Measurement of wall shear rate in large amplitude unsteady reversing flows

Wall shear rates in large amplitude unsteady flows that cause flow reversal can be measured by using two rectangular electrodes in a sandwich arrangement. The frequency response of this sandwich probe is studied numerically. An inverse mass transfer method is applied to recover the instantaneous shear rate from the measured difference in the mass transfer rate to the two segments. Experimental results for a turbulent pipe flow with imposed large amplitude sinusoidal oscillations are used to test the method.     

A dual-camera cinematographic PIV measurement system at kilohertz frame rate for high-speed, unsteady flows

A digital dual-camera cinematographic particle image velocimetry (CPIV) system has been developed to provide time-resolved, high resolution flow measurements in high-Reynolds number, turbulent flows. Two high-speed CMOS cameras were optically combined to acquire double-pulsed CPIV images at kilohertz frame rates. Bias and random errors due to camera misalignment, camera vibration, and lens aberration were corrected or estimated. Systematic errors due to the camera misalignment were reduced to less than 2 pixels throughout the image plane using mechanical alignment, resulting in 3.1% positional uncertainty of velocity measurements. Frame-to-frame uncertainties caused by mechanical vibration were eliminated with the aid of digital image calibration and frame-to-frame camera registration. This dual-camera CPIV system is capable of resolving high speed, unsteady flows with high temporal and spatial resolutions. It also allows time intervals between the two exposures down to 4 μs, enabling the measurements of speed flows 5–10 times higher than possible with frame-straddling using similar cameras. A turbulent shallow cavity was then chosen as the experimental object investigated by this dual-camera CPIV technique.     

A kilohertz frame rate cinemagraphic PIV system for laboratory-scale turbulent and unsteady flows

A kilohertz frame rate cinemagraphic particle image velocimetry (PIV) system has been developed for acquiring time-resolved image sequences of laboratory-scale gas and liquid-phase turbulent flows. Up to 8000 instantaneous PIV images per second are obtained, with sequence lengths exceeding 4000 images. The two-frame cross-correlation method employed precludes directional ambiguity and has a higher signal-to-noise ratio than single-frame autocorrelation or cross-correlation methods, facilitating acquisition of long uninterrupted sequences of valid PIV images. Low and high velocities can be measured simultaneously with similar accuracy by adaptively cross-correlating images with the appropriate time delay. Seed particle illumination is provided by two frequency-doubled Nd:YAG lasers producing Q-switched pulses at the camera frame rate. PIV images are acquired using a 16 mm high-speed rotating prism camera. Frame-to-frame registration is accomplished by imaging two pairs of crossed lines onto each frame and aligning the digitized image sequence to these markers using image processing algorithms. No flow disturbance is created by the markers because only their image is projected to the PIV imaging plane, with the physical projection device residing outside the flow field. The frame-to-frame alignment uncertainty contributes 2% to the overall velocity measurement uncertainty, which is otherwise comparable to similar film-based PIV methods. Received: 11 July 2000 / Accepted: 21 June 2001 Published online: 29 November 2001     

A cavitation model for computations of unsteady cavitating flows

A local vortical cavitation(LVC) model for the computation of unsteady cavitation is proposed.The model is derived from the Rayleigh–Plesset equations,and takes into account the relations between the cavitation bubble radius and local vortical effects.Calculations of unsteady cloud cavitating fows around a Clark-Y hydrofoil are performed to assess the predictive capability of the LVC model using well-documented experimental data.Compared with the conventional Zwart's model,better agreement is observed between the predictions of the LVC model and experimental data,including measurements of time-averaged fl w structures,instantaneous cavity shapes and the frequency of the cloud cavity shedding process.Based on the predictions of the LVC model,it is demonstrated that the evaporation process largely concentrates in the core region of the leading edge vorticity in accordance with the growth in the attached cavity,and the condensation process concentrates in the core region of the trailing edge vorticity,which corresponds to the spread of the rear component of the attached cavity.When the attached cavity breaks up and moves downstream,the condensation area fully transports to the wake region,which is in accordance with the dissipation of the detached cavity.Furthermore,using vorticity transport equations,we also fin that the periodic formation,breakup,and shedding of the sheet/cloud cavities,along with the associated baroclinic torque,are important mechanisms for vorticity production and modification When the attached cavity grows,the liquid–vapour interface that moves towards the trailing edge enhances the vorticity in the attached cav-ity closure region.As the re-entrant jet moves upstream,the wavy/bubbly cavity interface enhances the vorticity near the trailing edge.At the end of the cycle,the break-up of the stable attached cavity is the main reason for the vorticity enhancement near the suction surface.     

A SOLVER USING NEWTON‘S METHOD FOR UNSTEADY VISCOUS FLOWS

A solver is developed for time-accurate computations of viscous flows based on the conception of Newton‘s method. A set of pseudo-time derivatives are added into governing equations and the discretized system is solved using GMRES algorithm. Due to some special properties of GMRES algorithm, the solution procedure for unsteady flows could be regarded as a kind of Newton iteration. The physical-time derivatives of governing equations are discretized using two different approaches, I.e., 3-point Euler backward, and Crank-Nicolson formulas, both with 2nd-order accuracy in time but with different truncation errors. The turbulent eddy viscosity is calculated by using a version of Spalart~Allmaras one-equation model modified by authors for turbulent flows. Two cases of unsteady viscous flow are investigated to validate and assess the solver, I.e., low Reynolds number flow around a row of cylinders and transonic bi-circular-arc airfoil flow featuring the vortex shedding and shock buffeting problems, respectively. Meanwhile, comparisons between the two schemes of timederivative discretizations are carefully made. It is illustrated that the developed unsteady flow solver shows a considerable efficiency and the Crank-Nicolson scheme gives better results compared with Euler method.     

A finite volume approach for unsteady viscoelastic fluid flows

A finite volume, time‐marching for solving time‐dependent viscoelastic flow in two space dimensions for Oldroyd‐B and Phan Thien–Tanner fluids, is presented. A non‐uniform staggered grid system is used. The conservation and constitutive equations are solved using the finite volume method with an upwind scheme for the viscoelastic stresses and an hybrid scheme for the velocities. To calculate the pressure field, the semi‐implicit method for the pressure linked equation revised method is used. The discretized equations are solved sequentially, using the tridiagonal matrix algorithm solver with under‐relaxation. In both, the full approximation storage multigrid algorithm is used to speed up the convergence rate. Simulations of viscoelastic flows in four‐to‐one abrupt plane contraction are carried out. We will study the behaviour at the entrance corner of the four‐to‐one planar abrupt contraction. Using this solver, we show convergence up to a Weissenberg number We of 20 for the Oldroyd‐B model. No limiting Weissenberg number is observed even though a Phan Thien–Tanner model is used. Several numerical results are presented. Smooth and stable solutions are obtained for high Weissenberg number. Copyright © 2002 John Wiley & Sons, Ltd.     

Differential interferometry for studying hypersonic flows

The purpose of this article is to describe an optical technique based on differential interferometry with strongly phase-shifted beams using a white light source and a Wollaston prism. This technique is recommonded particularly for measuring very small index variations. It has been used for analyzing hypersonic flows around slender axisymmetrical bodies. The radial gas density distributions obtained in the shock layers were compared with the analytical solutions developed by Merlen and Andriamanalina (1992) and with Jones' tabulated computations (1969).List of Symbols m exponent of the obstacle's power law - R, R radii of the shock and of the obstacle, respectively - R _c radius of curvature of the spherical mirror - r radial coordinate - L obstacle length - L _m distance from model to spherical mirror - x, y cartesian coordinates with origin at obstacle nose - geometric angle of incidence - birefringence angle of the Wollaston prism, =() - wavelength - relative thickness of the obstacle - _c cone apex semi-angle - Y distance between the two partial beams at the level of the test section - n refractive index of the medium - E optical thickness - e test section width - _y light deviation along the y axis - h length of the path traveled by one of the two beams through the shock layer - gas density - _s gas density under standard conditions - freestream gas density - _min minimum detectable phase difference     

A continuous shape sensitivity equation method for unsteady laminar flows

This paper presents the application of a general shape sensitivity equation method (SEM) to unsteady laminar flows. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. The flow and sensitivity equations are solved on 3D meshes using a Streamline-Upwind Petrov Galerkin (SUPG) finite element method. In the case of shape parameters, boundary conditions for sensitivities depend on the flow gradient at the boundary. Therefore, an accurate recovery of solution gradients is crucial to the success of shape sensitivity computations. In this work, solution gradients at boundary points are extracted using the Finite Node Displacement (FiND) method on which the finite element discretization is enriched locally via the insertion of nodes close to the boundary points. The normal derivative of the solution is then determined using finite differences. This approach to evaluate shape sensitivity boundary conditions is embedded in the continuous SEM. The methodology is applied to the flow past a cylinder in ground proximity. First, the proposed method is verified on a steady state problem. The computed sensitivity is compared to the actual change in the solution when a small perturbation is imposed to the shape parameter. Then, the study investigates the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. A reduction of the gap causes damping of the vortex shedding while an increase amplifies the unsteadiness.     

Multiscale block spectral solution for unsteady flows

Many problems of interest are characterized by 2 distinctive and disparate scales and a huge multiplicity of similar small‐scale elements. The corresponding scale‐dependent solvability manifests itself in the high gradient flow around each element needing a fine mesh locally and the similar flow patterns among all elements globally. In a block spectral approach making use of the scale‐dependent solvability, the global domain is decomposed into a large number of similar small blocks. The mesh‐pointwise block spectra will establish the block‐block variation, for which only a small set of blocks need to be solved with a fine mesh resolution. The solution can then be very efficiently obtained by coupling the local fine mesh solution and the global coarse mesh solution through a block spectral mapping. Previously, the block spectral method has only been developed for steady flows. The present work extends the methodology to unsteady flows of short temporal and spatial scales (eg, those due to self‐excited unsteady vortices and turbulence disturbances). A source term–based approach is adopted to facilitate a two‐way coupling in terms of time‐averaged flow solutions. The global coarse base mesh solution provides an appropriate environment and boundary condition to the local fine mesh blocks, while the local fine mesh solution provides the source terms (propagated through the block spectral mapping) to the global coarse mesh domain. The computational method will be presented with several numerical examples and sensitivity studies. The results consistently demonstrate the validity and potential of the proposed approach.     

An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows

An unsteady incompressible Navier–Stokes solver that uses a dual time stepping method combined with spatially high‐order‐accurate finite differences, is developed for large eddy simulation (LES) of turbulent flows. The present solver uses a primitive variable formulation that is based on the artificial compressibility method and various convergence–acceleration techniques are incorporated to efficiently simulate unsteady flows. A localized dynamic subgrid model, which is formulated using the subgrid kinetic energy, is employed for subgrid turbulence modeling. To evaluate the accuracy and the efficiency of the new solver, a posteriori tests for various turbulent flows are carried out and the resulting turbulence statistics are compared with existing experimental and direct numerical simulation (DNS) data. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

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     

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller(HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257–311(2004)). By analyzing the distribution of the finite-time Lyapunov exponent(FTLE) along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE.This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.     

A simplified marker and cell method for unsteady flows on non-staggered grids

The SMAC (simplified marker and cell) time-advancing method for solving the unsteady incompressible Navier-Stokes equations on non-staggered grids is developed in generalized co-ordinate systems. The primitive variable formulation uses Cartesian velocities and pressure, all defined at the centre of the control volume, as the dependent variables. A special elliptic flux correction at the faces of the finite volume is utilized in discretizing the continuity equation to suppress pressure oscillations. The test flows considered are a polar cavity flow starting from rest and the flow around a circular cylinder. The numerical results are compared with experimental results and results obtained by the well-known SIMPLEC and PISO methods. The comparisons show that the elliptic flux correction technique works well in suppressing pressure oscillations and that the SMAC method is more efficient than the SIMPLEC and PISO methods for both steady and unsteady flows.     

Newtonian drop in a Newtonian matrix subjected to large amplitude oscillatory shear flows

The dynamics of a single Newtonian drop immersed in a Newtonian matrix subjected to large-amplitude oscillatory shear flow is investigated. The ratio of the drop and matrix viscosity is above criticality, and thus break-up is absent under constant shear flow. At small forcing amplitudes the drop shape follows a regular oscillation. As the forcing amplitude increases, multipeaked oscillations of drop shape and orientation are observed. Experimental results are compared with predictions obtained with a phenomenological model. Model predictions are in qualitative good agreement with experimental data. The model suggests that the appearance of higher harmonics in the drop response is mainly due to flow nonaffinity.     

Time marching integral equation method for unsteady transonic flows

In this paper, we have proposed a time marching intregral equation method which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfactorily simulate the shock-wave motions. Firstly, a model problem—one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method. Then the method is implemented for 2-D and 3-D unsteady transonic flow problems. The introduction of the concept of a quasi-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition. The numerical calculations show that the method is reasonable and reliable.     

A level set technique applied to unsteady free surface flows

An unsteady Navier–Stokes solver for incompressible fluid is coupled with a level set approach to describe free surface motions. The two‐phase flow of air and water is approximated by the flow of a single fluid whose properties, such as density and viscosity, change across the interface. The free surface location is captured as the zero level of a distance function convected by the flow field. To validate the numerical procedure, two classical two‐dimensional free surface problems in hydrodynamics, namely the oscillating flow in a tank and the waves generated by the flow over a bottom bump, are studied in non‐breaking conditions, and the results are compared with those obtained with other numerical approaches. To check the capability of the method in dealing with complex free surface configurations, the breaking regime produced by the flow over a high bump is analyzed. The analysis covers the successive stages of the breaking phenomenon: the steep wave evolution, the falling jet, the splash‐up and the air entrainment. In all phases, numerical results qualitatively agree with the experimental observations. Finally, to investigate a flow in which viscous effects are relevant, the numerical scheme is applied to study the wavy flow past a submerged hydrofoil. Copyright © 2001 John Wiley & Sons, Ltd.