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NASA NTRS1988

Three-dimensional elliptic grid generation technique with application to turbomachinery cascades

Described is a numerical method for generating 3-D grids for turbomachinery computational fluid dynamic codes. The basic method is general and involves the solution of a quasi-linear elliptic partial differential equation via pointwise relaxation with a local relaxation factor. It allows specification of the grid point distribution on the boundary surfaces, the grid spacing off the boundary surfaces, and the grid orthogonality at the boundary surfaces. A geometry preprocessor constructs the grid point distributions on the boundary surfaces for general turbomachinery cascades. Representative results are shown for a C-grid and an H-grid for a turbine rotor. Two appendices serve as user's manuals for the basic solver and the geometry preprocessor.

Chen, S. C.↗

NASA NTRS1991

A conformal block structured grid for turbomachinery cascades in two dimensions

A block structured conformal transformation is presented for application to turbomachinery cascades. In comparison with the traditional single block cases that are, at best, supplemented with branch cuts, there is a richer variety of choices for the grid topology. The choice presented leads to a substantial improvement in the grid quality. This is reflected in a relatively uniform covering of the cascade region. While grid clustering is not intended or supplied with the block conformal structure, it can be injected afterwards. When viewed as a controlled experiment, the present study provides a significant example of the effect of grid topology upon the grid quality. In a larger sense, this puts some focus upon the effects of grid topology in more general situations.

Wang, Zhu↗

NASA NTRS1982

A computational design method for transonic turbomachinery cascades

This paper describes a systematical computational procedure to find configuration changes necessary to modify the resulting flow past turbomachinery cascades, channels and nozzles, to be shock-free at prescribed transonic operating conditions. The method is based on a finite area transonic analysis technique and the fictitious gas approach. This design scheme has two major areas of application. First, it can be used for design of supercritical cascades, with applications mainly in compressor blade design. Second, it provides subsonic inlet shapes including sonic surfaces with suitable initial data for the design of supersonic (accelerated) exits, like nozzles and turbine cascade shapes. This fast, accurate and economical method with a proven potential for applications to three-dimensional flows is illustrated by some design examples.

Sobieczky, H.↗

NASA NTRS1983

Computation of viscous flows in turbomachinery cascades

Analytic and numerical experiments involving the use of the space-marching method for the prediction of the viscous flow field in turbomachinery cascades indicate that the grid lines in the physical domain must be nearly orthogonal in order to arrive at accurate predictions. For staggered cascades, a nonperiodic grid system was used and appropriate approximations were applied in place of the periodicity boundary conditions upstream and downstream of the cascade. Predicted drag coefficient, turning angle, boundary layer momentum thicknesses, and velocity profiles are compared with experimental data. Good agreement is obtained in most cases.

Pouagare, M.↗

NASA NTRS1983

Hybrid C-H grids for turbomachinery cascades

The three basic types of grids available for two-dimensional cascade configurations are examined with respect to their relative advantages and disadvantages. Subsequently, a hybrid coordinate system is proposed such that it combines the major advantages of the C-type and the H-type meshes. The development of the hybrid grid system employs the patching of appropriate regions of these two basic mesh systems such that the transformed domain has a multi-block structure. Viewing the transformed domain as a three-dimensional surface enables the coordinates to be continuous across the boundaries of the patches in a natural manner.

Ghia, U.↗

NASA NTRS1986

Computation of viscous flows in turbomachinery cascades with a space-marching method

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Pouagare, M.↗

NASA NTRS1988

Progress towards the development of an inviscid-viscous interaction method for unsteady flows in turbomachinery cascades

The velocity and heat transfer characteristics of blade passage flows subject to onset velocities that vary in space and time are calculated by means of a general method involving the solution of inviscid and boundary-layer equations coupled with the Hilbert integral. The performance of this boundary layer method for flows with prescribed pressure distribution is evaluated in terms of two model problems that give attention to the stagnation region. One model corresponds to an oscillating airfoil with moving stagnation point; the other is a simulation of a blade which is subject to a uniform onset velocity.

Cebeci, T.↗

NASA NTRS1991

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Usab, William J., Jr.↗

NASA NTRS1991

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

A new inverse inviscid method suitable for the design of rotating blade sections lying on an arbitrary axisymmetric stream-surface with varying streamtube width is presented. The geometry of the axisymmetric stream-surface and the streamtube width variation with meridional distance, the number of blades, the inlet flow conditions, the rotational speed and the suction and pressure side velocity distributions as functions of the normalized arc-length are given. The flow is considered irrotational in the absolute frame of reference and compressible. The output of the computation is the blade section that satisfies the above data. The method solves the flow equations on a (phi 1, psi) potential function-streamfunction plane for the velocity modulus, W and the flow angle beta; the blade section shape can then be obtained as part of the physical plane geometry by integrating the flow angle distribution along streamlines. The (phi 1, psi) plane is defined so that the monotonic behavior of the potential function is guaranteed, even in cases with high peripheral velocities. The method is validated on a rotating turbine case and used to design new blades. To obtain a closed blade, a set of closure conditions were developed and referred.

Bonataki, E.↗

NASA NTRS1984

Calculation of transonic flow in a linear cascade

Turbomachinery blade designs are becoming more aggressive in order to achieve higher loading and greater range. New analysis tools are required to cope with these heavily loaded blades that may operate with a thin separated region near the trailing edge on the suction surface. An existing, viscous airfoil code was adapted to cascade conditions in an attempt to provide this capability. Comparisons with recently obtained data show that calculated and experimental surface Mach numbers were in good agreement but loss coefficients and outlet air angles were not.

Donovan, L. F.↗

NASA NTRS1984

Calculation of transonic flow in a linear cascade

Donovan, L. F.↗

NASA NTRS1975

On the investigation of cascade and turbomachinery rotor wake characteristics

The objective of the investigation reported in this thesis is to study the characteristics of a turbomachinery rotor wake, both analytically and experimentally. The constitutive equations for the rotor wake are developed using generalized tensors and a non-inertial frame of reference. Analytical and experimental investigation is carried out in two phases; the first phase involved the study of a cascade wake in the absence of rotation and three dimensionality. In the second phase the wake of a rotor is studied. Simplified two- and three-dimensional models are developed for the prediction of the mean velocity profile of the cascade and the rotor wake, respectively, using the principle of self-similarity. The effect of various major parameters of the rotor and the flow geometry is studied on the development of a rotor wake. Laws governing the decay of the wake velocity defect in a cascade and rotor wake as a function of downstream distance from the trailing edge, pressure gradient and other parameters are derived.

Raj, R.↗

NASA NTRS1993

Finite element calculations of transonic flutter in cascades

Aeroelastic stability and response of turbomachinery cascades operating in the transonic regime are explored using a new computational approach. The two-dimensional unsteady Euler equations are used to model the transonic cascade flows, and the cascade blades are modeled as thin plates. To minimize the discretization incompatibility, both the fluid and the solid domains are discretized using finite element procedures. The fluid and the structural models are coupled at the element level by introducing a channel theory, which is analogous to a strip theory in the classical sense. The system of space-discretized equations is marched forward in time using an explicit four-stage Runge-Kutta scheme. Results of free vibration analyses of typical blades are presented and compared to published finite element and Rayleigh-Ritz results. Aeroelastic stability and response characteristics of several transonic cascades are investigated using the new quasi-3D model. These results demonstrate the present 3D finite element blade model is capable of capturing aeroelastic instabilities involving higher modes, including (plate-type) camber bending modes.

Hsiao, Chingteng↗

NASA NTRS1976

The effects of trailing vorticity on the flow through highly loaded cascades

This paper presents a procedure whereby three-dimensional inviscid flow through a highly loaded turbomachinery cascade of lifting lines can be treated by methods corresponding to classical aerodynamic theory. In contrast to earlier linearized (thin airfoil) three-dimensional theory, the present study allows analysis of the flow corresponding to the large turning and/or large pressure ratios induced by practical rotors or stators. For the sake of simplicity, the present paper is limited to incompressible flow through a highly loaded rectilinear cascade and to the design problem; i.e., given blade loading. Formulas are derived for both the mean and the three-dimensional components of the flow; in particular, the velocities at the blades induced by the trailing vorticity associated with nonuniform blade circulation are determined.

Mccune, J. E.↗

NASA NTRS1984

Analysis of inviscid and viscous flows in cascades with an explicit multiple-grid algorithm

A rapid technique is used for calculating inviscid and viscous flows in turbomachinery cascades. The Euler and thin-layer Navier-Stokes equations are solved using the original explicit MacCormack algorithm. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. Convergence to a steady state is accelerated by use of a variable time-step and a multiple-grid scheme. Computer time is reduced through vectorization. Details of the numerical method are presented along with computed results for two low-speed wind tunnel turning vanes, a space shuttle fuel pump turbine rotor, and a supersonic inflow compressor rotor. The method can predict subtle viscous flow phenomena in cascades and is fast enough to be used as a design tool.

Chima, R. V.↗

NASA NTRS1984

Analysis of inviscid and viscous flows in cascades with an explicit multiple-grid algorithm

Chima, R. V.↗

NASA NTRS1991

Computation of supersonic and low subsonic cascade flows using an explicit Navier-Stokes technique and the kappa-epsilon turbulence model

A fully explicit two-dimensional flow solver, based on a four-stage Runge-Kutta scheme, was developed and utilized to predict two-dimensional viscous flow through turbomachinery cascades for which experimental data is available. The formulation is applied to the density averaged Navier-Stokes equations. Several features of the technique improve the ability of the code to predict high Reynolds number flows on highly stretched grids. These include a low Reynolds number compressible form of the k-epsilon turbulence model, anisotropic scaling of artificial dissipation terms and locally varying timestep evaluation based on hyperbolic and parabolic stability considerations. Comparisons between computation and experiment are presented for both a supersonic and a low-subsonic compressor cascade. These results indicate that the code is capable of predicting steady two-dimensional viscous cascade flows over a wide range of Mach numbers in reasonable computational times.

Kunz, R. F.↗

NASA NTRS1983

Computation of internal flows: Methods and applications; Proceedings of the Energy Sources Technology Conference, New Orleans, LA, February 12-16, 1984

The present conference covers computational method applications, viscous-inviscid interaction techniques, viscous flow computational methods, and design-related methods. Attention is given to viscous flows in turbomachinery cascades, forbidden signals and apparent Mach numbers in supersonic cascades, the flow field in an engine particle separator, two-dimensional separated channel flows, turbulent separating flows over a rearward-facing step, the semielliptic analysis of two-dimensional internal and compressible viscous flows, spline solutions of the incompressible Navier-Stokes equations in a mildly nonorthogonal coordinate system, the design of highly loaded blades with blockage in cascade, and a finite analytic method for unsteady, three-dimensional Navier-Stokes equations.

Sockol, P. M.↗