A viscous blade body force model for computational fluid dynamics–based throughflow analysis of axial compressors

In recent years, the computational fluid dynamics (CFD) techniques have attracted enormous interest in the throughflow calculations, and one of the major concerns in the CFD-based throughflow method is the modeling of blade forces. In this article, a viscous blade force model in the CFD-based throughflow program was proposed to account for the loss generation. The throughflow code is based on the axisymmetric Navier–Stokes equations. The inviscid blade force is determined by calculating a pressure difference between the pressure and suction surfaces, and the viscous blade force is related to the local kinetic energy through a skin friction coefficient. The viscous blade force model was validated by a linear controlled diffusion airfoil cascade, and the results showed that it can correctly introduce the loss into the CFD-based throughflow model. Then, the code was applied to calculate the transonic NASA rotor 67, and the calculated results were in good agreement with the measured results, which showed that the calculated shock losses reduce the dependence of the throughflow calculation on the empirical correlation. Last, the 3.5-stage compressor P&W3S1 at 85%, 100%, and 105% of the design speed was performed to demonstrate the reliability of the viscous blade force model in a multistage environment. The results showed that the CFD-based throughflow method can easily predict the spanwise mixing due to the inclusion of the turbulence model, and predicted results were in acceptable agreement with the experimental results. In a word, the proposed viscous blade force model and CFD-based throughflow model can achieve the throughflow analysis with an acceptable level of accuracy and a little time-consuming.

The Effects of Incidence and Deviation on the CFD-Based Throughflow Analysis

A major concern in the Computational Fluid Dynamics (CFD)-based throughflow calculation is the treatment of the incidence and deviation. This paper investigates the effects of the incidence and deviation on the CFD-based throughflow analysis by a time-marching throughflow model. The model is realized by solving complete Navier-Stokes equations with a single grid in the g-wise direction. The inviscid blade force is determined by calculating a pressure difference between the pressure and suction surfaces. The losses are introduced by imposing a blade surface skin friction factor converted from the pressure loss coefficient. And the flow discontinuity problem at the leading and trailing edges is resolved by modifying the mean blade surface to accommodate the incidence and deviation. The sensitivity of the throughflow results to the modification strategy of the mean blade surface is studied through response surface method. And the Kriging-assisted genetic algorithm (GA) is applied to determine the optimal distributions of incidence and deviation in the streamwise direction for NASA Rotor 37. Finally, four examples are provided to validate the throughflow model and to demonstrate the effects of incidence and deviation on CFD-based throughflow analysis at off-design conditions.

Time-marching throughflow analysis of multistage axial compressors based on a novel inviscid blade force model

A time-marching throughflow method for the off-design performance analysis of axial compressors is described. The method is based on the Euler equations, and a new inviscid blade force model is proposed in order to achieve desired flow deflection. The flow discontinuity problems at the leading and trailing edges are tackled by automatic correction of blade mean surface using cubic spline interpolation. Empirical loss models have been integrated into the throughflow model in order to simulate the viscous force effects in the real three-dimensional flow. Two test cases have been presented to validate the throughflow model, including the transonic fan rotor – NASA Rotor 67 working at a near-peak-efficiency point and a 1.5-stage high-speed axial compressor with inlet guide vane operating at 68% nominal speed. Reasonable flow parameters distributions have been obtained in the Rotor 67 fan calculating results, and accurate overall performance characteristics have also been predicted at the strong off-design condition for the 1.5-stage axial compressor. The CPU time of both cases cost less than one minute at one operating point. The results indicate that the developed time-marching throughflow model is effective and efficient in the turbomachinery performance analysis.

Modeling and Analysis of the Inlet Circumferential Fluctuations in Subsonic Rotors

Throughflow method has the limitation inherited from the axisymmetric assumption. With this assumption, the effects induced by three-dimensional blade shaping, such as sweep, cannot be sufficiently described. To conquer these shortcomings, a transport model for the circumferential fluctuation (CF) stresses is developed and integrated into a throughflow model. Three subsonic rotors are selected to validate the transport model and investigate the effect of the CF source terms on the flow fields. The results show that the CF source terms can affect the prediction of mass flow, and redistribute the radial distribution of blade loading. Besides, the radial equilibrium at the inlet of the blade passage is also altered by the CF source terms. Moreover, the CF source terms may have different effects for different swept blades.

Numerical Tools for High Performance Axial Compressor Design for Teaching Purpose

The preliminary design tools, for the design and performance analysis of axial flow compressors, has been developed based on reduced-order throughflow model. The in-house numerical tools developed specially for turbomachinery preliminary sizing and calculation of its operational characteristics is being an interesting experience in both under- and graduate lectures. Appropriate loss correlations have been selected aiming at good geometrical initial sizing. Flow properties distribution has been obtained using meanline code combined with a quasi-3D streamline curvature code. Any number of sections from hub to tip of each blade can be used for the determination of the blade shape. The compressor operation map calculated is validated against published test data. Details of the developed methodology and implementation are discussed.

Toward a High Order Throughflow––Investigation of the Nonlinear Harmonic Method Coupled With an Immersed Boundary Method for the Modeling of the Circumferential Stresses

Capturing a level of modeling of the flow inside a multistage turbomachine, such as unsteadiness for example, can be done at different levels of detail, either by capturing all deterministic features of the flow with a pure unsteady method or by settling for an approximated solution at a lower computational cost. The harmonic methods stand in this second category. Among them, the “nonlinear harmonic method” (NLHM) from He and Ning [1998, “Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines,” AIAA J., 36, pp. 2005–2012] revealed the most efficient. This method consists of solving the fully nonlinear 3D steady problem and a linearized perturbation system in the frequency domain. As it has been shown by the authors that the circumferential variations exhibit a harmonic behavior, it is proposed here to adapt the NLHM to the throughflow model, where the main nonlinear system would be the common throughflow equations and the auxiliary system would give access to the circumferential stresses. As the numerical local explicit impermeability conditions are unsupported by Fourier series, the adaptation of this technique to the throughflow model relies on a reformulation of the blade effect by a smooth force field as in the “immersed boundary method” from Peskin [2002, “The Immersed Boundary Method,” Acta Numerica, 11, pp. 1–39]. A simple example of an inviscid flow around a cylinder will illustrate the preceding developments, bringing back the mean effect of the circumferential nonuniformities into the meridional flow.

On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

This paper presents a throughflow analysis tool developed in the context of the average-passage flow model elaborated by Adamczyk. The Adamczyk’s flow model describes the 3D time-averaged flow field within a blade row passage. The set of equations that governs this flow field is obtained by performing a Reynolds averaging, a time averaging, and a passage-to-passage averaging on the Navier–Stokes equations. The throughflow level of approximation is obtained by performing an additional circumferential averaging on the 3D average-passage flow. The resulting set of equations is similar to the 2D axisymmetric Navier–Stokes equations, but additional terms resulting from the averages show up: blade forces, blade blockage factor, Reynolds stresses, deterministic stresses, passage-to-passage stresses, and circumferential stresses. This set of equations represents the ultimate throughflow model provided that all stresses and blade forces can be modeled. The relative importance of these additional terms is studied in the present contribution. The stresses and the blade forces are determined from 3D steady and unsteady databases (a low-speed compressor stage and a transonic turbine stage) and incorporated in a throughflow model based on the axisymmetric Navier–Stokes equations. A good agreement between the throughflow solution and the averaged 3D results is obtained. These results are also compared to those obtained with a more “classical” throughflow approach based on a Navier–Stokes formulation for the endwall losses, correlations for profile losses, and a simple radial mixing model assuming turbulent diffusion.

On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

This paper presents a throughflow analysis tool developed in the context of the average-passage flow model elaborated by Adamczyk. The Adamczyk’s flow model describes the 3-D time-averaged flow field within a blade row passage. The set of equations that governs this flow field is obtained by performing a Reynolds averaging, a time averaging and a passage-to-passage averaging on the Navier-Stokes equations. The throughflow level of approximation is obtained by performing an additional circumferential averaging on the 3-D average-passage flow. The resulting set of equations is similar to the 2-D axisymmetric Navier-Stokes equations but additional terms resulting from the averages show up: blade forces, blade blockage factor, Reynolds stresses, deterministic stresses, passage-to-passage stresses and circumferential stresses. This set of equations represents the ultimate throughflow model provided that all stresses and blade forces can be modeled. The relative importance of these additional terms is studied in the present contribution. The stresses and the blade forces are determined from 3-D steady and unsteady databases (a low speed compressor stage and a transonic turbine stage) and incorporated in a throughflow model based on the axisymmetric Navier-Stokes equations. A good agreement between the throughflow solution and the averaged 3-D results is obtained. These results are also compared to those obtained with a more “classical” throughflow approach based on a Navier-Stokes formulation for the endwall losses, correlations for profile losses and a simple radial mixing model assuming turbulent diffusion.