Xiaodong Ren

A multi-dimensional high-order DG-ALE method based on gas-kinetic theory with application to oscillating bodies

This paper presents a multi-dimensional high-order discontinuous Galerkin (DG) method in an arbitrary Lagrangian-Eulerian (ALE) formulation to simulate flows over variable domains with moving and deforming meshes. It is an extension of the gas-kinetic DG method proposed by the authors for static domains (X. Ren et al., 2015 22). A moving mesh gas kinetic DG method is proposed for both inviscid and viscous flow computations. A flux integration method across a translating and deforming cell interface has been constructed. Differently from the previous ALE-type gas kinetic method with piecewise constant mesh velocity at each cell interface within each time step, the mesh velocity variation inside a cell and the mesh moving and rotating at a cell interface have been accounted for in the finite element framework. As a result, the current scheme is applicable for any kind of mesh movement, such as translation, rotation, and deformation. The accuracy and robustness of the scheme have been improved significantly in the oscillating airfoil calculations. All computations are conducted in a physical domain rather than in a reference domain, and the basis functions move with the grid movement. Therefore, the numerical scheme can preserve the uniform flow automatically, and satisfy the geometric conservation law (GCL). The numerical accuracy can be maintained even for a largely moving and deforming mesh. Several test cases are presented to demonstrate the performance of the gas-kinetic DG-ALE method.

Investigation of Compressor Tip Clearance Flow Based on the Discontinuous Galerkin Methods

The tip clearance flow has a significant influence on the compressor performance and stability. CFD, which is a current tool, has been widely used to investigate the flow by many researchers. In this paper, an unstructured-grid code based on a RKDG method was developed with an improved vertex-based slope limiter to ensure the nonlinear stability. The limiter tests show that the improved limiter has less numerical dissipation and it can keep the high-order accuracy.The performance for NASA Rotor 37 was simulated to validate the RKDG code. The results are compared with the experimental data and the ones computed by NUMECA FINE™/Turbo. It is shown that the results computed by the RKDG code are in better agreement with the experimental data, which implies that the high-order accuracy method is very important for improving the CFD reliability.Finally, the tip clearance flow of the compressor was investigated using the RKDG code. It is found that the tip leakage jet flow could be separated into two parts and they go downstream separately without mixing.© 2013 ASME

Numerical investigation of subsynchronous vibration in floating ring bearings

Floating ring bearings are popular among turbochargers due to their simplicity and reliability. The disappearance of subsynchronous vibration with the increase of shaft speed in a low oil-supplied pressure floating ring bearing is reported by Hatakenaka and Yanai. This finding may help eliminate the noise and decrease the loss of turbochargers. This work aims to explain this phenomenon in the low oil-supplied floating ring bearing using computational fluid dynamic. Steady computational fluid dynamic calculation is conducted to validate the effect of air entrainment. Transient computational fluid dynamic calculation method with mesh motion method is established. The subsynchronous vibration of the shaft can be obtained by discrete Fourier transform analysis. The results are validated by comparing them with those in the literature. It is found that the disappearance of the subsynchronous vibration is the result of the change in lubricant properties caused by the air entrainment.

Aero-thermal coupled through-flow method for cooled turbines with new cooling model

The aero-thermal–coupled phenomenon is significant in modern cooled turbines, and an aero-thermal coupled through-flow method has previously been developed by the authors for considering the influence of heat transfer and coolant mixing in through-flow design. However, the original cooling model is not capable of calculating the distribution of the coolant mass flow rate and pressure loss in complex cooling structures. Therefore, in this paper, a one-dimensional flow calculation for the internal coolant is introduced into the heat transfer calculation to further improve the through-flow cooling model. Based on various empirical correlations, the cooling model can be used to simulate different cooling structures, such as ribbed channels and cooling holes. Three operating conditions were selected for verification of the NASA-C3X vane, which has 10 internal radial cooling channels. The calculated Nusselt number of internal cooling channels strongly agrees with the experimental data, and the predicted blade surface pressure and temperature distributions at mid span are also in good agreement with the experimental data. The convergence history of the meridional velocity and blade surface temperature demonstrates effective convergence properties. Therefore, the aero-thermal–coupled through-flow method with the new cooling model can provide a reliable tool for cooled turbine through-flow design and analysis.

Numerical Investigation of Turbulence Models for a Superlaminar Journal Bearing

With rotating machineries working at high speeds, oil flow in bearings becomes superlaminar. Under superlaminar conditions, flow exhibits between laminar and fully developed turbulence. In this study, superlaminar oil flow in an oil-lubricated tilting-pad journal bearing is analyzed through computational fluid dynamics (CFD). A three-dimensional bearing model is established. CFD results from the laminar model and 14 turbulence models are compared with experimental findings. The laminar simulation results of pad-side pressure are inconsistent with the experimental data. Thus, the turbulence effects on superlaminar flow should be considered. The simulated temperature and pressure distributions from the classical fully developed turbulence models cannot correctly fit the experimental data. As such, turbulence models should be corrected for superlaminar flow. However, several corrections, such as transition correction, are unsuitable. Among all the flow models, the SST model with low-Re correction exhibits the best pressure distribution and turbulence viscosity ratio. Velocity profile analysis confirms that a buffer layer plays an important role in the superlaminar boundary layer. Classical fully developed turbulence models cannot accurately predict the buffer layer, but this problem can be resolved by initiating an appropriate low-Re correction. Therefore, the SST model with low-Re correction yields suitable results for superlaminar flows in bearings.

An Investigation of Conjugate Heat Transfer Simulations Based on Discontinuous Galerkin Methods on Unstructured Grids

A framework for the simulations of conjugate heat transfer (CHT) problems using discontinuous Galerkin (DG) methods on unstructured grids is presented. The compressible fluid dynamic equations and solid heat conduction equations are discretized into the explicit DG formulations simultaneously. The Bassi-Rebay method is used in the gradients computation inside both fluid and solid domains. Fully coupled strategy based on the data exchange process via the numerical flux of interface quadrature points is devised. Various turbulence models and the local-variable-based transition model γ -Reθ are assimilated into the unified algorithm framework. The feasibility of the methodology is validated by some test cases. The work can be viewed as a primary attempt towards further investigations of DG and other high-accuracy methods applications in the engineering CHT problems.Copyright

Investigation of Cooling Effect on the Aerodynamic Performance in the Intercooled Compressor

An intercooling technique using convective cooling channels in the compressor stator vanes has been proposed recently. In this paper, two cooling methods are presented, and numerical simulation is ...

An Aero-Thermal Coupled Throughflow Method for Convective Cooled Turbines

Cooling technologies have been widely applied to protect the turbine blades at high inlet temperature, which also makes the aero-thermal coupled phenomenon more remarkable. Nevertheless, the aero-thermal phenomenon had not been considered in traditional throughflow methods and led to challenges of cooled turbine design. This paper proposes a new cooling model for the aero-thermal coupled throughflow method which was first proposed by the same author. The cooling model considers the variation of the temperature caused by air cooling both along the stream and span direction to improve the heat flux calculation accuracy. The impacts of heat transfer on mainstream enthalpy and entropy are further studied in this paper. The equivalent blade thickness and the estimation method of the heat exchange area were also introduced into the cooling model. The cooling model is validated with experimental data of the Mark II profile. This paper applies the method in the design of a high-pressure axial turbine, of which the first stator is cooled with convective cooling. With the prescribed blade temperature limitation, the flow field properties and the coolant requirement are predicted. The three dimensional CHT analysis is performed to validate the aerothermal coupled throughflow method, and the aerodynamic parameter predicted by the throughflow method is in accordance with the 3-D CHT analysis.Copyright

Applications of Explicit Algebraic Reynolds Stress Models to Transonic Turbulence Flow Simulations Based on Discontinuous Galerkin Methods

Two applications of the non-linear eddy-viscosity model EARSM are presented in the simulations of transonic turbulent flow involving shock waves and other related complex features. The simulations are implemented applying an in-house CFD program based on the unstructured discontinuous Galerkin method, an alternative discretization method of the classical finite volume one to precisely capture the flow features. A series of turbulence feature variables in boundary layers are comparatively observed and analyzed. For the first case of transonic flow over a bump, the redistribution effect of Reynolds stress components rooted in the non-linear constitution relation promotes streamwise turbulence fluctuation and suppresses the normal one in boundary layer, comparing with the traditional linear constitution relation, especially when passing the shocks. The production magnitudes of the turbulence shear stress and kinetic energy for the non-linear model show slightly more sensitive to perturbations, such as the occurrence of shock front or compression corner, than the linear one. For the second case of a transonic turbine vane, similar redistribution effect of the non-linear model is also verified on suction surface around the strong shock. The straightforward redistribution effect is absent on pressure surface around middle part of the vane with favorable pressure gradients. There the non-linear model evaluates higher magnitudes of streamwise, normal and shear Reynolds stress components than the linear one, thus resulting locally stronger heat convection and higher surface temperature.Copyright