Laser-induced fluorescence modulation techniques for velocity measurements in gas flows

Broadband fluorescence of iodine, excited at 514.5 nm by a single-mode argon-ion laser tuned to the quasi-linear part of an absorption line, was used to detect the Doppler shift and hence the velocity of iodine molecules seeded in a nitrogen jet flow. The slope of the absorption line profile was measured directly using a frequency shift introduced by acoustooptic modulators (AOMs). A velocity of 36 m/s was measured in a jet of N₂ at 60 Torr in 2 ms with an accuracy of 11%. To reduce experimental noise, the laser beams were switched at 125 KHz and signal-tuned amplification was used.     

Unsteady wall-shear measurements in turbulent boundary layers using MEMS

Fluctuating skin friction is measured in two- and three-dimensional turbulent boundary layers using a MEMS sensor and a wall-wire as reference. Skewness, flatness and spectra of the turbulent skin friction are presented to demonstrate the potential and limitations of the MEMS sensor. The measured turbulence intensities of the order of 0.4 are in general agreement with a number of experimental and DNS studies. However, the fluctuating quantities measured with this MEMS sensor, operated at an over-heat ratio of 1.3, are shown to depend on the Reynolds number or mean skin friction. Therefore, such a high over-heat ratio, which was proven to dramatically increase the accuracy of mean skin friction measurements in a previous study by the authors, may not be appropriate for the measurement of fluctuating wall-shear with MEMS sensors, particularly at low mean shear values.     

Pulsatile flows and wall-shear stresses in models simulating normal and stenosed aortic arches

Pulsatile aqueous glycerol solution flows in the models simulating normal and stenosed human aortic arches are measured by means of particle image velocimetry. Three transparent models were used: normal, 25% stenosed, and 50% stenosed aortic arches. The Womersley parameter, Dean number, and time-averaged Reynolds number are 17.31, 725, and 1,081, respectively. The Reynolds numbers based on the peak velocities of the normal, 25% stenosed, and 50% stenosed aortic arches are 2,484, 3,456, and 3,931, respectively. The study presents the temporal/spatial evolution processes of the flow pattern, velocity distribution, and wall-shear stress during the systolic and diastolic phases. It is found that the flow pattern evolving in the central plane of normal and stenosed aortic arches exhibits (1) a separation bubble around the inner arch, (2) a recirculation vortex around the outer arch wall upstream of the junction of the brachiocephalic artery, (3) an accelerated main stream around the outer arch wall near the junctions of the left carotid and the left subclavian arteries, and (4) the vortices around the entrances of the three main branches. The study identifies and discusses the reasons for the flow physics’ contribution to the formation of these features. The oscillating wall-shear stress distributions are closely related to the featured flow structures. On the outer wall of normal and slightly stenosed aortas, large wall-shear stresses appear in the regions upstream of the junction of the brachiocephalic artery as well as the corner near the junctions of the left carotid artery and the left subclavian artery. On the inner wall, the largest wall-shear stress appears in the region where the boundary layer separates.     

Planar measurements of the full three-dimensional scalar dissipation rate in gas-phase turbulent flows

A simultaneous planar Rayleigh scattering and planar laser-induced fluorescence (PLIF) technique is described which allows planar measurement of the full three-dimensional scalar gradient, ∇C (x, t), and scalar energy dissipation rate, χ≡D ∇C·∇C, in gas-phase turbulent flows. The conserved scalar used is the jet fluid concentration, where the jet consists of propane and seeded acetone. The propane serves as the primary Rayleigh scattering medium, while the acetone is used for fluorescence. For a given amount of available laser energy, this planar Rayleigh scattering/PLIF technique yields much higher signals levels than would, for example, a two-plane Rayleigh scattering technique. By applying the current technique to a single spatial plane, the errors incurred in measuring a spatial derivative across distinct planes are quantified. The errors are found to be well described by a random distribution, and the magnitude of these errors is found to be smaller than the magnitude of significant events in the true scalar gradient fields. Sample results for the fields of the three-dimensional scalar gradient and scalar energy dissipation in a planar turbulent jet, with outer scale Reynolds numbers between 3200 and 8400, are shown, demonstrating the applicability of these measurements to analyses of the fine scale mixing in turbulent flows. The application of these measurements to determination of the scaling properties of the dissipation rate is also discussed. Received: 3 June 1998/Accepted: 12 February 1999     

Marginal separation in three-dimensional flows

The boundary layer in the vicinity of the zero skin-friction point on the leeward symmetry line of a prolate spheroid placed at an angle of attack is considered. The existence of this flow was established by Cebeci et al. (1980) for an angle of attack =40°. The current study is based on the results of Brown (1985) who described the marginal separation in the symmetry plane for a zero skin-friction point and on the results of Zametaev (1989) who included the spatial extension of Brown's solution but without interaction between the boundary layer and the outer flow. It is found that the three-dimensional boundary-layer equations in the vicinity of the zero skin-friction point are reduced to a single nonlinear partial differential equation of hyperbolic type which governs the longitudinal skin-friction component. Smooth solutions of this equation may be found which contain separation lines as well as double-valued regions. It is likely that the latter regions are related to the tip of the separation line obtained as a result of calculations of the full boundary-layer equations. The influence of interaction is also considered, in which case the flow is governed by a partial integro-differential equation. Numerical solutions are given for each of these problems.This study was supported by the United Technologies Research Center     

Measurement techniques for unsteady flows in turbomachines

 The growing interest for unsteady flows in turbomachines over the last two decades has led to an intensive development of fast response measurement techniques, capable of resolving with high frequency phenomena related to inlet distortion, rotating stall and blade row interference effects with blade passing frequencies ranging from 3 to 30 kHz. This development was favoured by major advances in sensor technology and data acquisition systems. The paper reviews the progress in fast response measurement techniques for high speed turbomachinery and application with emphasis on fast response pressure and temperature probes and blade surface sensors including pressure, heat transfer and shear stress determination. Received: 9 November 1998/Accepted: 21 September 1999     

An Euler solver for three-dimensional turbomachinery flows

A time-marching finite volume numerical procedure is presented for three-dimensional Euler analysis of turbomachinery flows. The proposed scheme is applied to the conservative form of the Euler equations written in general curvilinear co-ordinates. A simple but computationally efficient grid is constructed. Numerical solution results for three 3D turbine cascade flows have been presented and compared with available measurements as well as with another state-of-the-art 3D Euler analysis numerical solution in order to demonstrate the accuracy and computational efficiency of the analysis method. Also, the predicted results are compared with a 3D potential flow solver and comparison is made with the analytical solution. The proposed method is an accurate and reliable technique for solving the compressible flow equations in turbomachinery geometries.     

Aerodynamic shape optimization for unsteady three-dimensional flows

This paper presents an adjoint method for the optimum shape design of unsteady flows. The goal is to develop a set of discrete unsteady adjoint equations and the corresponding boundary condition for the non-linear frequency domain method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the non-linear frequency domain adjoint equations for three-dimensional flows. Third, we present results that demonstrate the application of the theory to a three-dimensional wing.     

Particle tracking velocimetry in three-dimensional flows

The photogrammetric determination of three-dimensional particle coordinates from a 3-camera system is described in Part I. In Part II we describe a fully automated tracking scheme for the determination of a sequence of velocity vectors within a three-dimensional observation volume of a fluid flow. From this sequence long-time particle trajectories are reconstructed.The tracking scheme is tested on trajectories obtained using the Kinematic Simulation Inertial Model (KSIM). Estimates of the yield of links between adjacent data sets of particle positions and of the yield of long-time particle trajectories are obtained. The limits of efficient tracking as a function of the spacing-displacement ratio p = _o/ut are also obtained. The effect of noise, in the form of the apparent appearance and disappearance of particles between one image and the next, and of jitter, which is the error in the determination of particle coordinates, is examined. It is shown that noise reduces the number of links per frame, but does not increase the number of erroneous links which is always small. However, the yield of long trajectories drops sharply with increasing noise. A small level of jitter, on the other hand, does not significantly influence any of the results.The tracking scheme is used on two sets of particle coordinate data obtained from real flows: a non-turbulent flow in a small water tank and a turbulent open channel flow.     

Boundary layer interaction in three-dimensional flows

An approach known from the theory of matched asymptotic expansions involving the isolation of subregions with different scales is used to study flows which are assumed to be described by the boundary layer equations almost everywhere near the surface except for a fairly narrow zone in which the inflowing boundary layers interact. Two characteristic types of interaction are identified. An approximate theory describing the flow in the interaction zone, which makes it possible to locate the position of the interaction zone on the surface, is proposed. The interaction flow on the end wall of a vane channel is calculated subject to certain simplifications. The results of an experimental investigation of this flow are presented and it is shown that the theoretical model proposed describes the three-dimensional corner separation which occurs in the neighborhood of the line of intersection of the end wall and the convex edge of the vane.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 116–123, May–June, 1988.     

Particle tracking velocimetry in three-dimensional flows

Particle Tracking Velocimetry (PTV) is a well-known technique for the determination of velocity vectors within an observation volume. However, for a long time it has rarely been applied because of the intensive effort necessary to measure coordinates of a large number of flow marker particles in many images. With today's imaging hardware in combination with the methods of digital image processing and digital photogrammetry, however, new possibilities have arisen for the design of completely automatic PTV systems. A powerful 3D PTV has been developed in a cooperation of the Institute of Geodesy and Photogrammetry with the Institute of Hydromechanics and Water Resources Management at the Swiss Federal Institute of Technology. In this paper hardware components for 3D PTV systems wil be discussed, and a strict mathematical model of photogrammetric 3D coordinate determination, taking into account the different refractive indices in the optical path, will be presented. The system described is capable of determining coordinate sets of some 1000 particles in a flow field at a time resolution of 25 datasets per second and almost arbitrary sequence length completely automatically after an initialization by an operator. The strict mathematical modelling of the measurement geometry, together with a thorough calibration of the system provide for a coordinate accuracy of typically 0.06 mm in X, Y and 0.18 mm in Z (depth coordinate) in a volume of 200 × 160 × 50 mm³.     

ADI approximate factorization procedures for three-dimensional inviscid flows

A solution procedure is developed for the numerical solution of inviscid rotational flow past three-dimensional wing configuration. This procedure solves the three-dimensional Euler equations in a body-fitted coordinate system and strong conservation form. The delta ADI approximate finite-difference factorization technique is developed and used to solve the resulting set of algebraic equations. Fast convergence was attained by using the Newton linearization technique. The present procedure is coded into a FORTRAN program called WING3D. A number of test cases were conducted to check the validity and the accuracy of the procedure and the code. Finally the code was run for transonic flow (M = 0.84) over a rectangular wing at angle of attack of 3.06° and aspect ratio of 14. The results are plotted in pressure curves and mach contours at different sections along the wing. The solutions are discussed and analysed. The shock properties on the upper and lower surfaces are demonstrated.In dieser Untersuchung wurde eine Prozedur zur numerischen Lösung von nichtviskoser Rotationsströmung über eine dreidimensionale Flügelkonfiguration entwickelt. Diese Prozedur löst die dreidimensionalen Eulergleichungen in einem angepaßten Koordinatensystem und in einer strikten Erhaltungsform. Das Delta-ADI-Faktorisierungsverfahren wird entwickelt und angewandt um die resultierenden algebraischen Gleichungen zu lösen. Mittels der Newtonschen Linearisierungstechnik wurde schnelle Konvergenz erreicht. Die vorliegende Prozedur wurde in FORTRAN programmiert. Der Programmname ist WING3D. Eine Reihe von Testrechnungen wurden durchgeführt, um die Gültigkeit und die Exaktheit der Prozedur und des Programmes zu testen. Schließlich wurde das Programm für transsonische Strömung (M = 0.84) über einen rechtwinkeligen Flügel mit einem Anströmwinkel von 3.06° und einem Seitenverhältnis von 14 gestartet. Die Ergebnisse werden in Isobaren und Machlinien von verschiedenen Stellen des Flügels dargestellt, diskutiert und analysiert. Die Eigenschaften des Aufpralls auf die oberen und unteren Oberflächen werden dargestellt.     

Numbering techniques for preconditioners in iterative solvers for compressible flows

We consider Newton–Krylov methods for solving discretized compressible Euler equations. A good preconditioner in the Krylov subspace method is crucial for the efficiency of the solver. In this paper we consider a point‐block Gauss–Seidel method as preconditioner. We describe and compare renumbering strategies that aim at improving the quality of this preconditioner. A variant of reordering methods known from multigrid for convection‐dominated elliptic problems is introduced. This reordering algorithm is essentially black‐box and significantly improves the robustness and efficiency of the point‐block Gauss–Seidel preconditioner. Results of numerical experiments using the QUADFLOW solver and the PETSc library are given. Copyright © 2007 John Wiley & Sons, Ltd.     

Vorticity measurements in turbulent grid flows

Results of direct simultaneous measurements of vorticity and velocity are reported for a turbulent flow past a grid of air and (slightly salted) water by two qualitatively different methods. Both experiments were preformed in the same geometry and at the same Taylor microscale Reynolds number 75. The experiments with salted water flow were performed in water tunnel of the laboratory for vorticity-helicity studiesx Faculty of Engineering, Tel-Aviv University and the experiments with air flow were performed in the wind tunnel of the Turbulent Flow Laboratory, University of Maryland. One of the most striking results is that in both experiments the flow is found to lack reflexional symmetry.     

Stability of nonplane-parallel three-dimensional jet flows

The problem of the stability of nonplane-parallel flows is one of the most difficult and least studied problems in the theory of hydrodynamic stability [1]. In contrast to the Heisenberg approximation [1], the basic state whose stability is investigated depends on several variables, and the stability problem reduces to the solution of an eigenvalue problem for partial differential equations in which the coefficients depend on several variables [2–7]. In the case of a periodic dependence of these coefficients on the time [2] or the spatial coordinates [3, 4], the analog of Floquet theory for the partial differential equations is constructed. With rare exceptions, the case of a nonperiodic dependence has usually been considered under the assumption of weak nonplane-parallelism, i.e., a fairly small deviation from the plane-parallel case has been assumed and the corresponding asymptotic expansions in the linear [6] and nonlinear [7] stability analyses considered. The present paper considers the case of an arbitrary dependence of the velocity profile of the basic flow on two spatial variables. The deviation from the plane-parallel case is not assumed to be small, and the corresponding eigenvalue problem for the partial differential equations is solved by means of the direct methods of [5], which were introduced for the first time and justified in the theory of hydrodynamic stability by Petrov [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 21–28, May–June, 1987.     

Some properties of three-dimensional Biltrami flows

The investigation of Beltrami flows is important for the research on the mechanism of turbulent structure. In this paper the general solutions of the Beltrami flows are given, which depend explicitly on the solutions of three independent Helmholtz equations with scalar unknowns. Velocity fields of Beltrami flows can then be obtained explicitly after the application of some curl operations on the solutions of Helmholtz equations. On the basis of the exact solutions of Euler equations given above, we obtain one kind of exact solutions of non-steady Navier-Stokes equations which are also the Beltrami flows. Some interesting examples of Beltrami flows other than “ABC flows”, “Kolmogolov flows”, “Rayleigh-Bernard flows”, “Q-flows” are given. The detailed analytic results of these examples will be published in the near future.     

Measurement techniques in low-speed turbulent flows

Measurement techniques in low-speed turbulent flows were discussed at the EUROMECH 202 Colloquium at NLR in Marknesse, The Netherlands, October 7–10, 1985. A total of 54 participants from 9 countries attended, and 38 papers were given in two sessions, each closed with a general discussion.     

Theory of slightly perturbed three-dimensional flows in nozzles

The theory of slightly perturbed flows in conical nozzles is used to determine the transverse force and moment generated in the presence of asymmetric perturbations. A system of ordinary differential equations is derived for finding the transverse force and moment. An approximate analytical solution of this system is constructed and its qualitative features are studied. A comparison is made with a numerical solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 146–154, January–February, 1977.