Density field of supersonic separated flow past an afterbody nozzle using tomographic reconstruction of BOS data

The background oriented Schlieren (BOS) technique has been applied to determine the density field in an oblique shock-separated turbulent boundary flow. Measurements were made for two cases, namely, with/without jet flow from the afterbody which is a nozzle. In addition, oil flow and Schlieren visualizations were carried out—the results show certain upstream features of interest including shock excursions. The mean density field from BOS is discussed along with results from conventional Schlieren flow visualization. The data extracted from the mean density field obtained through BOS have been compared for the jet-off and jet-on cases. The data obtained also show the mean density in the base region (jet-off case) to be about 50% of the freestream density and match the isentropic values for the underexpanded jet at the exit. The study involving shock–boundary interaction, movement of freestream shock over the afterbody in the presence of a jet plume provides understanding of flow physics in a flow regime where whole field velocity measurements are extremely difficult.     

Assessment and application of quantitative schlieren methods: Calibrated color schlieren and background oriented schlieren

Two quantitative schlieren methods are assessed and compared: calibrated color schlieren (CCS) and background oriented schlieren (BOS). Both methods are capable of measuring the light deflection angle in two spatial directions, and hence the projected density gradient vector field. Spatial integration using the conjugate gradient method returns the projected density field. To assess the performance of CCS and BOS, density measurements of a two-dimensional benchmark flow (a Prandtl-Meyer expansion fan) are compared with the theoretical density field and with the density inferred from PIV velocity measurements. The methods performance is also evaluated a priori from an experiment ray-tracing simulation. The density measurements show good agreement with theory. Moreover, CCS and BOS return comparable results with respect to each other and with respect to the PIV measurements. BOS proves to be very sensitive to displacements of the wind tunnel during the experiment and requires a correction for it, making it necessary to apply extra boundary conditions in the integration procedure. Furthermore, spatial resolution can be a limiting factor for accurate measurements using BOS. CCS suffers from relatively high noise in the density gradient measurement due to camera noise and has a smaller dynamic range when compared to BOS. Finally the application of the two schlieren methods to a separated wake flow is demonstrated. Flow features such as shear layers and expansion and recompression waves are measured with both methods.     

Experimental study of simultaneous measurement of velocity and surface topography: in the wake of a circular cylinder at low Reynolds number

A technique to provide simultaneous measurement on both free surface topography and the velocity vector field of free surface flows is further developed and validated. Testing was performed on the topography measurement by imaging static plastic wave samples over a wide range of amplitudes. Analysis on the accuracy of the topography reconstruction, the sensitivity to noise and the dependence on spatial resolution are presented. The displacement of the free surface is insensitive to noisy input and the sensitivity shows a linear dependence with the sample spacing. Simultaneous measurements of the free surface and associated velocity field in the wake of a circular cylinder are presented for Reynolds numbers between 55 and 100.     

Phase-locked analysis of velocity fluctuations in a turbulent free swirling jet after vortex breakdown

Large-scale organized vortical structures were studied experimentally in a free swirling jet of air experiencing vortex precession (PVC) at ambient conditions. Detailed measurements were performed in the region near the nozzle exit using phase-locked LDV and PIV, at a Reynolds number of Re ?? 24,400 and a swirl parameter S ?? 1.0. The investigation allowed reconstruction of the time-averaged flowfield, with the associated distribution of turbulent fluctuations, the phase-locked structure of the jet and the associated precessing vortex structure. An original joint analysis of power spectra and probability density functions of velocity data led to quantification of the PVC effect on turbulent fluctuations. This analysis showed that the PVC contribution can be properly separated from the background random turbulence, reproducing the results of phase-locked measurements. It is found that the background turbulence in the near field is substantially weaker if compared to the coherent fluctuations induced by vortex precession.     

Background oriented schlieren for flow visualisation in hypersonic impulse facilities

Experiments to demonstrate the use of the background-oriented schlieren (BOS) technique in hypersonic impulse facilities are reported. BOS uses a simple optical set-up consisting of a structured background pattern, an electronic camera with a high shutter speed and a high intensity light source. The visualization technique is demonstrated in a small reflected shock tunnel with a Mach 4 conical nozzle, nozzle supply pressure of 2.2 MPa and nozzle supply enthalpy of 1.8 MJ/kg. A 20° sharp circular cone and a model of the MUSES-C re-entry body were tested. Images captured were processed using PIV-style image analysis to visualize variations in the density field. The shock angle on the cone measured from the BOS images agreed with theoretical calculations to within 0.5°. Shock standoff distances could be measured from the BOS image for the re-entry body. Preliminary experiments are also reported in higher enthalpy facilities where flow luminosity can interfere with imaging of the background pattern. A version of this paper was presented at the 25th International Symposium on Shock Waves in Bangalore in July 2005.     

Impact of density stratification on the global mode in a swirling jet: Stochastic modelling and Lagrangian coherent structures

In an experimental investigation, the stochastic dynamics of the global mode in a turbulent swirling jet are considered. From the application of the swirling jet in gas turbine combustors, it was observed that a specific density gradient in the flow leads to a suppression of the global mode. This phenomenon was replicated in a generic swirling jet using an electrical heating coil placed inside the breakdown bubble. In the present investigation, the dynamics of the global mode obtained from PIV and pressure measurements are analysed using a stochastic reduced-order model to describe the instability. The stochastic model is necessary to explain the interaction between the deterministic dynamics of the global mode and the perturbations by the background turbulence. The calibration of the stochastic model provides the amplification rate of the global mode that defines the transition of the flow, dependent on the swirling strength and the density difference. The spatial structure of the global mode is further investigated from Lagrangian coherent structures of the flow field which are computed from the 3D time-resolved velocity field reconstruction based on planar PIV measurements. The Lagrangian visualisations and schlieren visualisations are used to explain the absence of the density effects on the global mode at larger Reynolds numbers. The analysis gives a detailed view of the stochastic dynamics of a hydrodynamic instability in a turbulent flow.     

Three-dimensional imaging of a turbulent jet using shearing interferometry and optical tomography

The 3-D density field of a round, neutrally buoyant turbulent jet is obtained using a finite-fringe, shearing interferometer. A He–Ne laser beam (λ=632.8 nm) is subdivided into six beams of equal intensity, which intersect a helium–argon jet flowing from a vertical nozzle. Two-dimensional projection data of the jet are captured simultaneously from six viewing directions distributed over 140°. The desired phase is removed from the spatial carrier using the Fourier transform method. A tomographic reconstruction technique, using a truncated Fourier–Bessel expansion is performed to obtain the complete 3-D density field. The Reynolds number, based on the exit mean velocity and the nozzle diameter, is 5890. Received: 22 December 1999/Accepted: 20 January 2000     

Background-oriented schlieren with natural background for quantitative visualization of open-air explosions

This study describes an attempt of quantitative visualization of open-air explosions via the background-oriented schlieren method (BOS). The shock wave propagation curve and overpressure distribution were extracted from the obtained images and compared with the results of the numerical analysis. The potential of extracting the density distribution behind the shock front is also demonstrated. Two open-air explosions were conducted; one with a $36$ -kg emulsion explosive and the other with a $7.89$ -kg composition C4 explosive. A high-speed digital video camera was used with a frame rate of $10{,}000\,\mathrm{Hz}$ and a pixel size of $800 \times 600$ . A natural background, including trees and grass, was used for BOS measurements instead of the random dots used in a laboratory. The overpressure distribution given by the passing shock was estimated from the visualized images. The estimated overpressures agreed with the values recorded by pressure transducers in the test field. The background displacement caused by light diffraction inside the spherical shock waves was in good agreement, except at the shock front. The results shown here suggest that the BOS method for open-air experiments could provide increasingly better quantitative and conventional visualization results with increasing spatial resolution of high-speed cameras.     

Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density

Optical tomography is applied to the speckle photographic measurement of an asymmetric flow field with variable fluid density. The convolution back projection algorithm is used for obtaining the 3-D density distribution. Noise in the experimental data is reduced by spline smoothing. The method is verified with a steady, laminar, axisymmetric helium jet exhausting vertically into the ambient air, and then applied to a non-axisymmetric helium jet for determining the helium concentration. It is found that speckle photographic recordings are very adequate for tomographic reconstruction, because they provide a high number of data points from each projection. The influence of the limited number of projections on the reconstruction quality is particularly investigated. Dedicated to Professor Dr.-Ing. J. Zierep on the occasion of his 60th birthday     

Dual hologram technique with enhanced sensitivity for measurements of weak phase objects

Conventional interferometric measurements of weak phase objects run into serious accuracy problems due to low sensitivity and/or optical aberrations. This paper describes an optical method, based on the dual hologram technique, with enhanced sensitivity and with compensating for the optical aberrations. It provides a reliable acquisition of the phase information from wide range of weak phase objects including high speed flow fields. The method was demonstrated by mapping the density field of a small size axisymmetric supersonic jet as a representative weak phase object. Received: 8 July 1996 / Accepted: 26 September 1996     

Natural-background-oriented schlieren imaging

The background-oriented schlieren (BOS) flow visualization method has the potential for large-scale flow imaging outside the laboratory by using natural backgrounds instead of the artificial patterns normally used indoors. The natural surroundings of an outdoor test site can sometimes be used as such a background, subject to criteria of fine scale, randomness and contrast that are developed here. Some natural backgrounds are more appropriate than others for a given application. Backgrounds used here to visualize both high- and low-speed schlieren disturbances include a sunlit cornfield and a backlit grove of trees. A range of image post-processing methods is considered for qualitative BOS. It is found that high sensitivity and a broad measuring range are in conflict here, much as they are in traditional schlieren instruments. Applications of natural-BOS include explosive characterization, firearms and artillery testing, chemical and natural-gas leak detection, and related phenomena.     

Some problems in the theory of plane jets of conducting fluid

Using the boundary-layer equations as a basis, the author considers the propagation of plane jets of conducting fluid in a transverse magnetic field (noninductive approximation).The propagation of plane jets of conducting fluid is considered in several studies [1–12]. In the first few studies jet flow in a nonuniform magnetic field is considered; here the field strength distribution along the jet axis was chosen in order to obtain self-similar solutions. The solution to such a problem given a constant conductivity of the medium is given in [1–3] for a free jet and in [4] for a semibounded jet; reference [5] contains a solution to the problem of a free jet allowing for the dependence of conductivity on temperature. References [6–8] attempt an exact solution to the problem of jet propagation in any magnetic field. An approximate solution to problems of this type can be obtained by using the integral method. References [9–10] contain the solution obtained by this method for a free jet propagating in a uniform magnetic field.The last study [10] also gives a comparison of the exact solution obtained in [3] with the solution obtained by the integral method using as an example the propagation of a jet in a nonuniform magnetic field. It is shown that for scale values of the jet velocity and thickness the integral method yields almost-exact values. In this study [10], the propagation of a free jet is considered allowing for conduction anisotropy. The solution to the problem of a free jet within the asymptotic boundary layer is obtained in [1] by applying the expansion method to the small magnetic-interaction parameter. With this method, the problem of a turbulent jet is considered in terms of the Prandtl scheme. The Boussinesq formula for the turbulent-viscosity coefficient is used in [12].This study considers the dynamic and thermal problems involved with a laminar free and semibounded jet within the asymptotic boundary layer, propagating in a magnetic field with any distribution. A system of ordinary differential equations and the integral condition are obtained from the initial partial differential equations. The solution of the derived equations is illustrated by the example of jet propagation in a uniform magnetic field. A similar solution is obtained for a turbulent free jet with the turbulent-exchange coefficient defined by the Prandtl scheme.     

水下爆炸气泡射流载荷计算的新方法研究

由于存在强冲击、多相界面复杂运动等强非线性效应,目前对于水下爆炸气泡运动的计算方法无法给出较为可信的水射流运动特征及其载荷形式.本文基于多相可压缩流体的five-equation计算模型,引入界面函数和界面密度压缩技术,采用5阶WENO重构与HLLC近似Riemann求解器进行空间离散,时间离散采用3阶TVD Rung...     

Linear Longwave Instability of a Single Class of Steady-State Jet Flows of an Ideal Fluid in the Field of a Self-Electric Current

A necessary and sufficient condition of linear stability of a certain two-parameter class of cylindrical steady-state shear jet MHD flows of an inviscid incompressible ideally-conducting fluid with a free boundary is obtained by the direct Lyapunov method. The magnetic field is induced by a direct current flowing along the jet so that the field linearly depends on the radius. The stability with respect to small axisymmetric longwave perturbations is considered. The perturbations conserve leave the ratio of the distance between a fluid particle and the jet axis to the azimuthal vorticity component unchanged in each fluid particle. Two-sided exponential estimates of the perturbation growth are derived in the case of violation of the stability condition obtained.     

Application of particle image velocimetry and the background-oriented schlieren technique in the high-enthalpy shock tunnel G?ttingen

The applicability of the particle image velocimetry (PIV) and the background-oriented schlieren (BOS) techniques in the high-enthalpy shock tunnel G?ttingen of the German Aerospace Center, DLR is demonstrated. As a part of this feasibility study two different experiments are performed. The velocity field past a wedge in a Mach 6 flow at a total specific enthalpy of 1.5 MJ/kg is determined by means of PIV and the results are compared to numerical predictions. The BOS technique is applied to investigate the density field in the shock layer of a sphere at 12 and 22 MJ/kg total specific enthalpies. Using a ray tracer method, the BOS results are compared to the data obtained by corresponding numerical computations.     

On the Reconstruction of Darcy Velocity in Finite-Volume Methods

The accuracy of particle tracking methods for advective transport in porous media depends in turn upon the accuracy of the computed velocity. In many advanced finite-volume methods used in practical applications, the velocity field is often only accurate up to the first order, and is typically defined only on mesh edges. We develop an inexpensive method for reconstructing a quasi-optimal accuracy-preserving velocity field inside the elements of a polygonal mesh. Numerical verification on quadrilateral meshes shows reduction of L ²-error in comparison with conventional reconstruction strategies.     

数字全息粒子图像测速技术(DHPIV)研究进展

全息粒子图像测速技术(DHPIV)是当前非常具有发展潜力的非定常三维流场测量技术,是一种具有点空间分辨力的三维空间三维速度场和时间历程的实验观测方法和技术. 本文介绍了该项技术(数字全息DH和粒子图像测速PIV)的发展背景和近20年来的研究进展,并介绍了已测得的非定常复杂流动的初步结果. 详细论述了DHPIV技术所面临的关键性问题和应用基础问题以及相应的进展:粒子空间场的重建与再现的空间分辨率问题、粒子定位或位移精度问题、信噪比和数字再现的光学与快速算法以及测量空间的扩展等问题.同时讨论了数字离轴全息等有关技术的潜力, 介绍了进一步的研究发展方向.      

A Cartesian cut cell free surface capturing method for 3D water impact problems

A Cartesian cut cell mesh generation procedure is developed together with a finite volume Euler solver for a two‐fluid system with a free surface. A fast and robust triangle to triangle overlap scheme is used to determine the intersection of a body‐surface with the background Cartesian mesh. Improvements to the cut cell routines include a new treatment for multiple cuts within a single cell and a surface trimming procedure to ensure a good quality mesh around solid boundaries. The formulae for calculating all necessary information about a cut cell are also presented. These are generic and can be used for arbitrarily irregular boundary elements. A collocated finite volume method with a high resolution Godunov‐type scheme in space is used for discretization of the governing flow equations. By computing in both the air and water regions simultaneously in a consistent manner, the free surface is automatically captured as a contact discontinuity in the density field without the need for any special free surface tracking method. The algorithm incorporates the artificial compressibility method with a dual time stepping strategy to maintain a divergence free velocity field. The mathematical formulation including its numerical implementation of the method is reviewed and results for a number of test cases are also presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical and experimental study of shock waves emanating from an open-ended rectangular tube

We examine the dynamics of a high-speed shock-induced flow near the open end of a shock tube using the particle image velocimetry (PIV) and the background oriented schlieren (BOS) methods along with two- and three-dimensional numerical simulations. In experiments, planar shock waves (\(M=1.3\)–1.6) are discharged from a rectangular (\(24\,\hbox {mm} \times 48\,\hbox {mm}\)) low-pressure section of a shock tube open to the atmosphere. Due to the rectangular exit geometry, the resulting flow is highly three-dimensional and, thus, more complicated, compared to well-studied circular/axisymmetric geometries. The study focuses on the spatio-temporal flow structure up to 1 ms after the shock wave diffraction. PIV and BOS visualization techniques share the same post-processing principle, and the iterative multi-step cross-correlation algorithm applied in the PIV software is adapted here for the calculation of background pattern displacement on the BOS images. Particular attention is given to the resolution of flow regions where sharp gradients are present, such as a diffracted shock front or embedded shocks. Computational fluid dynamic simulations of the problem are also conducted to validate the experimental results and methods and to gain more insight into the three-dimensional flow dynamics. PIV and BOS images are found to be consistent with the corresponding numerical flow visualizations.     

An evaluation of optical flow algorithms for background oriented schlieren imaging

The background oriented schlieren method (BOS) allows for accurate flow measurements with a simple experimental configuration. To estimate per-pixel displacement vectors between two images, BOS systems traditionally borrow window-based algorithms from particle image velocimetry. In this paper, we evaluate the performance of more recent optical flow methods in BOS settings. We also analyze the impact of different background patterns, suggesting the use of a pattern with detail at many scales. Experiments with both synthetic and real datasets show that the performance of BOS systems can be significantly improved through a combination of optical flow algorithms and multiscale background.