Fundamentals of rotating detonations

A rotating detonation propagating at nearly Chapman–Jouguet velocity is numerically stabilized on a two-dimensional simple chemistry flow model. Under purely axial injection of a combustible mixture from the head end of a toroidal section of coaxial cylinders, the rotating detonation is proven to give no average angular momentum at any cross section, giving an axial flow. The detonation wavelet connected with an oblique shock wave ensuing to the downstream has a feature of unconfined detonation, causing a deficit in its propagation velocity. Due to Kelvin–Helmholtz instability existing on the interface of an injected combustible, unburnt gas pockets are formed to enter the junction between the detonation and oblique shock waves, generating strong explosions propagating to both directions. Calculated specific impulse is as high as 4,700 s.      

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China     

Parametric instability of cylindrical thin shell with periodic rotating speeds

Parametric instability of a cylindrical thin shell with periodically time-varying rotating speeds is studied in the paper. Energy formulation based upon Love's thin shell theory and the assumed mode method is utilized to obtain the governing equations of a rotating cylindrical shell under simply supported condition. Considering the time-varying rotating speeds, the second order differential equations of the system have time-periodic gyroscopic and stiffness coefficients. The multiple scales method is utilized to obtain the boundaries of both primary and combination instabilities analytically. The primary instability occurs when the excitation frequency is near twice of the natural frequency. The excitation frequency close to the sum of two natural frequencies might lead to the occurrence of combination instability. Numerical simulations are conducted to verify the analytical results. It is shown that the primary instability regions for each mode always appear in the periodically rotating cylindrical shell. Their widths increase continually with excitation amplitude of the time-periodic rotating speed. For certain modes, the combination instability region might not exist. The conditions for its existence are obtained analytically and verified by numerical simulations. Increasing the constant rotating speed would greatly enhance the instability regions. Moreover, it might also cause the appearance of combination instability region.     

Recognition of coherent structures in the boundary layer of a low-pressure-turbine blade for different free-stream turbulence intensity levels

Particle Image Velocimetry (PIV) has been adopted to analyze the instantaneous flow field developing on a high-lift turbine blade profile operating under low and elevated free-stream turbulence conditions (FSTI). Results reported in the paper allow us to analyze the dynamics leading to transition and separation of the suction side boundary layer, looking to generation, propagation and breakdown of coherent structures observed in the two different FSTI cases. To this end, measurements have been performed in two orthogonal planes. Results obtained in the blade-to-blade plane allow the detailed characterization of the propagation of Kelvin–Helmholtz (KH) rolls generating, at low FSTI condition, as a consequence of a non-reattaching separation. Otherwise, data in the wall-parallel plane allow recognizing the presence of three-dimensional disuniformities induced at high FSTI by low and high speed streaks (Klebanoff mode). The sinuous breakdown of boundary layer streaks generates other complex three-dimensional coherent structures such as hairpin or cane-like vortices that induce transition. Proper Orthogonal Decomposition (POD) has been adopted to in depth characterize these structures, thus further explaining the mechanisms through which the free-stream turbulence intensity modify the transition/separation processes of the suction side boundary layer of an highly loaded low pressure turbine blade.     

A design of a two-dimensional,supersonic KH experiment on OMEGA-EP

An experiment meant to investigate the evolution of single mode Kelvin–Helmholtz (KH) instability in the supersonic regime is presented and theoretically analyzed. This experiment is intended to provide a direct measurement of the two-dimensional vortex evolution so that the high-Mach-number effects can be measured. The proposed design takes advantage of the ability of OMEGA-EP to drive experiments for up to 30 ns to produce steady conditions for KH that endure long enough to observe substantial growth. KH growth for the proposed design has been analyzed using two-dimensional numerical simulations. The results were compared to synthetic temporal KH numerical simulations using non-dimensional scaling in the low and high Mach number regime. The comparisons show that the growth in the high Mach number regime is expected to be suppressed by up to a factor of two. The effects of two-dimensional rarefactions from the lateral boundaries of the experimental system were also investigated. It was found that they introduce no major uncertainties or hazards to the experiment. We produced simulated radiographs, which show that the proposed experimental system will enable observation of the KH structures. An experiment of this kind has not yet been performed, and therefore would serve to validate numerical results and analytical models presented here and in the literature.     

The instability of water-mud interface in viscous two-layer flow with large viscosity contrast

The temporal instability of parallel viscous two-phase mixing layers is extended to current-fluid mud by considering a composite error function velocity profile. The influence of viscosity ratio, Reynolds number, and Froude number on the instability of the system are discussed and a new phenomenon never discussed is investigated based on our numerical results. It is shown that viscosity can enlarge the unstable wave number range, cause new instability modes, and certainly reduce the growth rate of Kelvin—Helmholtz (K—H) instability.     

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads

Parametric instability of a rotating truncated conical shell subjected to periodic axial loads is studied in the paper. Through deriving accurate expressions of inertial force and initial hoop tension, a rotating conical shell model is presented based upon the Love's thin shell theory. Considering the periodic axial loads, equations of motion of the system with periodic stiffness coefficients are obtained utilizing the generalized differential quadrature (GDQ) method. Hill's method is introduced for parametric instability analysis. Primary instability regions for various natural modes are computed. Effects of rotational speed, constant axial load, cone angle and other geometrical parameters on the location and width of various instability regions are examined.     

Analysis of dynamic instability of interfacial slip waves based on the surface impedance tensor

A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves. The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value, and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor. Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle. As an example, the steady frictional sliding of an elastic half-space in contact with a rigid flat surface was considered in details. A quartic complex characteristic equation was derived and its solution behavior in the unit circle was discussed. An explicit expression for the instability condition of the interfacial slip waves was presented.     

不同当量比下喷管对旋转爆震特性的影响研究

为研究不同当量比下喷管构型对旋转爆震特性的影响,以煤油预燃裂解气为燃料,氧气体积分数为30%的富氧空气为氧化剂,开展了无喷管、收敛喷管、扩张喷管和收敛扩张喷管等工况下旋转爆震特性实验研究。实验发现,当量比为0.73～1.30时旋转爆震可稳定工作。随着当量比和喷管构型的变化,爆震波出现了单波、不稳定的对撞双波和稳定的对撞双波等3种传播模态。喷管构型对模态转换和旋转爆震波速有重要影响,收敛和收敛扩张喷管会促使新波头的产生,导致爆震波主要以双波对撞模态传播;而扩张喷管工况下,爆震波主要以单波模态传播。收敛喷管和收敛扩张喷管会使得波速最大值偏离化学恰当比,收敛扩张喷管可以提升爆震波速。

     

Experimental study on the effect of pulsating inflow to an enclosure for improved mixing

Optimal control of inlet jet flows is of broad interest for enhanced mixing in ventilated rooms. The general approach in mechanical ventilation is forced convection by means of a constant flow rate supply. However, this type of ventilation may cause several problems such as draught and appearance of stagnation zones, which reduces the ventilation efficiency. A potential way to improve the ventilation quality is to apply a pulsating inflow, which has been hypothesised to reduce the stagnation zones due to enhanced mixing. The present study aims at testing this hypothesis, experimentally, in a small-scale two-dimensional water model using Particle Image Velocimetry with an in-house vortex detection program. We are able to show that for an increase in pulsation frequency or alternatively in the flow rate the stagnation zones are reduced in size and the distribution of vortices becomes more homogeneous over the considered domain. The number of vortices (all scales) increases by a factor of four and the swirl-strength by about 50% simply by turning on the inflow pulsation. Furthermore, the vortices are well balanced in terms of their rotational direction, which is validated by the symmetric Probability Density Functions of vortex circulation (Γ) around Γ = 0. There are two dominating vortex length scales in the flow, namely 0.6 and 0.8 inlet diameters and the spectrum of vortex diameters become broader by turning on the inflow pulsation. We conclude that the positive effect for enhanced mixing by increasing the flow rate can equally be accomplished by applying a pulsating inflow.     

Frontal collision of internal solitary waves of first mode

The dynamics and energetics of a frontal collision of internal solitary waves (ISW) of first mode in a fluid with two homogeneous layers separated by a thin interfacial layer are studied numerically within the framework of the Navier–Stokes equations for stratified fluid. It was shown that the head-on collision of internal solitary waves of small and moderate amplitude results in a small phase shift and in the generation of dispersive wave train travelling behind the transmitted solitary wave. The phase shift grows as amplitudes of the interacting waves increase. The maximum run-up amplitude during the wave collision reaches a value larger than the sum of the amplitudes of the incident solitary waves. The excess of the maximum run-up amplitude over the sum of the amplitudes of the colliding waves grows with the increasing amplitude of interacting waves of small and moderate amplitudes whereas it decreases for colliding waves of large amplitude. Unlike the waves of small and moderate amplitudes collision of ISWs of large amplitude was accompanied by shear instability and the formation of Kelvin–Helmholtz (KH) vortices in the interface layer, however, subsequently waves again become stable. The loss of energy due to the KH instability does not exceed 5%–6%. An interaction of large amplitude ISW with even small amplitude ISW can trigger instability of larger wave and development of KH billows in larger wave. When smaller wave amplitude increases the wave interaction was accompanied by KH instability of both waves.     

Numerical study on bifurcations in the wake of a circular disk

Using Large-eddy simulation (LES), the dynamics in the wake of a circular disk with an aspect ratio of d/w = 5 is numerically studied. The circular disk is normal to the main flow, and Reynolds number ranges from 115 to 300. The first bifurcation is confirmed for Re = 120, leading to the steady state mode with a reflectional symmetry and a double-thread wake extending to the downstream. The Hopf bifurcation is found for Re = 152, and the planar symmetry is lost, which is different from that observed in the sphere wake; it is called the “reflectional-symmetry-breaking (RSB)” mode and the hairpin vortices in this mode are always shedding in a fixed orientation. The third bifurcation is captured for Re = 166, which is named the “standing wave (SW)” mode; the planar symmetry lost in RSB mode is recovered and the hairpin vortices are shedding in the oppositely sided orientations, unlike the ones observed in the sphere wake. The fourth bifurcation, referred to as “zigzag (ZZ)” mode, is observed for Re = 265 and the planar symmetry is lost again; the hairpin vortices are shedding in an irregular orientation and propagating in a zigzagged way; and a few small-scale structures begin to appear. Three different vortex shedding regimes are found in RSB, SW and ZZ modes, respectively. Results show that the recirculation region plays a significant role in the mode transitions, and the stagnation point of recirculation zone is conjectured to be the initial region causing the wake instability.     

The problem of parametric integration to the slip line field in the compression of thick workpiece

An integration depending on a parameter to the compression of a thick workpiece has been obtained.For the conventional prevailing numerical formulaa definite functional relationship betweenφand y is found.Therefore a parametric integration can be used to get an analytical solution.Take the slip line field for1/h=0.121 as an example,the analytical solution is basically the same as the prevailing numerical one.It is justified theoretically that for the slip line field a parametric integration is perfectly possible for a satisfactory analytical solution.     

Trailing-edge dynamics of a morphing NACA0012 aileron at high Reynolds number by high-speed PIV

Particle image velocimetry (piv) measurements are made at the trailing edge of a piezoelectric actuated aileron in order to investigate the physical effect on the flow via high-frequency low-amplitude actuation at high Reynolds numbers. The measurements at different actuation frequencies show the modification of the primary frequency components of the flow with the actuation frequency. A statistical analysis reveals the reduction of the Reynolds stress components which increases with the actuation frequency. Proper orthogonal decomposition (pod) analysis shows the modification of the spatial modes illustrating the vortex breakdown in the shear-layer and the reduction of the temporal mode spectral energy depending on the actuation. It has been shown that a specific low amplitude actuation frequency produces a significant reduction of the predominant shear-layer frequency.     

Effect of ion‐slip current on the thermal instability of mixed connection in a boundary layer flow

Effect of ion‐slip current on the thermal instability in a boundary layer is studied. The criterion on the position marking the onset of longitudinal vortices is defined in the present paper. The results show that the onset position characterized by the Grashof number depends on the Prandtl number, the Reynolds number, the wave number, the Hall parameter, the ion‐slip parameter, and the Hartmann number. The flow becomes more stable as the magnetic field increases. However, the destabilizing effects are found on the flow when the Hall and ion‐slip currents are presented. The results of the present numerical prediction show reasonable agreement with the experimental data in the case of zero Hartmann number, ion‐slip parameter, and Hall parameter in the open literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical simulations of compressible flows using multi-fluid models

Numerical simulations of two-fluid flow models based on the full Navier–Stokes equations are presented. The models include six and seven partial differential equations, namely, six- and seven-equation models. The seven-equation model consists of a non-conservative equation for volume fraction evolution of one of the fluids and two sets of balance equations. Each set describes the motion of the corresponding fluid, which has its own pressure, velocity, and temperature. The closure is achieved by two stiffened gas equations of state. Instantaneous relaxation towards equilibrium is achieved by velocity and pressure relaxation terms. The six-equation model is deduced from the seven-equation model by assuming an infinite rate of velocity relaxation. In this model, a single velocity is used for both fluids. The numerical solutions are obtained by applying the Strang splitting technique. The numerical solutions are examined in a set of one, two, and three dimensions for both the six- and seven-equation models. The results indicate very good agreement with the experimental results. There is an insignificant difference between the results of the two models, but the six-equation model is much more economical compared to the seven-equation model.     

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a ‘high-lift’ and an ‘ultra high-lift’ turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in ‘ultra high-lift’ design when compared to the ‘high-lift’ design. Stronger ‘Klebanoff streaks’ are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The ‘part-span’ Kelvin–Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging.     

Wall slip and extrudate instability of 4-arm star polybutadienes in capillary flow

This paper presents experimental research on wall slip and extrusion instability behavior of a series of monodisperse 4-arm star polybutadienes (PBD) of different molecular weights during fast capillary flow. The star PBDs reveal a slope of 3.0 in the capillary flow curve, showing a faster non-linear response than linear PBDs. The global stick-slip transition of star PBD is weaker than linear PBD of the same molecular weight, as indicated by a smaller extrapolation length b of star PBD. The sharkskin fracture takes place without a global stick-slip transition for a star PBD with molecular weight of 200 K, suggesting the sharkskin instability may not originate from an oscillating stick-slip transition at die exit. The flow splitting, i.e., the phenomenon that the extrudate breaks into two or more branches after the die exit, is observed in star PBDs with molecular weights higher than 200 K. The flow splitting, accompanied by a precession motion, is found to be an exit instability behavior. The flow splitting is related to the long bulk relaxation time of the star polymers and more likely to occur in a solid-like state, where the storage modulus G is higher than the loss modulus G. A rotating-breaking hypothesis is proposed to explain the flow splitting and sharkskin instability behavior of star PBDs based on a stretch induced rupture at die exit in a rotating pattern.     

Dynamics of trailing vortices in the wake of a generic high-speed train

The three-dimensional dynamics of a pair of counter-rotating streamwise vortices that are present in the wake of an ICE3 high-speed train typical of modern, streamlined vehicles in operation, is investigated in a 1/10th-scale wind-tunnel experiment. Velocity mapping, frequency analysis, phase-averaging and proper orthogonal decomposition of data from high-frequency multi-hole dynamic pressure probes, two-dimensional total pressure arrays and one-dimensional multi-hole arrays was performed. Sinusoidal, antisymmetric motion of the pair of counter-rotating streamwise vortices in the wake is observed. These unsteady characteristics are proposed to be representative of full-scale operational high-speed trains, in spite of the experimental limitations: static floor, reduced model length and reduced Reynolds number. This conclusion is drawn from favourable comparisons with numerical literature, and the ability of the identified characteristics to explain phenomena established in full-scale and scaled moving-model experiments.