Calculation of Horseshoe Vortex Flow Without Numerical Mixing

The usefulness of three-dimensional flow calculations has frequently been obscured by the numerical mixing present in the calculation methods. This paper describes a new method of forming the finite difference momentum equations. The new method results in well posed equations which introduce no numerical mixing. It may be used with orthogonal or non-orthogonal grids and with uniform or highly non-uniform grid spacing. The method is demonstrated by comparing it with upwind differencing on the calculation of a simple example. It is then used in an elliptic pressure-correction calculation procedure to calculate a leading edge horseshoe vortex about a Rankine half body. The results compare well with the experimental data presented in a companion paper.

Use of an Inverse Method for the Design of High Efficiency Compressor and Turbine Blades With Large Change in Radius

Extension of the time-marching computations of flows in 2-D blade cascades to the case of cascades with variable radius and stream tube thickness. One of the specific cases analyzed is that of purely radial cascades. Direct and inverse calculations are made, in non-viscous subsonic or supersonic flows, with or without shock waves. Examples of the design of high efficiency airfoil optimization for radial flow compressor rotors or Stators or inward flow turbine inlet guide vanes are presented.

Computation of Secondary Flows in an Axial Flow Compressor Including Inviscid and Viscous Flow Computation

A computational method for secondary flows in a compressor has been extended to treat stalled flows. An integral equation is used which simulates the inviscid flow at the wall, under the viscous flow influence. We present comparisons with experimental results for a 2D stalled boundary layer, and for the secondary flow in a highly loaded stator of an axial flow compressor.

The Active Magnetic Bearing Enables Optimum Damping of Flexible Rotor

The active magnetic bearing is based on the use of forces created by a magnetic field to levitate the rotor without mechanical contact between the stationary and moving parts. A ferromagnetic ring fixed on the rotor “floats” in the magnetic fields generated by the electromagnets, which are mounted as two sets of opposing pairs. The current is transmitted to the electromagnetic coils through amplifiers. The four electromagnets control the rotor’s position in response to the signals transmitted from the sensors. The rotor is maintained in equilibrium under the control of the electromagnetic forces. Its position is determined by means of sensors which continuously monitor any displacements through an electronic control system. As in every control system, damping of the loop is provided by means of a phase advance command from one or more differenciating circuits of the position error signal. The capability of modifying the electromagnetic force both in terms of amplitude and phase leads to the benefit of specific properties for the application, in particular: - automatic balancing characterized by the rotation of the moving part around its main axis of inertia, and not around the axis of the bearings allowing operation without vibrations, - adjustable damping of the suspension allowing easy passing of the critical speeds of the rotor, - high and adjustable stiffness yielding maximum accuracy of rotor equilibrium position, - permanent diagnosis of machine operation due to the knowledge of all rotation characteristics (speed, loads on the bearings, position of the rotation axis, eccentricity, out-of-balance, disturbance frequency).

An Investigation of the Transverse Velocity Profile in the Case of Internal Viscous Aerodynamic Problems

The development of transverse velocity profile is directly related to the development of secondary vorticity. In the internal aerodynamics case with potential external flow, although vorticity remains confined inside the viscous shear layer, secondary vorticity induced velocities exist outside of it. If the secondary vorticity field is known, the induced secondary velocity field is well approximated following Hawthorne’s classical analysis. In the present work, the above analysis is used to separate the velocity field in the transverse plane into a potential and a rotational part. In the case of confined flows, the rotational part is confined inside the viscous shear layer, while the potential part occupies the whole flow field. This last part is the consequence of the “displacement” effects of the shear layer in the transverse plane. Therefore, the present work allows a re-examination of the flow two-zone model (separation of the flow field in a viscous and an inviscid part) in confined flows. On the other hand, the limitations of Hawthorne’s theory are examined, while a parallel analysis is presented for the case where the secondary vorticity distribution varies not only along the blade height, but also circumferentially.

Penalty Function Finite Element Analysis of Steady Viscous Incompressible Flow in Rotating Coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuille flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimental measurements.

Simplified Method for Flow Analysis and Performance Calculation Through an Axial Compressor

This paper describes a fast computation method of the flow through multistage axial compressors of the industrial type. The flow is assumed to be axisymmetric between the blade rows which are represented by actuator disks. Blade row losses and turning are calculated by means of correlations. The equations of motion are linearized with respect to the log of static pressure, whose variation along the radius is usually of limited extent for the type of machines for which the method has been developed. In each computing plane (i.e. between the blade rows) two flows are combined: a basic flow with constant pressure satisfying the mass flow requirements and a perturbation flow fulfilling the radial equilibrium condition. The results of a few sample calculations are given. They show a satisfactory agreement with a classical duct flow method although the computing time is reduced by a factor five. The method has also been coupled with a surge line prediction calculation.

A New Diffuser Mapping Technique

A rigorous derivation of the K = Cpi − Cp diffuser recovery and loss equation is presented and the critical assumptions to yield this simplified relationship are critiqued. Confirmation of the equation is achieved using precise laboratory data and a new diffuser loss-map is presented which facilitates engineering diffuser design work, even when a Kline-map is unavailable. Numerous application examples for turbomachinery analysis are given.

Size Effects in Small Radial Turbines

The existence of size effects in small radial flow turbines, such as those used in automotive turbocharger units, has been investigated under steady flow conditions. Three geometrically similar turbines (rotor diameters 101.6, 67.73 and 50.8 mm respectively) have been tested and a ‘size’ effect was observed with the dimensionless mass flow and peak efficiency diminishing with a decrease in rotor diameter. Internal pressure variations were observed in all three turbines which could have a significant influence in relation to blade fatigue failure.

Relative Flow Structure at Exit From an Axial Compressor Rotor in Rotating Stall

The phase-lock-averaging (PLA) technique is used in association with a traverse gear mounted on an axial compressor rotor to explore the flow field at exit from the rotor during rotating stall. The technique requires the use of a trigger hot-wire anemometer also mounted on the rotor to ensure the proper location of the stall cell in relation to the measurement probe. The probe consists of a three-wire non-orthogonal array which may be traversed radially and peripherally over a complete blade passage. By a systematic adjustment of the probe orientation angle, the presence of reverse flow is detected. A mathematical procedure for the determination of the magnitude and direction of the flow vector is presented. On the basis of a large collection of phase-locked data it is demonstrated that the leading and trailing edges of the cell travel at a non-uniform rate and in such a way as to vary cyclically in peripheral extent with a period related to the blade passing fequency. The peripheral distribution of the flow vector at successive instants of relative time is also produced from the data collection and the evolution of the stall cell structure is presented.