Analysis of pressure field in time domain using nonlinear reduced frequency approach in unsteady transonic flows

Abstract

Purpose -The purpose of this paper is to discuss the capability of nonlinear frequency domain (NLFD) method in predicting surface pressure coefficient presented in the time domain in unsteady transonic flows. Design/methodology/approach -In this research, the solution and spatial operator are approximated by discrete form of Fourier transformation and resulting nonlinear equations are solved by use of pseudo-spectral approach. Considered transonic flows involve different flow pattern on the airfoil surfaces. One of the test cases involves moving shocks on both lower and upper airfoil surfaces and in the two other test cases a moving shock occurs only on the upper surface. Findings -Pressure distributions presented in the time domain using NLFD are compared with three test cases. Results show that NLFD predicts reasonable pressure distributions in time domain except in vicinity of shock positions. Although this method may predict unfair results near shock positions, however gives good estimates for global properties such as lift coefficient. Originality/value -In the previous works on NLFD method, the flow field results have been limited to representing the pressure in the frequency domain or global coefficients such as lift coefficients. No details of pressure distributions in the time domain have been provided in such investigations. In this research, by presenting the pressure in the time domain, the conditions on which good pressure distributions are obtained are demonstrated. IntroductionThe calculation of unsteady flows continues to challenge computational fluid dynamists (CFD). This challenge comes from the fact that in addition to preserving the accurate spatial discretization for steady-state solutions, unsteady codes should also accurately resolve the time history of the solution. The challenge to CFD lies in this added dimension and its associated computational cost.The time accurate methods are common ones in solving unsteady flows. These methods include explicit and implicit time stepping schemes and factored ADI. Although these methods are applicable to a wide range of unsteady flows, they consume more computational time than steady-state solvers. In these methods, the semi-discrete form of governing equations is constructed by discretizing the space while leaving the time term. Finally, advancing in time leads to the solution.An alternative to the time accurate methods is to assume a periodic solution over a time interval regarding the fact that transient portion of solution is of less importance. Examples of such solutions are among unsteady flows in turbomachinery cascades. Given the assumption of periodicity, some special methods can be used to calculate the solution. It is evident that the transient decay of the solution using these methods cannot be admitted as a part of the solution.

Flow Frictional Characteristics of Air–Water Flow Characteristics under Stable and Transverse Vibration Conditions in Horizontal Channels

“…Two-phase flow status widely consists of the power, petroleum, chemical employment, aerospace, and the nuclear energy [1][2][3][4][5] fields. Therefore, the complex free interfacial motion analysis between two phases is significant.…”

Assessment of turbulence models for transonic oscillating airfoil

“…In comparison to the URANS models, ZDES is more compatible with the experimental data, especially in the higher frequencies. Capability of nonlinear frequency domain (NLFD) method in predicting details of unsteady transonic flow-fields was investigated by Kharati Koopaee et al (2010). Results showed that NLFD method could predict reasonable pressure distribution in the time domain except in vicinity of moving shock positions.…”