Dual hologram shearing interference technique for wind tunnel flow fields testing

 A novel optical diagnostic technique, dual hologram shearing interferometry, for measuring density gradients of different phase objects is proposed and demonstrated. The lateral shearing is achieved by using a phase grating. A holographic interferometer has been developed and designed on the base of a single pass Z type conventional schlieren device. The interferometer’s scheme is insensitive to acoustical disturbances, similarly to the conventional schlieren layout, and is capable of recording holograms with a continuous wave laser during the wind tunnel run. The features of the technique make it tolerant to both the temporal coherence of the laser light source and to the relatively low, schlieren quality optical windows of the wind tunnel’s test section. The obtained reconstructed lateral shearing interferograms with a large region of overlap have high contrast and may have an arbitrary orientation and/or spacing of the background interference fringes. It is believed that the proposed approach will become a useful tool for visualization and accurate mapping of the density gradients of gas dynamic flow fields, in wind and shock tunnels, where acoustic noise problems may dramatically affect reference beam holographic schemes. Received: 9 January 1997 / Accepted: 12 April 1997     

Differential interferometry with adjustable spatial carrier fringes for turbine blade cascade flow investigations

 Digital evaluated differential interferometry using adjustable spatial carrier fringes was applied to flow measurements in a transonic turbine blade cascade. The interferograms were evaluated using a two-dimensional Fourier Analysis. This evaluation provided density gradient maps of the flow field in a digital form. A specially designed interferometer was used allowing adjustment of sensitivity and superposition of carrier-fringe system separately. This type of interferometer is also highly insensitive to vibration noise. For a turbine blade cooling film a comparison of this type of differential interferometry with holographic interferometry and a Schlieren visualisation is also given. As a result differential interferometry using adjustable spatial carrier fringes and digital fringe analysis gave density-gradient maps similar to Schlieren recordings but of quantitative nature, thus enabling compensation of wave front distortions. Integration of these density gradient maps resulted in density maps which were then compared to recordings done with pulsed holographic interferometry. Received: 27 December 1996/Accepted: 30 April 1997     

超声速射流装置的流场特性研究

超声速射流装置能很好地模拟榴弹引信发电机飞行时大气环境的工况,已成为地面考核和验收必不可少的设备。本文结合双曝光全息干涉技术和数值模拟方法,对超声速射流装置有无模型的流场进行了研究,将实验干涉图与数值模拟结果进行了比较,从而辨识出实验干涉图中的条纹级数并计算了条纹位移量,由此得出实验干涉图的密度场,经适当的修正就可应用到实物飞行中,解决了过去引信电机选取当地参考密度难的问题。另外由实验结果也验证了数值模拟结果的可靠性。     

Application of digital phase-shift holographic interferometry to weak shock waves propagating at Mach 1.007

Digital phase-shift holographic interferometry was applied to visualize weak shock waves and related phenomena quantitatively. This method of interferometry is an improved version of double-exposure holographic interferometry using digital image processing and a phase shift method. The obtained interferograms were analyzed using the Carré method. To evaluate the applicability of the interferometry to quantitatively visualize the phenomena, density profiles behind weak spherical shock waves generated with 500 μg of silver azide were examined. The results of the numerical analysis performed with the hydrocode AUTODYN were compared with those of the experiment. The Mach number of visualized shock waves was estimated to be 1.007 ± 0.001 at the pressure transducer near the test section. At the shock fronts, the density difference between the experimental and numerical results was within 0.3%.     

Complementary measurement techniques for the detection of wall conditions in supersonic flow

The possibility of indirectly and non-intrusively determining wall temperature or alternatively wall pressure in a 2-D supersonic flow is shown using equations of state and interferograms which yield the accompanying density field close to the wall. In the first case, the detection of recovery temperature is circumvented; in the second case, pressure distribution of higher resolution is attained in regions of unfavorable wall geometry. Received: 25 May 2000/Accepted: 11 December 2000     

Abel inversion of axially-symmetric shock wave flows

Finite-fringe interferograms produced for axisymmetric shock wave flows are analyzed by Fourier transform fringe analysis and an Abel inversion method to produce density field data for the validation of numerical models. For the Abel inversion process, we use basis functions to model phase data from axially-symmetric shock wave structure. Steady and unsteady flow problems are studied, and compared with numerical simulations. Good agreement between theoretical and experimental results is obtained when one set of basis functions is used during the inversion process, but the shock front is smeared when another is used. This is because each function in the second set of basis functions is infinitely differentiable, making them poorly-suited to the modelling of a step function as is required in the representation of a shock wave.Received: 12 November 2003, Accepted: 21 October 2004, Published online: 31 March 2005[/PUBLISHED]PACS: 47.40.-x, 42.40.Kw, 02.30.Zz     

Numerical simulation of shock wave interaction with a water column

The paper describes a scheme which is based on the CIP scheme and modified to properly describe a gas/liquid interface without smearing the density jump across the interface. This was achieved by calculating the density separately for each phase. The density at each grid point was determined by using a density function in a similar fashion as CIP. As a result a sharp density gradient was obtainable throughout the flow field and the scheme could handle properly gas/liquid interfaces having a large density ratio. Shock wave interaction with a cylindrical water column was simulated. The numerical results were compared with appropriate interferograms. Good agreement was found between the two. The results obtained for the cylindrical water column were compared with a similar solid cylinder case. The comparison reveled that even 40 s after shock impingement some differences were found between a liquid column and the solid cylinder. Received 11 July 2000 / Accepted 28 March 2001     

Phase step holographic interferometry applied to hypervelocity,non-equilibrium cylinder flow

For blunt bodies the reduced bow shock wave stand-off distance and the shock layer density rise in the stagnation region as compared to ideal gas flow are phenomena caused by dissociative effects. In this work experiments with aR _BODY=45 mm radius cylinder and an aspect ratio ofL/R _BODY 11 are described. The tests were carried out in the High Enthalpy Shock Tunnel in Göttingen (HEG), a free piston driven shock tunnel. Two different test conditions at reservoir enthalpies of around 21 MJ/kg and Mach numbers of around 9 in air and nitrogen were available.Optical measurements with a holographic phase step interferometer to obtain complete flow field density gradients have been carried out. By increasing the signal-to-noise ratio with the technique of phase stepping over the original recording quality, high quality interferograms are obtained. The high spatial resolution of the holograms results in the creation of hologram-schlieren images which are compared to directly recorded laser-schlieren images.Infinite and finite fringe interferograms and the complete density fields for the two free-stream conditions are presented. The stagnation line densities are quantified. The measured results are shown and compared with Navier-Stokes calculations which account for chemical reactions in the flow. The numerical code underpredicts the stand-off distance of the bow shock wave. It is shown that the flow behind the bow shock wave is in non-equilibrium and that it reaches equilibrium before the body for one condition.This work was an offshoot of an ESA research contract monitored by Dr. D. Vennemann, whose support is gratefully acknowledged. This study of stagnating high enthalpy flows has exceedingly benefited from discussions with S. Brück and V. Hannemann. The operation of the large wind tunnel HEG is the result of a team effort. The with to thank the whole team, represented by Dr. W.H. Beck, for keeping the tunnel going.     

Recording and processing of interferograms by spectral characterization of the interferometric setup

 This paper describes how the scale of experimental tints of an interferometer using a known white light source and a Wollaston prism is reproduced on a microcomputer equipped with an image processing board. Taking the spectral characteristics of the light source and the three RGB camera filters into account, it is possible to analytically express the luminous intensity of the interference fringes as a function of the path difference and to reproduce the experimentally visualized colours on the monitor. The knowledge of the interferometer colour scale allows to optimize the prism position when recording the interferograms and to process them automatically with very high accuracy. Received: 3 May 1995/Accepted: 26 January 1997     

Computer aided evaluation of interferograms

A semi-automatic technique is presented for obtaining the density field from interferograms provided by a Mach-Zehnder setup in infinite fringe width adjustment using short exposure times. The algorithm relies on extracting the fringe edges from the original image and then numbering the resulting polygons according to their order of interference using a graphical editor. The density field is then interpolated between the polygons by calculating its value from the intensity in the original interferogram. This results in highly accurate, high resolution scalar data fields. The results may then be presented in a quasi three-dimensional form using a shading model.     

The calculation of the density field from axisymmetric schlieren interferograms by the image processing techniques

The schlieren interferograms used to be analyzed in a qualitative way. In this paper, by means of the powerful computational ability and the large memory of computer; the image processing method is investigated for the digitalization of an axisymmetric schlieren interferogram and the determination of the density field. This method includes the 2-D low-pass filtering, the thinning of interferometric fringes, the extraction of physical information and the numerical integration of the density field. The image processing results show that the accuracy of the quantitative analysis of the schlieren interferogram can be improved and a lot of time can be saved in dealing with optical experimental results. Therefore, the algorithm used here is useful and efficient.     

Application of holographic interferometry for evaluation of 3D Navier-Stokes calculations

Holographic interferometry is a non-intrusive optical measuring technique which can potentially capture instantaneous information about a complete three-dimensional flow field onto a single holographic image. However subsequently extracting the flow data so that it can be used to validate CFD results, is for most practical wind tunnel applications not yet possible.An approach applied in this paper, is to compare experimental interferograms with equivalent images obtained by post-processing the CFD solution. We have investigated transonic flow in a wind tunnel environment and computationally reconstructed both 2D image-plane interferograms and full 3D holographic interferograms. These comparisons have subsequently helped us to evaluate and improve our 3D Reynolds Averaged Navier-Stokes calculations.The main part of this study was conducted by the authors at Cambridge University Engineering Department where the work was funded by RAE Farnborough under contract 2029/233 XR Aero and monitored by Dr. B. Williams and Dr. P. Smith     

Computer-aided evaluation method for interferograms

For the quantitative evaluation of interferograms a video camera is used to digitize the interferograms in frames up to 512 by 512 pixels which are transmitted to a host computer. Quantitative data of the whole field are obtained by the following procedure: First the fringes are extracted with the help of binarization methods. Then to each fringe boundary a value is assigned in a certain point. Starting from this point the boundaries are traced through the whole pattern. Finally the data between the fringe boundaries are determined by linear interpolation. Other operations like smoothing can be done before the results are printed.     

Calibrated multichannel electronic interferometry for quantitative flow visualization

Calibrated multichannel electronic interferometry, a new technique for quantitative flow visualization of transient phenomena, is discussed. This technique uses an interferometer combined with diffraction gratings to generate three phase shifted interferograms simultaneously which are used to perform multichannel phase shifting. The optical system is calibrated with no phase object present using standard piezoelectric phase shifting, and this calibration information is stored as an electro-optic hologram. The calibration information is used along with the three phase-shifted interferograms that exist with a phase object present to perform time-resolved phase shifting. Examples using natural convection and separated flows are presented.     

A Novel Phase Shifting Technique of Coherent Gradient Sensing Method for Measuring Crack-tip <Emphasis Type="Italic">K</Emphasis>-Dominance

A novel phase shifting method for coherent gradient sensing (CGS) is proposed to automate fringe processing. The phase shifting of CGS interferograms can be simply realized by placing three plane-parallel plates sequentially between the two gratings in the traditional CGS method. The phase shifting method is deduced theoretically and the full-field wrapped phase value can be calculated accurately from four or more interferograms. A calibration test that determines the elasto-optic constant for a polymethyl methacrylate (PMMA) sheet is implemented as a verification experiment. Results show the proposed phase shifting method is valid for transmission CGS measurement. As an application, the proposed phase-shifted CGS method is applied to measure the crack tip K-dominance in a PMMA sheet. In addition, the phase shifting method is shown to be valid for reflective CGS measurement.     

Correlation coefficients of the fluctuating density in turbulent premixed flames

 Two-point density measurements by laser induced Rayleigh scattering are used in this study to fully characterise the scalar field in a Bunsen type turbulent premixed flame. The two points are separated within the flame brush in the axial or radial directions. Correlation coefficients are obtained by comparing the evolution of one-point density fluctuations in time or the two-point density fluctuations in both space and time. Time and length scales of the scalar field, and the mean convection velocity of the turbulent scalar structures are deduced from these correlation coefficients. Time scales are calculated from the auto-correlation coefficients, length scales are determined from the space correlation coefficients and the mean convection velocity of the scalar structures in the axial direction is deduced from the space–time correlation coefficients. The relevance of these results for analysing and modelling the structure of turbulent premixed flames is discussed. Received: 30 April 1996 / Accepted: 2 September 1997     

The shift of Curie temperature and evolution of ferroelectric domain in ferroelectric crystals

A micromechanics-based thermodynamic model for the phase transition of ferroelectric crystals is developed and, with it, the shift of Curie temperature and evolution of ferroelectric phase upon cooling are examined. This approach differs from the classical phenomenological one in that the evolution of new domain concentration can be predicted. We start out by formulating the Gibbs free energy of a generic, two-phase crystal consisting of the parent paraelectric phase and the transformed ferroelectric phase, at a given level of temperature, stress, and electric field. The thermodynamic driving force for domain growth is then derived and, together with the resistance force, a kinetic equation is established. The derived driving force is found to arise from three different sources of Gibbs free energy: (i) the interaction energy due to the heterogeneity of electromechanical moduli of the parent and product phases, (ii) the energy dissipation due to spontaneous polarization, and (iii) the self-energy of the dual-phase system due to the existence of polarization strain and electric polarization. For a BaTiO₃ crystal the electromechanical heterogeneity is found to play a rather significant role that seems not to have been recognized before. The derived shift recovers to the Clausius-Clapeyron relation if such heterogeneity disappears. We have examined in detail several factors that affect the shift of Curie temperature, and calculated the evolution of overall polarization and dielectric constant of a BaTiO₃ crystal. The results are found to be consistent with available test data.     

Interferometry and reconstruction of strongly refracting fields in two-dimensional boundary layer flow

 Optical methods like interferometry as non-intrusive experimental techniques are used for fine analysis of flowfields. The accuracy of the measuring method is very important for the applicability of its results to CFD validation. A common evaluation method to reconstruct interferograms is based on the assumption, that the object ray propagates along a straight line. But the strong bending of rays that occurs, e.g. in supersonic boundary layer flow, cannot be neglected without losses in reconstruction quality. Since the reconstruction of a two-dimensional boundary layer flow can be considered as an one-dimensional problem, the phase difference of the object and reference ray at the interferogram can be related analytically to the refractive-index distribution using a Taylor series expansion. The resulting interferometric equation is an ordinary non-linear second-order differential equation, which can be integrated by numerical methods. By application of this interferometric equation on the one hand, the error in the “classical” interferometry resulting from the ray bending neglection can be estimated. On the other hand, the accuracy in evaluation of interferograms of two-dimensional boundary layer flow can be improved by solving this equation. Received: 23 May 1996 / Accepted: 21 September 1996     

Resonant double Hopf bifurcation in a diffusive Ginzburg–Landau model with delayed feedback

We investigate the resonant double Hopf bifurcation in a diffusive complex Ginzburg–Landau model with delayed feedback and phase shift. The conditions for the existence of resonant double Hopf bifurcation are obtained by analyzing the roots’ distribution of the characteristic equation, and a general formula to determine the bifurcation point is given. For the cases of 1:2 and 1:3 resonance, we choose time delay, feedback strength and phase shift as bifurcation parameters and derive the normal forms which are proved to be the same as those in non-resonant cases. The impact of cubic terms on the unfolding types is discussed after obtaining the normal form till 3rd order. By fixing phase shift, we find that varying time delay and feedback strength simultaneously can induce the coexistence of two different periodic solutions, the existence of quasi-periodic solutions and strange attractors. Also, the effects on the existence of transient quasi-periodic solution exerted by the phase shift are illustrated.