Organised modes and shock-vortex interaction in unsteady viscous transonic flows around an aerofoil: Part II: Reynolds number effect

The modification of the transonic flow structure around a NACA0012 aerofoil at free-stream Mach number 0.85 and at zero angle of incidence is studied as a function of Reynolds number in the range (500, 10,000) by solving the time-dependent Navier-Stokes equations as described in part I. At the selected value of the Mach number, the flow is subjected only to the von Kármán instability mode developed downstream of the trailing edge shock, as has been studied in part I. By using the time-dependent amplitude evolution versus the period of the fundamental mode, the coefficients of the Stuart-Landau global oscillator model have been evaluated, yielding the linear and non-linear parts of the instability process. The supercritical nature of mode I instability as well as the critical Reynolds number of this instability (Re=2070) have been determined for the transonic regime. The spatial growth and decay of mode I instability are evaluated in the near wake by means of a detailed spectral analysis of the time-dependent signals. The variation law for the location of the maximum amplification of this near wake mode as a function of Reynolds number has been established and found to scale as: X_max∼Re^−0.2.     

Large eddy simulation of turbulent flow past a square cylinder confined in a channel

Turbulent flow past a square cylinder confined in a channel is numerically investigated by large eddy simulation (LES). The main objectives of this study are to extensively verify the experimental results of Nakagawa et al. [Exp. Fluids 27(3) (1999) 284] by LES and to identify the features of flows past a square cylinder confined in a channel in comparison with the conventional one in an infinite domain. The LES results obtained are in excellent agreement with the experiment both qualitatively and quantitatively. The well-known Kármán vortex shedding is observed. However, the vortices shed from the cylinder are significantly affected by the presence of the plates; mean drag and fluctuation of lift force increase significantly. Furthermore, periodic and alternating vortex-rollups are observed in the vicinity of the plates. The rolled-up vortex is convected downstream together with the corresponding Kármán vortex; they form a counter-rotating vortex pair. It is also revealed that the cylinder greatly enhances mixing process of the flow.     

Particle mixing and reactive front motion in unsteady open shallow flow - Modelled using singular value decomposition

Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction, A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.     

A heuristic approach to effective sensor placement for modeling of a cylinder wake

The effectiveness of a sensor configuration for feedback flow control on the wake of a circular cylinder is investigated in both direct numerical simulation as well as in a water tunnel experiment. The research program is aimed at suppressing the von Kármán vortex street in the wake of a cylinder at a Reynolds number of 100. The design of sensor number and placement was based on data from a laminar two-dimensional simulation of the Navier-Stokes equations for the unforced condition. A low-dimensional proper orthogonal decomposition (POD) was applied to the vorticity calculated from the flow field and sensor placement was based on the intensity of the resulting spatial eigenfunctions. The numerically generated data was comprised of 70 snapshots taken over three cycles from the steady state regime. A linear stochastic estimator (LSE) was employed to map the velocity data to the temporal coefficients of the reduced order model. The capability of the sensor configuration to provide accurate estimates of the four low-dimensional states was validated experimentally in a water tunnel at a Reynolds number of 108. For the experimental wake, a sample of 200 particle image velocimetry (PIV) measurements was used. Results show that for experimental data, the root mean square estimation error of the estimates of the first two modes was within 6% of the desired values and for the next two modes was within 20% of the desired values. This level of error is acceptable for a moderately robust controller.     

Investigation of Kuroshio-induced cold-core eddy trains in the lee of the Izu Islands using high-resolution satellite images and numerical simulations

A series of Synthetic Aperture Radar (SAR) images acquired during the summer of 2006 revealed island wakes in the lee of the Izu Islands, south of Japan. The wakes were formed of not only meandering disturbances but also a series of eddies with diameters on the order of those of the islands. The Kuroshio flowed near these islands in the summer of 2006, indicating that the island wakes were induced by a Kuroshio-island interaction. Satellite sea-surface temperature (SST) and Chlorophyll-a (Chl-a) images observed during the summer of 2006 revealed low-SST and high Chl-a wakes, some of which included low-SST eddy trains. It is thus inferred that the phenomenon entailed upwelling and mixing processes and biological productivity known as the “island-mass effect.” High-spatial-resolution SST derived by combining a LANDSAT infrared channel and AVHRR SST clearly revealed a well-defined SST front associated with the island wakes and a 1 km-scale low-SST wake pattern. A numerical simulation was performed to investigate the formation mechanism. The simulation qualitatively reproduced the cold-eddy pattern, with eddy-driven mixing developing a mixed layer down to 200 m, causing low-SST island wakes. The shedding frequency and spacing of the model-produced eddies were roughly close to those of the Kármán vortex theory, suggesting that Kármán-type cold-eddy trains are commonly formed behind the islands when the Kuroshio strong flow impinges on them.     

Bifurcations and buffet of transonic flow past flattened surfaces

Turbulent transonic flow past flattened aerodynamic surfaces is investigated numerically using the RANS equations. The study is focused on: (★) a buffet onset caused by instability of the shock wave/boundary layer interaction, (★★) instability of the entire flow structure and related flow bifurcations.For a symmetric airfoil at zero angle of attack, computations reveal both bifurcations and buffet in a range of the freestream Mach number M_∞. At nonzero angles of attack, α=±1°, there are two ranges of M_∞ in which the buffet onset takes place. For a Whitcomb type airfoil, computations demonstrate instability of the flow structure only at negative α. Axisymmetric flow past axisymmetric bodies is also considered, and instability of the flow structure at certain freestream Mach numbers is shown.     

On post-buckling analysis and experimental correlation of cylindrical composite shells with Reissner-Mindlin-Von Kármán type facet model

In this paper post-buckling analysis of carbon fibre reinforced plastic cylindrical shells under axial compression is considered. Reissner-Mindlin-Von Kármán type shell facet model is used in the computations. The effect of geometric imperfection shape and amplitude on nonlinear analysis results is discussed. Numerical-experimental correlation is performed using the results of experimental buckling tests found in the literature. Results show that bringing the diamond shape geometric imperfection in the model significantly improves the correlation and gives good accuracy in simulating cylindrical shell post-buckling behaviour.     

Development of a MEMS-based control system for compressible flow separation

A MEMS-based sensor and actuator system has been designed and fabricated for separation control in the compressible flow regime. The MEMS sensors in the system are surface-micromachined shear stress sensors and the actuators are bulk-micromachined balloon vortex generators (VGs). A three-dimensional (3-D) wing model embedded with the shear stress sensors and balloon VGs was tested in a transonic wind tunnel to evaluate the performance of the control system in a range of Mach number between 0.2 and 0.6. At each Mach number tested, the shear stress sensors quantify the boundary layer on the surface of the wing model while the balloon VGs interact with the boundary layer in an attempt to provide flow control. The shear stress measurements indicate the presence of a separated flow on the trailing ramp section of the wing model at all Mach numbers tested when the balloon VGs are not activated. This result is confirmed by total pressure measurements downstream from the wing model where a wake profile is observed. When the balloon VGs are activated, the shear stress level on the trailing ramp increases with the Mach number. At the highest Mach number tested, this increase elevates the shear stress on the ramp to almost the same level as the unseparated flow, suggesting the possibility of a boundary layer reattachment. This result is supported by the downstream pressure measurements which show a large pressure recovery when the balloon VGs are activated. The wind tunnel experiment successfully demonstrated two aspects of the MEMS flow control system: the effectiveness of the microshear stress sensors in measuring the separation characteristics of a high-speed compressible flow and the ability of the microballoons in positively enhancing the aerodynamic performance of a high-speed wing through boundary layer modification.     

Optimal airfoil shapes for viscous transonic flows of Bethe-Zel’dovich-Thompson fluids

High-performance airfoils for transonic viscous flows of dense gases are constructed using an efficient high-order accurate flow solver coupled with a multi-objective genetic algorithm. Dense gases are theoretically characterized by reversed behavior of the speed of sound in isentropic perturbations for a range of temperatures and pressures in the vapor phase. A class of dense gases, namely the so-called Bethe-Zel’dovich-Thompson (BZT) fluids, might exhibit nonclassical gasdynamic behaviors in the transonic and supersonic regimes, such as the disintegration of compression shocks. Utilizing BZT gases as working fluids may result in low drag exerted on airfoils operating at high transonic speeds thanks to an increase in the airfoil critical Mach number. This advantage can be further improved by a proper design of the airfoil shape, also leading to the enlargement of the airfoil operation range within which BZT effects are significant. Such a result is of particular interest in view of the exploitation of BZT fluids for the development of high-efficiency turbomachinery.     

引射式跨声速风洞流场控制软件设计

目前提出的引射式跨声速风洞流场控制软件抽气端压力过大,导致排气阀气流排气速度变化过于剧烈;设计了一种新的引射式跨声速风洞流场控制软件,在风洞的控制程序中引入了马赫数和雷诺数,对控制质量进行试验检测,以实现风洞系统能够达到更精准快速的控制水平;在风洞流场控制系统中引入了解耦系统,对风洞测试各部分参数进行解耦筛选,提高各参数的准确度,有利于控制系统实现精准控制;实验结果表明,设计的引射式跨声速风洞流场控制软件能有效降低引射式跨声速风洞流场控制软件抽气端压力,使排气阀气流排气速度处于稳定状态。     

Numerical prediction of sound generated from flows with a low Mach number

Numerical computations of sound generated from flows with a low Mach number are presented based on Lighthill’s acoustic analogy with an assumption that sound does not alter the flow field from which it is generated. The source fluctuations of the flow field are computed by a large-eddy simulation (LES) with Dynamic Smagorinsky Model (DSM) and they are fed to the following acoustical computation as input data. An explicit/implicit finite element method with second order accuracy both in time and space is used for flow field discretization. The method is applied to the prediction of sound in three different classes of problems: far-field sound generated from flow around a bluff body, sound resulting from blade-stator interaction of turbomachinery and sound due to a turbulent boundary layer on an aerofoil. The computed frequency spectra of the sound show a fairly good agreement with the measured spectra for all the cases.     

Numerical studies of specific features of the transonic flow reconstruction on a hammerhead model

The results of the numerical studies of transonic flow reconstruction occurring with an increase in the free stream Mach number on a hammerhead cone-cylinder body with a small break angle in the generatrix are presented. A turbulent flow regime is considered. The Reynolds equations with different turbulence models are used. The numerical results are compared to the experimental data and the results of the calculation using the Euler model.     

Numerical simulation of the transonic turbulent flow around a wedge-shaped body with a backward-facing step

A fully three-dimensional near-wall complex turbulent flow around a wedge-shaped body with a backward-facing step is considered with the transonic flow regime (Mach number M = 0.913) at the Reynolds number Re = 7.2 × 10⁶. The technology of the numerical simulation of problems of the class under study is represented in detail. A series of preliminary auxiliary calculations is carried out for choosing the optimal computational algorithm. The numerical results of the problem simulation based on the eddy-resolving hybrid RANS-LES approach IDDES are finally given for the full configuration. The validity of the results obtained is confirmed by comparing them to the corresponding experimental data.     

Mathematical simulation of turbulent separated transonic flows around the bodies of revolution

The properties of the turbulent separated flows around boat-tailed objects, especially in transonic regimes, are very complex and have still not been fully understood. With a variation of the free-stream Mach number, the flow structure, the size and location of separation areas, internal supersonic regions, and the position and intensity of internal shocks vary significantly. These flow properties determine the complexity of the numerical modeling problem and high demands on the algorithms used. The paper presents a comparison of the numerical results obtained on the basis of different mathematical models with the experimental data. The investigations into fundamental properties of transonic flow transformation are presented as well.     

Instability of stagnation line icing

A high Reynolds number analysis is used to investigate the stability of an ice surface lying beneath a low Mach number stagnation-line air flow. The ice surface is covered by a thin water film, whose thickness is consistent with the water mass densities typically encountered in aircraft icing cloud conditions. A multiple scales stability analysis is used to show that the ice surface can become unstable near the stagnation line. The ice surface is found to admit strongly three-dimensional linear instabilities, and increasing the Mach number suppresses the instability.     

Further Results on Guderley Mach Reflection and the Triple Point Paradox

Recent numerical solutions and shock tube experiments have shown the existence of a complex reflection pattern, known as Guderley Mach reflection, which provides a resolution of the von Neumann paradox of weak shock reflection. In this pattern, there is a sequence of tiny supersonic patches, reflected shocks and expansion waves behind the triple point, with a discontinuous transition from supersonic to subsonic flow across a shock at the rear of each supersonic patch. In some experiments, however, and in some numerical computations, a distinctly different structure which has been termed Guderley reflection has been found. In this structure, there appears to be a single expansion fan at the triple point, a single supersonic patch, and a smooth transition from supersonic to subsonic flow at the rear of the patch. In this work, we present numerical solutions of the compressible Euler equations written in self-similar coordinates at a set of parameter values that were used in previous computations which found the simple single patch structure described above. Our solutions are more finely resolved than these previous solutions, and they show that Guderley Mach reflection occurs at this set of parameter values. These solutions lead one to conjecture that the two patterns are not distinct: rather, Guderley reflection is actually underresolved Guderley Mach reflection.     

Influence of exit-to-throat width ratio on performance of high pressure convergent-divergent rotor in a vaneless counter-rotating turbine

This paper describes the redesign of a high pressure rotor (with exit Mach number around 1.5) for the vaneless counter-rotating turbine by choosing adequate exit-to-throat width ratio. Based on the previous design analysis and test results, effects of the exit-to-throat width ratio on the performance of the transonic turbine cascade were proposed. In order to investigate the influence of the exit-to-throat width ratio on the performance of the turbine cascade, a flow model of the convergent-divergent turbin...     

On the discontinuous Galerkin method for the simulation of compressible flow with wide range of Mach numbers

The paper is concerned with the numerical simulation of compressible flow with wide range of Mach numbers. We present a new technique which combines the discontinuous Galerkin space discretization, a semi-implicit time discretization and a special treatment of boundary conditions in inviscid convective terms. It is applicable to the solution of steady and unsteady compressible flow with high Mach numbers as well as low Mach number flow at incompressible limit without any modification of the Euler or Navier–Stokes equations.     

Direct numerical simulation of compressible turbulent channel flows using the discontinuous Galerkin method

Direct numerical simulation of turbulent channel flows between isothermal walls have been carried out using discontinuous Galerkin method. Three Mach numbers are considered (0.2, 0.7, and 1.5) at a fixed Reynolds number ≈2800, based on the bulk velocity, bulk density, half channel width, and dynamic viscosity at the wall. Power law and log-law with the scaling of the mean streamwise velocity are considered to study their performance on compressible flows and their dependence on Mach numbers. It indicates that power law seems slightly better and less dependent on Mach number than the log-law in the overlap region. Mach number effects on the second-order (velocity, pressure, density, temperature, shear stress, and vorticity fluctuations) and higher-order (skewness and flatness of velocity, pressure, density, and temperature fluctuations) statistics are explored and discussed. Both inner (that is wall variables) and outer (that is global) scalings (with Mach number) are considered. It is found that for some second-order statistics (i.e. velocity, density, and temperature), the outer scaling collapses better than the inner scaling. It is also found that near-wall large-scale motions are affected by Mach number. The near-wall spanwise streak spacing increases with increasing Mach number. Iso-surfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Mach number increases, which is similar to the distribution of near-wall low speed streaks.