• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.3 s.108
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• pp.263-269
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• 2006

The objective of the present work is to develop a time-domain numerical method of broadband noise in a cascade of airfoils. This paper focuses on dipolar broadband noise sources, resulting from the interaction of turbulent inflows with the flat-plate airfoil cascade. The turbulence response of a two-dimensional cascade is studied by solving both of the linearised and the full nonlinear Euler equations employing accurate higher order spatial differencing, time stepping techniques and non-reflecting inflow/outflow boundary condition. The time-domain result using the linearised Euler equations shows good agreement with the analytical solution using the modified LINSUB code. Through the comparison of the nonlinear time-domain result using the full nonlinear Euler equations with the linear, it is found that the acoustic mode amplitude of the nonlinear response is less than that of the linear response due to the energy cascade from low frequency components to the high frequency ones. Considering the merits of the time-domain methods over the typical time-linearised frequency-domain analysis, the current method is expected to be promising tools for analyzing the effects of the airfoil shapes, non-uniform background flow, linear-nonliear regimes on the broadband noise due to turbulence-cascade interaction.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.812-817
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• 2005

The objective of the present work is to develop a time-domain numerical method of broadband noise in a cascade of airfoils. This paper focuses on dipole broadband noise sources, resulting from the interaction of turbulent inflows with the flat-plate airfoil cascade. The turbulence response of a two-dimensional cascade is studied by solving both of the linearised and full nonlinear Euler equations employing accurate higher order spatial differencing, time stepping techniques and non-reflecting inflow/outflow boundary condition. The time-domain result using the linearised Euler equations shows good agreement with the analytical solution using the modified LINSUB code. Through the comparison of the nonlinear time-domain result using the full nonlinear Euler equations with the linear, it is found that the acoustic mode amplitude of the nonlinear response is less than that of the linear response due to the energy cascade from low frequency components to the high frequency ones. Considering the merits of the time-domain methods over the typical time-linearised frequency-domain analysis, the current method is expected to be promising tools for analyzing the effects of the airfoil shapes, non-uniform background flow, linear-nonliear regimes on the broadband noise due to gust-cascade interaction.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2010.05a
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• pp.74-75
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• 2010

Inflow broadband noise is generated when turbulence in the rotor wakes impinges on the downstream stator vanes. In this paper a three-dimensional model is developed to investigate the broadband noise due to turbulence-cascade interaction. In the newly-developed model, we consider the effects of incident turbulent gust component in span-wise direction on the inflow broadband noise. The quasi-three-dimensional theory is deduced based on the tonal analytic theory of Smith (1972) and two-dimensional broadband noise generalization by Cheong et al. (2006; 2009). Extending the modified LINSUB code, quasi-three-dimensional computational results are presented. Finally, we compare these computational results with time-domain results to validate the theory.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.7
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• pp.685-691
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• 2012

It is essential for the accurate time-domain prediction of broadband noise due to turbulence-cascade interaction to develop inflow/outflow boundary conditions to satisfy the following three requirements: to maintain the back ground mean flow, to nonreflect the outgoing disturbances and to generate the specified input gust. The preceding study showed that perfectly matched layer(PML) boundary condition was successfully applied to absorb the outgoing disturbances and to generate the specified gust in the time-domain computations of broadband noise due to interaction of incident gust with a cascade of flat-plates. In present study, PML boundary condition is extended in order to predict steady mean flow that is needed for the computation of noise due to interaction of incident gust with a cascade of airfoils. PML boundary condition is originally designed to absorb flow disturbances superimposed on the steady meanflow in the buffer zone. However, the steady meanflow must be computed before PML boundary condition is applied on the flow computation. In the present paper, PML equations are extended by introducing source term to maintain desired mean flow conditions. The extended boundary condition is applied to the benchmark problem where the meanflow around a cascade of airfoils is predicted. These illustrative computations reveal that the extended PML equations can effectively provide and maintain the target meanflow.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.9 s.114
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• pp.937-948
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• 2006

In this study, a fluid/structure coupled analysis system for simulating complex flow-induced vibration (FIV) phenomenon of cascades has been developed. The flow is modeled using Euler and Wavier-Stokes equations with different turbulent models. The fluid domains are modeled using the unstructured grid system with dynamic deformations due to the motion of structural boundary. The Spalart-Allmaras (S-A) and the SST ${\kappa}-{\omega}$ turbulent models are used to predict the transonic turbulent flows. A fully implicit time marching scheme based on the Newmark direct integration method is used in order to solve the coupled governing equations for viscous flow-induced vibration phenomena. For the purpose of validation for the developed FIV analysis system, comparison results for computational analyses of steady and unsteady aerodynamics and flutter analyses are presented in the transonic flow region. In addition, flow-induced vibration analyses for the isolated cascade and multi-blades cascade models have been conducted to show the physical fluid-structure interaction effects in the time domain.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.793-802
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• 2006

In this study, a fluid/structure coupled analysis system for simulating complex flow-induced vibration (FIV) phenomenon of cascades has been developed. The flow is modeled using Euler and Wavier-Stokes equations with different turbulent models. The fluid domains are modeled using the unstructured grid system with dynamic deformations due to the motion of structural boundary. The Spalart-Allmaras (S-A) and the SST ${\kappa}-{\omega}$ turbulent models are used to predict the transonic turbulent flows. A fully implicit time marching scheme based on the Newmark direct integration method is used in order to solve the coupled governing equations for viscous flow-induced vibration phenomena. For the purpose of validation for the developed FIV analysis system, comparison results for computational analyses of steady and unsteady aerodynamics and flutter analyses are presented in the transonic flow region. In addition, flow-induced vibration analyses for the isolated cascade and multi-blades cascade models have been conducted to show the physical fluid-structure interaction effects in the time domain.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.6 s.99
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• pp.687-696
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• 2005

Acoustic power spectrum of the upstream and downstream sound field due to an isotropic frozen turbulent gust impinging on a cascade of flat plate airfoils are computed by using a analytic formulation derived from Smith's method, and Whitehead's LINSUB codes. A parametric study of the effects on sound power of the number of blades and turbulence length scale is performed with an emphasis on analyzing the characteristics of sound power spectrum. Through the comparison of the computed results of sound power, it is found that acoustic power spectrum from the 2-D cascade subject to a ingested turbulence can be categorized into two distinct regions. one is lower frequency region where some spectral components of turbulence do not contribute to the cut-on acoustic modes and therefore the effect of the cascade geometry is more dominant ; the other is higher frequency region where all of spectral components of turbulence make contributions to cut-on acoustic modes and thus acoustic power is approximately proportional to the blade number.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.1467-1475
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• 2007

This paper investigates the modal acoustic power by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. Basic formulation for the acoustic power upstream and downstream is based on the analytical theory of Smith and its generalization due to Cheong et al. The acoustic power spectrum has been expressed as the sum of cut-on acoustic modes, whose modal power is the product of three terms: a turbulence series, an upstream or downstream power factor and an upstream or downstream acoustic response function. The effect of these terms in the modal acoustic power has been examined. For isotropic turbulence gust, the turbulent series are only reducing factor of the modal acoustic power. The power factor tends to reduce the modal acoustic power in the upstream direction, although the power factor is liable to increase the modal acoustic power in the downstream direction. The modes close to cut-off are decreasing strongly, especially in the downstream direction. Therefore the modes close to cut-off don't contribute highly to the radiated acoustic power in the downstream direction, although the modal acoustic pressure is high for these modes.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.1
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• pp.61-70
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• 2008

This paper investigates the modal acoustic power by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. Basic formulation for the acoustic power upstream and downstream is based on the analytical theory of Smith and its generalization due to Cheong et al. The acoustic power spectrum has been expressed as the sum of cut-on acoustic modes, whose modal power is the product of three terms: a turbulence series, an upstream or downstream power factor and an upstream or downstream acoustic response function. The effect of these terms in the modal acoustic power has been examined. For isotropic turbulence gust, the turbulent series are only reducing factor of the modal acoustic power. The power factor tends to reduce the modal acoustic power in the upstream direction, although the power factor is liable to increase the modal acoustic power in the downstream direction. The modes close to cut-off are decreasing strongly, especially in the downstream direction. Therefore the modes close to cut-off don't contribute highly to the radiated acoustic power in the downstream direction, although the modal acoustic pressure is high for these modes.