Rotor Flow Field Research Articles

A note on a class of exact solutions in inviscid rotational flows : Shankar, P.N., 1985. Z. angew. Math. Phys., 36(1):172–173. Fluid Mech. Div., Natl. Aeronautical Lab., Bangalore 560037, India

The inviscid rotational flow field about an infinite cylinder of arbitrary cross-section is determined when the free stream velocity has a component perpendicular to the generators of the cylinder and an arbitrary non-uniform component parallel to the generators.

Linear polymers in nonhomogeneous flow fields. II. The cross‐stream migration velocity

AbstractThe cross‐stream migration velocity v⊥ is that part of the velocity of a particle which has no component in the direction of the undistrubed flow. In order to obtain v⊥ for bead–spring model macromolecules, it is necessary to compute the trace of the matrix product \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell \cdot \underline {{\rm \hat C}} $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ \underline \ell $\end{document} denotes the migration matrix and \documentclass{article}\pagestyle{empty}\begin{document}$ \underline {{\rm \hat C}} $\end{document} is the modified Kramer's matrix. In this paper this is done via an eigenvalue calculation, where the eigenvalues are estimated by using the Rouse eigenfunctions. The results are then checked against the few known exact results and excellent agreement is found. It turns out that v⊥ depends on the third power of the molecular weight for free‐draining polymers. The dependence upon molecular weight becomes weaker with increasing hydrodynamic interaction until, in the nondraining limit, v⊥ ∝ M2.5. A simple yet accurate formula for v⊥ is proposed. In conjunction with the results for D (of Part I), purely rotational flow fields are shown to be characterized by a single parameter, the particle Peclet number Pe. Up to a constant of order one (actually a function of the hydrodynamic interaction parameters h* and h, which can vary only between 0.8 and 2.057), Pe depends only upon D, the mean‐square equilibrium extension R, and q0, the magnitude of the maximum shear rate for the flow.

A note on a class of exact solutions in inviscid rotational flows

The inviscid rotational flow field about an infinite cylinder of arbitrary cross-section is determined when the free stream velocity has a component perpendicular to the generators of the cylinder and an arbitrary non-uniform component parallel to the generators.

Measurements of the acoustic field of a turbulent vortex ring

Turbulent vortex rings are one of the few examples of nearly stable flow structures in high Reynold's number flows. An investigation of their pressure and flow field characteristics could contribute to our understanding of the processes that couple (dilitational) acoustic fields and rotational flow fields. For this study an electromagnetic method for generating vortex rings of highly repeatable form was developed. The propagating rings were visualized by means of laser sheet illumination and aerosol seeding of the flow. The velocity field associated with a vortex ring was measured by multiple pulse modulation of the illuminating laser beam and direct photographing of the observed particle motions. The pressure field associated with the ring was measured with an array of membranes. Numerical data processing methods were employed to distinguish the acoustic component of the total flow field at various distances from the turbulent core of the vortex ring. Some possible implications of the results for low‐wavenumber components of turbulent boundary layer flow will also be discussed. [Research sponsored by ONR.]Turbulent vortex rings are one of the few examples of nearly stable flow structures in high Reynold's number flows. An investigation of their pressure and flow field characteristics could contribute to our understanding of the processes that couple (dilitational) acoustic fields and rotational flow fields. For this study an electromagnetic method for generating vortex rings of highly repeatable form was developed. The propagating rings were visualized by means of laser sheet illumination and aerosol seeding of the flow. The velocity field associated with a vortex ring was measured by multiple pulse modulation of the illuminating laser beam and direct photographing of the observed particle motions. The pressure field associated with the ring was measured with an array of membranes. Numerical data processing methods were employed to distinguish the acoustic component of the total flow field at various distances from the turbulent core of the vortex ring. Some possible implications of the results for low‐wav...

Linearized analysis of the three-dimensional compressible flow through a rotating annular blade row

Linearized solutions for the flow field of a rotating blade row in an infinitely long annular duct are reviewed. An isolated rotor is assumed to operate in a uniform axial flow so that the disturbance field is steady in a blade fixed co-ordinate system. Both three-dimensional and compressibility effects are included, but attention is confined to subsonic flows. Previously published source-flow solutions omitted a term which affected the thickness part of the rotor flow field constructed from them. Corrected source and rotor-thickness solutions are given, and then the source or monopole solution is used to form a pressure dipole solution. The rotor-loading contribution to the flow field is found by superposition of the revised dipole solutions. The present version of the dipole representation of the steady-loading field is shown to be equivalent to an existing vortex representation, but different from an existing dipole representation. The behaviour of the blade-surface pressure and velocity distributions is described for both the thickness and loading cases. Sample numerical evaluations of the surface quantities are presented.

An Examination of Some Simple Numerical Schemes for Calculating Scalar Advection

Abstract The computational damping and dispersion errors of some simple numerical schemes for calculating the advection of a scalar are analyzed. Computation times and accuracy are compared in calculating the two-dimensional transport of a symmetrical distribution in a uniform rotational flow field. Amplification factors, computational phase velocities and effective diffusion coefficients are used to examine the properties of the schemes. Simple tests show that the more accurate methods do not require significantly more computing times in both one and two-dimensional constant and variable flows. Among the better schemes, none can be singled out as “best”. The cubic-spline and second-moment methods are particularly useful for regions of sharp concentration gradients or telescoping grids where the undamped, negative group velocities of the chapeau method prove troublesome. The “best” scheme depends heavily on the geometry and physics of the problem.

Shock Wave and Flow Velocity Measurements in a High Speed Fan Rotor Using the Laser Velocimeter

The laser velocimeter, an instrument capable of making nondisturbing gas velocity measurements, was used to determine shock wave locations and to make gas velocity measurements within the rotating blade row of a 550-m/s (1800-ft/s)-tip speed fan rotor. The velocimeter measures the transit time of a seed particle across interference fringes produced at the intersection of a split and crossed laser beam. The rotor flowfields were obtained at several radial immersions for operating-line and near-stall throttle settings. The results show the change in shock pattern and flow velocity as the compressor is throttled toward stall. Analytical predictions of the flowfield were also obtained using both the method of characteristics and a time-dependent, finite-difference solution of the fluid dynamic equations of motion. The analytical results and the flowfield measurements are considered to be in good agreement.

A New Approach to the Experimental Study of Turbomachinery Flow Phenomena

Measurements of the unsteady flow field over a rotor and within its wake are needed in the development of most turbomachines. The technique advocated is that of data acquisition by on-line computer, using the periodic passing of a blade as a phase reference. The phase-lock averaging process is described as is its use in reducing the noise of raw data traces. Measurements of the unsteady flow over a cascade and of the resulting boundary layer behavior are presented. The approach was used in interpreting the unsteady flow field of an axial-flow compressor rotor and the static pressure distribution over the rotor tip. Finally the application to centrifugal pumps is discussed, enabling the designer to obtain information on the suction pressures and the extent of any separated region.

Laminarization of turbulent flames in rotating environments

The stability limits for transition from laminar to turbulent flow in free boundary layers can be substantially increased by imposing an external centrifugal force field on the boundary layer. For the case of an axial jet introduced into a rotating cylindrical flow, the centrifugal forces can have a stabilizing effect and impede transverse motion of fluid. The centrifugal forces act against the turbulent viscous forces with a consequent reduction in the entrainment of surrounding fluid into the boundary layer. For the case of burning jets, strong density gradients are set up which further influence the stability of the flow. When the density increases radially outward within a centrifugal force field, a stable radial density stratification is set up which again impedes turbulent mixing. The combination of these two stabilizing forces leads to the “laminarization” of flames and results in an increase in the length of the diffusion flames. Experiments were carried out in three systems. In the first, a rotating wire-mesh screen generated a free vortex with a central fuel-gas jet diffusion flame. The second system consisted of a vertical stationary cylindrical tube mounted on a variable swirl generator with a central burning gaseous fuel jet. The third system used was an isothermal model of the second system with a helium jet replacing the fuel jet. Measurements of temperature, gas concentration, velocity, and turbulence characteristics show that the imposition of a rotating flow field on a turbulent diffusion flame results in increase in flame length, reduction of the rate of spread of the flame, and laminarization of the boundaries of the flame. A modified Richardson number is proposed as a criterion for laminar-turbulent transition stability.

Jet flames in rotating flow fields

Experimental studies have been made on methane and propane flames introduced along the axis of vertical free-vortex air flows set up by a cylindrical rotating wire-mesh screen. Flame lengths are shown to be mereased by a factor of 2, and blowoff velocties are increased by a factor of 7. Schlieren photographs, together with velocity and turbulence measurements in an isothermal model, show that mixing and entrainment are considerably reduced and that turbulence is damped over the major portion of the flame length. Near the nozzle exit high rates of mixing are found, which result in increased stability of the flames.

An Analytical Method for Predicting Rotor Wake Geometry

An analytical method for predicting the distorted geometry of a helicopter rotor wake is described. The development of this method is ultimately directed toward providing a more accurate aerodynamic theory for computing the instantaneous rotor flow field and associated blade airloads. It is shown that: (1) realistic self‐induced distortions of a rotor wake represented by numerous discrete vortex elements can be computed by application of the classical Biot‐Savart law and numerical integration techniques and (2) by dividing the wake into a series of near and far wake regions, the computation requirements which have previously prohibited the use of such an analysis as a cost‐effective engineering tool can be appreciably reduced. Sample comparisons of analytical and experimental wake geometries of a rotor in forward flight are presented and indicate the ability of the analysis to predict the characteristic distortion features of the wake.

Erratum: “Local Description of the Flow behind a Steady, Two-Dimensional, Curved Shock Wave”

The local properties of the rotational flow field behind a steady, two-dimensional, curved shock wave which occurs in a supersonic uniform flow of a perfect gas are considered. The states of flow field in the vicinity of a point on a shock wave are described as a power series about this point under the assumption that the shape of the shock wave is regular. The hodograph transformation of such a field becomes singular at the points where Jacobian relating to the transformation vanishes. The fields in the vicinity of such singular points are discussed in detail.

Local Description of the Flow behind a Steady, Two-Dimensional, Curved Shock Wave

The local properties of the rotational flow field behind a steady, two-dimensional, curved shock wave which occurs in a supersonic uniform flow of a perfect gas are considered. The states of flow field in the vicinity of a point on a shock wave are described as a power series about this point under the assumption that the shape of the shock wave is regular. The hodograph transformation of such a field becomes singular at the points where Jacobian relating to the transformation vanishes. The fields in the vicinity of such singular points are discussed in detail.

An Analytic Extension of the Shock-Expansion Method

The problem is considered of calculating approximately the inviscid rotational flow field and pressure distribution about a smooth two-dimensional airfoil with sharp leading and trailing edges in a uniform supersonic or hypersonic stream. The assumption of a perfect gas is made, and the basic flow pattern for the analysis is taken to be given by the simple isentropic shockexpansion method with straight characteristics. An elementary characteristics treatment is discussed to show when the simple shock-expansion method should be satisfactory for computing the surface pressure distribution, and under what circumstances it may be expected to break down. By utilizing characteristic variables the isentropic shock-expansion method is then formulated analytically, and an analytic result is obtained for the shock shape corresponding to this zero-order approximation. In the special case where hypersonic similitude is applicable, tha t is, for slender bodies and high Mach numbers, the shock-shape expression for large distances is found to reduce to the result previously given by Mahony, which for weak shocks and slender bodies in turn reduces to the simple-wave result first given by Friedrichs. Employing the analytic form of the isentropic shock-expansion method as a zero-order approximation, an analytically consistent perturbation method is developed by expanding the dependent flow variables in the exact partial differential equations in powers of the reflection coefficient for simple waves interacting with an oblique shock. The scheme by its nature helps to define those regions in which shock expansion can be used, in addition to taking into account in a perturbation sense the factors neglected in simple shock-expansion theory, namely, the curvature and reflection of the Mach waves and the correct boundary conditions at the shock wave. Analytic solutions are obtained for the first-order corrections, including the surface pressure distribution. The necessary numerical computation of the integrals involved is considerably simpler than a direct application of the method of characteristics. To illustrate the method and its accuracy, the zero-order shock shape and first-order pressure distribution are calculated for a family of parabolic arc airfoils at an infinite free-stream Mach number. These results are compared with rotational characteristic solutions where available, and the present method is found to be in excellent agreement.