K. D. Papailiou

Adaptive Simulation of Gas Turbine Performance

Greater use is being made of dynamic simulation of energy systems as a design tool for selecting control strategies and establishing operating procedures. This paper discusses the dynamic modeling of a gas-fired combined-cycle power plant with a gas turbine, a steam turbine, and an alternator-all rotating on a common shaft. A waste-heat boiler produces steam at two pressures using heat from the gas turbine flus gas. The transient behavior of the system predicted by the model for various upset situations appears physically reasonable and satisfactory for the operating constraints

Adaptive Modeling of Jet Engine Performance with Application to Condition Monitoring

A method of simulation of the performance of jet engines, with the possibility of adapting to engine particularities, is presented. It employs an adaptation procedure coupled to a performance model solving the component matching problem. The proposed method can provide accurate simulation for engines of the same type, with differences that are due to manufacturing or assembly tolerances. It does not require accurate component maps, because they are derived during the adaptation procedure. It can also be used for health monitoring purposes, for component fault identification, and condition assessment. The effectiveness of the proposed method is demonstrated by application to two commercial jet engines.

Gas Turbine Component Fault Identification by Means of Adaptive Performance Modeling

The method of adaptive modelling of Gas Turbine performance, proposed in the past by the present authors, is finding a new application in component fault detection. An appropriate choice of component characteristic parameters gives the possibility of characterizing their “health condition”, by appropriate processing of selected measured quantities according to the principles of adaptive modelling. Both a general deterioration of components and identification (kind, location) of component faults can be achieved. The proposed methodology is presented together with an experimental investigation of Gas Turbine faults. A commercial Gas Turbine has been used as a test vehicle and various kinds of faults have been implanted. An analysis of the results of the investigation provides information about the influence of the occurrence of such faults on engine performance. On the other hand, these data provide a basis for demonstrating the capabilities of the above mentioned methodology, as a powerful tool for diagnostic applications.Copyright

An inverse inviscid method for the design of quasi-three-dimensional turbomachinery cascades

The calculation of the blade shape, when the desired velocity distribution is imposed, has been the object of numerous investigations in the past. The object of this paper is to present a new method suitable for the design of turbomachinery stator and rotor blade sections, lying on an arbitrary axisymmetric stream-surface with varying streamtube width. The flow is considered irrotational in the absolute frame of reference and compressible. The given data are the streamtube geometry, the number of blades, the inlet flow conditions and the suction and pressure side velocity distributions as functions of the normalized arc-length. The output of the computation is the blade shape that satisfies the above data. The method solves an elliptic type partial differential equation for the velocity modulus with Dirichlet and periodic type boundary conditions on the (potential function, stream function)-plane ([Phi], [Psi]). The flow angle field is subsequently calculated solving an ordinary differential equation along the iso-[Phi] or iso-[Psi] lines. The blade coordinates are, finally, compared by numerical integration. A set of closure conditions has been developed and discussed in the paper. The method is validated on several test cases and a discussion is held concerning its application and limitations.

On the 3-D inverse potential target pressure problem. Part 1. Theoretical aspects and method formulation

An inverse potential methodology is introduced for the solution of the fully 3-D target pressure problem. The method is based on a potential function/stream function formulation, where the physical space is mapped onto a computational one via a body-fitted coordinate transformation. A potential function and two stream vectors are used as the independent natural coordinates, whilst the velocity magnitude, the aspect ratio and the skew angle of the elementary streamtube cross-section are assumed to be the dependent ones. A novel procedure based on differential geometry and generalized tensor analysis arguments is employed to formulate the method. The governing differential equations are derived by requiring the curvature tensor of the flat 3-D physical Eucledian space, expressed in terms of the curvilinear natural coordinates, to be zero. The resulting equations are discussed and investigated with particular emphasis on the existence and uniqueness of their solution. The general 3-D inverse potential problem, with ‘target pressure’ boundary conditions only, seems to be illposed accepting multiple solutions. This multiplicity is alleviated by considering elementary streamtubes with orthogonal cross-sections. The assumption of orthogonal stream surfaces reduces the number of dependent variables by one, simplifying the governing equations to an elliptic p.d.e. for the velocity magnitude and to a second-order o.d.e. for the streamtube aspect ratio. The solution of these two equations provides the flow field. Geometry is determined independently by integrating Frenet equations along the natural coordinate lines, after the flow field has been calculated. The numerical implementation as well as validation test cases for the proposed inverse methodology are presented in the companion paper (Paper 2).

Compressible flow airfoil design using natural coordinates

Abstract An irrotational inviscid compressible inverse design method for two-dimensional airfoil profiles is described. The potential (φ) and streamfunction (ψ) are used as the independent natural coordinates. The physical space on which the boundaries of the airfoil are sought, is mapped onto the (φ, ψ) space via a body-fitted coordinate transformation. A novel procedure based on differential geometry arguments is employed to derive the governing equations for the inverse problem, by requiring the curvature of the flat 2-D Euclidean space to be zero. An auxiliary coordinate transformation permits the definition of C-type computational grids on the (φ, ψ) plane resulting in a more accurate description of the leading edge region. Geometry is determined by integrating Frenet equations along the grid lines. A two-parameter iterative scheme has been incorporated in the design procedure in order to assure closure of the trailing edge. To validate the method, inverse calculation results are compared with direct, ‘reproduction’, calculation results. The design procedure of a new airfoil shape is also presented.

Numerical simulation of blade fault signatures from unsteady wall pressure signals

A method for establishing signatures of faults in the rotating blades ofa gas turbine compressor is presented. The method employs a panel technique for the calculation of the flow field around blade cascades, with disrupted periodicity, a situation encountered when a blade fault has occurred. From this calculation, time signals of the pressure at a location on the casing wall, facing the rotating blades, are constituted. Processing these signals, in combination with healthy pressure signals, allows the constitution of fault signatures. The proposed method employs geometric data, as well as data about the operating point of the engine. It gives the possibility of establishing the fault signatures without the need of performing experiments with implanted faults. The successful application ofthe method is demonstrated by comparison of signatures obtained by simulation to signatures derived from experiments with implanted blade faults, in an industrial.gas turbine.

Evaluation of beam refraction effects in a 3D laser Doppler anemometry system for turbomachinery applications

The paper presents a general mathematical procedure for the calculation of the measuring location of three pairs of laser beams and of the shape of the created measuring volumes after refraction at curved surfaces. The relative displacement in space of the beams and the corresponding velocity component inclinations are also calculated. The beam equations are solved, without any small-angle approximations, for an arrangement corresponding to a 3D laser Doppler anemometer. The proposed method has been validated by comparison with experimental results. The correction procedure has been applied to a typical configuration of a turbomachinery passage and representative beam displacement calculations are presented. Possibilities offered by the method in designing experiments as well as correcting obtained results are discussed.

On the 3-D inverse potential target pressure problem. Part 2. Numerical aspects and application to duct design

A potential function/stream function formulation is introduced for the solution of the fully 3-D inverse potential ‘target pressure’ problem. In the companion paper (Part 1) it is seen that the general 3-D inverse problem is ill-posed but accepts as a particular solution elementary streamtubes with orthogonal cross-section. Under this simplification, a novel set of flow equations was derived and discussed. The purpose of the present paper is to present the computational techniques used for the numerical integration of the flow and geometry equations proposed in Part 1. The governing flow equations are discretized with centred finite difference schemes on a staggered grid and solved in their linearized form using the preconditioned GMRES algorithm. The geometry equations which form a set of first-order 0.d.e.s are integrated numerically using a second-order-accurate space marching scheme. The resulting computational algorithm is applied to a double turning duct and a 3-D converging-diverging nozzle ‘reproduction’ test case.

A coupled two-phase shear layer/liquid film calculation method. Formulation of the physical problem and solution algorithm

Abstract A coupled two-phase shear layer/liquid film calculation method is presented for the prediction of the simultaneous motion of a wavy liquid film and the two-phase stream flowing above it. Conservation equations, for both the shear layer and the liquid film, are cast in a compatible integral form and solved together through a space-marching technique. The system of equations resulting for both streams is enhanced through a set of semi-empirical models, appropriately modified to match the proposed method, in order to effect closure. These models deal with various physical aspects including (a) velocity profiles within the liquid film, (b) the structure of the interface and (c) any exchange of information between the two streams. Evaluation of the method is performed in cases where liquid films are developed along flat surfaces, for which measurements and/or numerical results are available.