on both the vinyl moiety and the ring. On the other hand, the analyses performed at the high-temperature, highly-diluted conditions encountered in the shock tube study highlighted the importance of the fuel thermal decomposition steps for the simulation of the ignition delay time measurements. The model was also tested against the low-pressure flame and jet stirred reactor data by Yuan et al. (2015). The results highlight the need for future modifications in the benzene chemistry by Metcalfe et al. and inclusion of pressure dependent rate parameters in order to improve the prediction capabilities of the model.

Downstream plasma parameters in laminar shocks from ion kinetics

Ion dynamics in oblique shocks is governed by the macroscopic electric and magnetic fields of the shock front. In laminar shocks, these fields are time-independent and depend only on the coordinate along the shock normal. The shock ramp is narrow and the ion motion across the shock is manifestly non-adiabatic. The ion distribution just behind the ramp is significantly non-gyrotropic. Gyrotropy is achieved well behind the ramp mainly due to the gyrophase mixing. The asymptotic values of the ion density and temperature are determined by the eventual collisionless relaxation of the gyrating ion distribution. Given a distribution at the downstream edge of the ramp, the moments of the distribution after gyrophase mixing are derived using proper spatial averaging. The obtained expressions can be used for independent determination of the downstream plasma state and implementation in Rankine-Hugoniot relations.