Ch. Hirsch

Three Dimensional Flow in a Linear Compressor Cascade at Design Conditions

Experimental data measured upstream, inside and downstream of a large scale linear compressor cascade with NACA 65-1810 blade profile are presented. The flow is surveyed at 15 traverse planes with 14 (in half span) × 24 (in pitch) points inside a passage, and 14 × 33 points downstream exit plane. The measurements are obtained with a small size five hole probe, and wall static pressure taps. It is observed that the three dimensional flow inside and behind the cascade is characterized, not only by the conventional aspects, such as leading edge horseshoe vortices, passage vortices, trailing edge vortex sheet and corner vortices, but also by two spiral node points, formed from the three dimensional separation lines, on suction surface, and the resulting concentrated vortices.Copyright

Genuinely upwind algorithms for the multidimensional Euler equations

A new method for the solution of the multidimensional Euler equations is presented. As opposed to the classical schemes, it is genuinely multidimensional in that the local characteristic directions, into which information is propagated, are detected. Based on this approach, a conservative cell-centered scheme has been formulated. The numerical fluxes are evaluated using MUSCL extrapolations along the characteristic directions. This leads to a family of first- and second-order accurate schemes with an improved resolution as compared to the classical schemes

Rotational Flow Calculations in Three Dimensional Blade Passages

A method to calculate the three-dimensional, inviscid, rotational flow in blade passages is described. The three-dimensional flow is separated into a potential part and a rotational part. For a certain class of inlet flows, this rotational part can be described by a single additional function. The solution method can be seen as an extension of the procedure for solving the three-dimensional potential flow. The Finite Element technique is used and the method is illustrated by calculations of the flow in a rectangular elbow with 90 degrees of turning. Comparisons are made with experimental data and other calculation methods.Copyright

Turbulence Structure in the Wake of an Oscillating Airfoil.

An experimental set-up for turbulence measurements in the wake of a 60 cm chord NACA 0012 oscillating airfoil is described. The airfoil oscillates around an axis at 25% chord distance from the leading edge, with a sinusoidal motion. A slowly moving slanted hot wire anemometer technique combined with a space and time conditional averaging is used to determine all non zero Reynolds stress and velocity wake profiles. Data acquisition is performed through an on-line sampling, digitizing and recording microprocessor controlled system which records the hot wire anemometer signal as well as the probe and wing position as functions of time on digital tape.

Transonic Flow Calculations with Finite Elements

The full potential equation is formulated for transonic flow with an artificial compressibility and discretized with Finite Elements. Bilinear elements are used and the system of equationsis solved iteratively with a relaxation method and with an implicit factorized ADI technique. The methods are briefly described and results are discussed for the channel flow problem.

A Prediction Scheme for the Decay of a Turbomachine Blade Wake

The effect of a steamwise pressure gradient on the decay of a skewed turbomachinery wake is considered. These pressure gradients are generated by the overall radial equilibrium and by the blade boundary layer separation mechanism at the blade trailing edge. The existence of a separation bubble near this trailing edge is shown to exist and gives rise to a pressure rise in a free stagnation point. The ensuing downstream streamwise pressure gradient influences the decay rate of the wake and the transverse pressure gradient influences the momentum thickness. The streamwise velocity defect can be accurately predicted by taking this pressure gradient into account if a profile shape is assumed and with an eddy viscosity concept. The velocity defect of the axial and tangential velocity profiles can be derived from the streamwise velocity profile parameters.Copyright

An orthogonal finite element method for transonic flow calculations

A new method for the numerical integration of the time dependent Euler equations by Finite Elements is presented based on the introduction of orthogonal shape functions. This leads to a diagonal mass matrix. In certain cases, as linear triangular elements and bilinear quadrilateral elements with parallel sides, the obtained scheme is equivalent to a Finite Volume formulation. For a general mesh, the method automatically generates schemes for arbitrary geometries. Examples of applications are presented.

A Radial Mixing Computation Method

A radial mixing calculation method is presented where both convective and turbulent mixing processes are included. The secondary flows needed for the convective mixing are derived from pitch averaged vorticity equations combined with integral methods for the 3D end-wall boundary layers, 3D profile boundary layers and 3D asymmetric wakes. The convective transport due to secondary flows is computed explicitly. The method is applied to a cascade and two single stage rotors. The three test cases show a very different secondary flow behaviour which allows the analysis of the relative importance of the different secondary flow effects. Turbulent diffusion is found to be the most important mixing mechanism, whereas convective mixing becomes significant when overall radial velocities exceed about 5% of the main velocities. The wake diffusion coefficient is found to be representative for the turbulent radial mixing and is the only empirical constant to be determined.Copyright

Boundary Conditions for the Potential Equation in Transonic Internal Flow Calculation

An analysis of internal potential flow is presented showing the existence of multiple potential solutions with shocks for a given mass flow rate. These solutions are related to non isentropic Euler solutions.Inflow and outflow boundary conditions are proposed which uniquely determine the shock position allowing the calculation of potential flows which are either choked or have a supersonic inlet.Numerical computations using a multigrid finite element approach are presented and compared with exact quasi-one-dimensional Euler solutions confirming the ability of the potential method to solve accurately supersonic and choked nozzle flows.Copyright

Flow Prediction in Axial Flow Compressors Including End-Wall Boundary Layers

The end-wall boundary-layer theory of Mellor and Wood has been reformulated in streamline coordinates and extended to include predictions for complete velocity profiles in the end-wall regions. Application to a model compressor shows that all parameters vary in the sense expected from known experimental data. These parameters include variable shape factors, skin friction coefficient, and wall skewing angles. The analysis developed has been coupled to a mainstream flow calculations program based on finite elements. Application to axial flow compressors permits the prediction of the complete velocity triangles, including the wall regions and the end-wall losses. Comparisons with experimental results are presented.Copyright