Lattice of plates in an unsteady supersonic flow

The supersonic unsteady flow of a gas past a lattice of thin, slightly curved profiles has been investigated in several studies. The paper [1] is devoted to an evaluation of the effect of wind tunnel walls on the unsteady aerodynamic characteristics of a profile, and [2] investigates the effects of the boundaries of a free jet. These cases are equivalent respectively to the anti-phase and in-phase oscillations of the profiles of an unstaggered grid. In [3] consideration is given to a more general case of gas flow past a profile in a wind tunnel with perforated walls. Flow past a lattice of profiles with stagger is studied in [4], where the magnitude of the stagger angle is limited by the condition that the lattice leading edge is located in the undisturbed stream.In the present paper we present a method of calculation of the unsteady supersonic flow of a gas past a lattice of profiles with arbitrary stagger. As an example the results are presented of the calculation of the aerodynamic forces and moments acting on an oscillating profile in a wind tunnel with solid walls and in a free jet.     

Coherent structures in unsteady swirling jet flow

An LDA technique and phase-averaging analysis were used to study unsteady precessing flow in a model vortex burner. Detailed measurements were made for Re=15,000 and S=1.01. On the basis of the analysis of phase-averaged data and vortex detection by the λ₂-technique of Joeng and Hussain (1995), three precessing spiral vortex structures were identified: primary vortex (PV), inner secondary vortex (ISV), and outer secondary vortex (OSV). The PV is the primary and most powerful structure as it includes primary vorticity generated by the swirler; the ISV and OSV are considered here as secondary vortical structures. The jet breakdown zone is the conjunction of a pair of co-rotating co-winding spiral vortices, PV and ISV. The interesting new feature described is that the secondary vortices form a three-dimensional vortex dipole with a helical geometry. The effect of coupling of secondary vortices was suggested as a mechanism of enhanced stability reflected in their increased axial extent.     

Effects of sound on flow separation from blunt flat plates

The effect of sound on the flow around plates with semicircular or square leading edges and square trailing edges located in a low turbulence open jet has been studied. In all circumstances the length of the leading edge separation bubbles associated with square leading edge plates was found to oscillate. When sound was applied to the flow around these plates, the leading edge shear layers reattached closer to the leading edge and the oscillations in bubble length occurred at the applied sound frequency, generating patches of concentrated vorticity in the boundary layers. These vorticity patches moved downstream near the plate surface and then beyond the trailing edge to form vortex cores in a street with a Strouhal number equal to the applied sound value. Sometimes these vortex streets are unstable and break down into streets with Strouhal numbers approaching those observed without sound. These effects of sound were not observed in the flow around plates with semicircular leading edges. Without sound, square leading edge plates of intermediate length did not shed regular vortex streets.     

Lagrangian-based investigation of the transient flow structures around a pitching hydrofoil

The objective of this paper is to address the transient flow structures around a pitching hydrofoil by combining physical and numerical studies. In order to predict the dynamic behavior of the flow structure effectively, the Lagrangian coherent structures (LCS) defined by the ridges of the finite-time Lyapunov exponent (FTLE) are utilized under the framework of Navier–Stokes flow computations.In the numerical simulations, the k-ω shear stress transport (SST) turbulence model, coupled with a two-equationγ- Reθ transition model, is used for the turbulence closure.Results are presented for a NACA66 hydrofoil undergoing slowly and rapidly pitching motions from 0~?to 15~?then back to 0~?at a moderate Reynolds number Re = 7.5 × 10~5.The results reveal that the transient flow structures can be observed by the LCS method. For the slowly pitching case,it consists of five stages: quasi-steady and laminar, transition from laminar to turbulent, vortex development, large-scale vortex shedding, and reverting to laminar. The observation of LCS and Lagrangian particle tracers elucidates that the trailing edge vortex is nearly attached and stable during the vortex development stage and the interaction between the leading and trailing edge vortex caused by the adverse pressure gradient forces the vortexes to shed downstream during the large-scale vortex shedding stage, which corresponds to obvious fluctuations of the hydrodynamic response. For the rapidly pitching case, the inflection is hardly to be observedand the stall is delayed. The vortex formation, interaction, and shedding occurred once instead of being repeated three times,which is responsible for just one fluctuation in the hydrodynamic characteristics. The numerical results also show that the FTLE field has the potential to identify the transient flows,and the LCS can represent the divergence extent of infinite neighboring particles and capture the interface of the vortex region.     

Simulations of the unsteady separated flow past a normal flat plate

Well-resolved two-dimensional numerical simulations of the unsteady separated flow past a normal flat plate at low Reynolds numbers have been performed using a fractional step procedure with high-order spatial discretization. A fifth-order upwind-biased scheme is used for the convective terms and the diffusive terms are represented by a fourth-order central difference scheme. The pressure Poisson equation is solved using a direct method based on eigenvalue decomposition of the coefficient matrix. A systematic study of the flow has been conducted with high temporal and spatial resolutions for a series of Reynolds numbers. The interactions of the vortices shed form the shear layers in the near-and far-wake regions are studied. For Reynolds numbers less than 250 the vortices are observed to convect parallel to the freestream. However, at higher Reynolds numbers (500 and 1000), complex interactions including vortex pairing, tearing and deformations are seen to occur in the far-wake region. Values of the drag coefficient and the wake closure length are presented and compared with previous experimental and numerical studies.     

Investigation of the unsteady flow velocity field above an airfoil pitching under deep dynamic stall conditions

The unsteady flow field above a NACA 0012 airfoil pitching under deep dynamic stall conditions has been investigated in a low-speed wind tunnel by means of particle image velocimetry. The measurements of the instantaneous flow velocity field show the characteristic features of the dynamic stall process: formation and development of an organized vortex structure for increasing incidences and the subsequent separation. Vorticity and divergence estimated from the measured data give a good insight into the complex flow behaviour during the downstroke motion. Furthermore, small-scale structures could be observed in the separated flow field and even within the dynamic stall vortex.The authors would like to thank Dr. Schäfer (ISL) for his support in organizing the cooperative measurements, Mr. Seyb (DLR) for his help during the recording of PIV images, Dr. Bretthauer (DLR) and Mr. Vollmers (DLR) for his assistance during the phase of evaluation and post processing of the PIV recordings and Dr. Geißler (DLR) for helpful discussions on the dynamic stall problem.     

Three-dimensional analysis on plates

I.IntroductionGenerally,asathree-dimensionaI(3-D)solid-theplateshouldbeanalysedwiththethickplatetheory.Thethickplatetheoryismultifarious:Acust0marythick[heoryoriginatesfromvariousmodificationsofthethinplatetheory,whichisbasedonKirchhoffLovehypothesis'with…     

Three-dimensional unsteady flow simulations: Alternative strategies for a volume-averaged calculation

This work builds on a SIMPLE-type code to produce two numerical codes of greatly improved speed and accuracy for solution of the Navier–Stokes equations. Both implicit and explicit codes employ an improved QUICK (quadratic upstream interpolation for convective kinematics) scheme to finite difference convective terms for non-uniform grids. The PRIME (update pressure implicit, momentum explicit) algorithm is used as the computational procedure for the implicit code. Use of both the ICCG (incomplete Cholesky decomposition, conjugate gradient) method and the MG (multigrid) technique to enhance solution execution speed is illustrated. While the implicit code is first-order in time, the explicit is second-order accurate. Two- and three-dimensional forced convection and sidewall-heated natural convection flows in a cavity are chosen as test cases. Predictions with the new schemes show substantial computational savings and very good agreement when compared to previous simulations and experimental data.     

On heat and mass transfer in the unsteady squeezing flow between parallel plates

This paper reports the heat and mass transfer characteristics in a viscous fluid which is squeezed between parallel plates. The governing partial differential equations for unsteady two-dimensional flow with heat and mass transfer of a viscous fluid are reduced to ordinary differential equations by similarity transformations. Homotopy analysis method (HAM) is employed to construct the series solution of the problem. Physical interpretation to various embedding parameters is assigned through graphs for temperature and concentration profiles and tables for skin friction coefficient, local Nusselt number and local Sherwood number.     

Determining unsteady aerodynamic forces for three-dimensional plate cascade in subsonic gas flow

The general solution for the problem of three-dimensional gas flow through a cascade of plates was obtained in [1], It is shown below that in the considered direct and inverse aerodynamic problems there may exist nontrivial solutions for uniform boundary conditions. The flow regimes for which such solutions exist may be treated as aerodynamic resonance.The examples presented of the calculation for a plate cascade illustrate the behavior of the unsteady aerodynamic forces near the aerodynamic resonance regimes and make it possible to evaluate the limits of applicability of the hypothesis of plane sections. In addition, the calculation results show the possibility of self-induced vibrations of plate cascades with a single degree of freedom in a subsonic gas stream.     

Measurement and analysis of unsteady flow structures in rotor blade wakes

Time-variant data are obtained to investigate the exit flow field from a rotor in a research compressor. In the free-stream region, the instantaneous data are analogous to one another and to the ensemble averaged free-stream results. However, in the wake region, some of the instantaneous signals are similar to one another and to the ensemble averaged wake, but others differ significantly. These variations in the instantaneous data are interpreted and shown to be due to a vortex street structure in the wake. This is accomplished by: (1) developing a mathematical model of the rotor blade exit flow field based on a wake vortex street structure analogous to the unsteady flow field behind bluff bodies due to classical von Karman vortex shedding; and (2) correlating predictions of both the ensemble averaged and instantaneous rotor blade exit flow fields as well as the velocity probability density distributions from this vortex wake flow field model with the corresponding data. The correlation of the ensemble averaged rotor blade exit flow fields is very good and the flow angle distribution correlation excellent. The predicted instantaneous rotor blade exit flow field exhibits many of the flow features found in the data. Also, the probability density distributions for the data and the vortex wake flow field model are analogous to one another.List of symbols N number of rotor revolutions - S _w rotor blade wake width - S _x vortex core horizontal spacing - S _y vortex core vertical spacing - u velocity component parallel to vortex street motion - v velocity component normal to vortex street motion - W instantaneous relative velocity - W _i velocity induced by vortex street - W free-stream relative velocity - W _s velocity of vortex street - x coordinate parallel to vortex street motion - y coordinate normal to vortex street motion - free-stream relative flow angle - _inst instantaneous relative flow angle - vortex strength     

Effect of suction upon unsteady laminar free convection flow on a vertical infinite flat plate

Summary Unsteady laminar free convection flow past a vertical infinite flat plate subjected to suction is considered. Exact solutions of momentum and energy equations are obtained in two cases: (1) When the plate temperature is proportional to some power of time and (2) when the heat flux at the plate is proportional to some power of time. It is assumed that the suction velocity varies as (time)^–1/2. Expressions for the temperature and velocity profiles are obtained in closed forms in both the cases. Effect of suction on velocity, temperature, skin friction and rate of head transfer is studied for Prandtl numbers 0.02, 0.1, 0.72, 1 and 10.     

Subsonic rarefied gas flow over a rack of flat transverse plates

Parameters of a rarefied gas flow through a rack of flat plates aligned across the flow are studied by means of the joint numerical solution of the Boltzmann and Navier-Stokes equations. A subsonic flow regime is considered. The changes in flow characteristics are calculated as functions of the free-stream velocity and plate temperature. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 59–67, January–February, 2008.     

Linear theory of unsteady gas flow under the influence of nonpotential external forces

We determine in the linear formulation the velocity and pressure fields excited in a compressible medium by a lifting filament that displaces and deforms arbitrarily. For general unsteady motion of such a filament we give explicit formulas that express the velocity at a given point in terms of the intensity of the free vortices entering the audio signal audibility zone constructed for this point. We examine gas flow caused by an arbitrary external body force field.Studies devoted to the determination of gas velocity fields for flow past slender bodies relate primarily to translational motion of a body with a dominant constant velocity [1–3]. Gas velocities for helical motion of a rectilinear lifting filament within the gas have been examined in [4].     

An unsteady airfoil theory applied to pitching motions validated against experiment and computation

An inviscid theoretical method that is applicable to non-periodic motions and that accounts for large amplitudes and non-planar wakes (large-angle unsteady thin airfoil theory) is developed. A pitch-up, hold, pitch-down motion for a flat plate at Reynolds number 10,000 is studied using this theoretical method and also using computational (immersed boundary method) and experimental (water tunnel) methods. Results from theory are compared against those from computation and experiment which are also compared with each other. The variation of circulatory and apparent-mass loads as a function of pivot location for this motion is examined. The flow phenomena leading up to leading-edge vortex shedding and the limit of validity of the inviscid theory in the face of vortex-dominated flows are investigated. Also, the effect of pitch amplitude on leading-edge vortex shedding is examined, and two distinctly different vortex-dominated flows are studied using dye flow visualizations from experiment and vorticity plots from computation.