Chun-wei Gu

An All-Speed Roe-type scheme and its asymptotic analysis of low Mach number behaviour

A new scheme, All-Speed-Roe scheme, was proposed for all speed flows. Compared with traditional preconditioned Roe scheme, All-Speed-Roe scheme changes non-linear eigenvalues in the numerical dissipation terms of Roe-type schemes. With an asymptotic analysis, the low Mach number behaviour of the scheme is studied theoretically in two ways. In one way, All-Speed-Roe scheme is regarded as finite magnification of Low-Speed-Roe scheme in the low Mach number limit. In the other way, a general form of All-Speed-Roe scheme is analyzed. Both ways demonstrate that All-Speed-Roe scheme has the same low Mach number behaviour as the original governing equation in the continuous case, which includes three important features: pressure variation scales with the square of the Mach number, the zero order velocity field is subject to a divergence constraint, and the second order pressure satisfies a Poisson-type equation in the case of constant-entropy. The analysis also leads to an unexpected conclusion that the velocity filed computed by traditional preconditioned Roe scheme does not satisfy the divergence constraint as the Mach number vanishes. Moreover, the analysis explains the reason of checkerboard decoupling and shows that momentum interpolation method provides a similar mechanism as traditional preconditioned Roe scheme inherently possesses to suppress checkerboard decoupling. In the end, general rulers for modifying non-linear eigenvalues are obtained. Finally, several numerical experiments are provided to support the theoretical analysis. All-Speed-Roe scheme has a sound foundation and is expected to be widely studied and applied to all speed flow calculations.

Mechanism of Roe-type schemes for all-speed flows and its application

Based on the three rules developed from the Roe-type scheme, the mechanisms of the classical and preconditioned Harten-Lax-van Leer (HLL) schemes are analyzed. For the classical HLL scheme, the accuracy problem is attributable to the extremely large coefficient of the velocity-derivative term of the momentum equation. For the preconditioned HLL scheme, the global cut-off problem is attributable to the denominator of the coefficients, whereas the particular pressure gradient sensor problem results from the loss of the capability to suppress the checkerboard pressure-velocity decoupling. A new all-speed HLL scheme, which can overcome these problems by only multiplying the momentum-derivative term in the momentum equation by a function related to the local Mach number, is proposed. More importantly, the present study shows the generality of the three rules, which can be powerful tools for analyzing and proposing schemes. The second rule involving the checkerboard problem is also improved by emphasizing that the coefficients of pressure-derivative term in the continuity and energy equations should be changed simultaneously.In recent years, Roe-type schemes based on different ideas have been developed for all-speed flows, such as the preconditioned Roe, the All-Speed Roe, Thornbers modified Roe and the LM-Roe schemes. This work explores why these schemes succeed or fail with the accuracy and checkerboard problems. Comparison and analysis show that the accuracy and checkerboard problems are caused by the order of the sound speed being too large and too small in the coefficients of the velocity-derivative and pressure-derivative dissipation terms, respectively. These problems can be resolved by choosing coefficients with zero-order sound speed. In addition, to avoid the negative effects of the global cut-off strategy on accuracy while maintaining computational stability, the sound speed terms in the numerator of the coefficients can be determined by local variables, while those in the denominator remain the global cut-off. Two novel schemes are proposed as examples to demonstrate how these ideas can be applied to construct more satisfactory schemes for all-speed flows. Asymptotic analysis and numerical experiments support the theoretical analysis and the rules obtained in the work.

The momentum interpolation method based on the time-marching algorithm for All-Speed flows

The time-marching approach has clear physical meaning and strict mathematical nature and has been applied in computation of compressible flows widely and extended to many uniform algorithms for All-Speed flows. Remedy for its weakness in the problem of checkerboard decoupling of pressure field for incompressible flows is envisaged with the time-marching momentum interpolation method (MIM) taken into account in this paper. Existing preconditioning methods for suppressing decoupling and time-marching MIM are analyzed for this purpose, and algorithms of time-marching MIM are proposed for steady and unsteady flows and for All-Speed flows. Asymptotic analysis shows that the supposed time-marching MIM has at least a third-order accuracy, better than the existing time-marching coupling methods, which only have an accuracy of the same order as the adopted scheme has. Effects of the time step sizes on the ability of the time-marching MIM to suppress the checkerboard pressure decoupling are particularly discussed in terms of the dual-time stepping approach, and it is revealed how the decreased sizes of either the pseudo- or physical-time step increases the possibility of decoupling and how Chois modification, in which the history of the interface velocity is decided by itself instead of the arithmetic average of the velocities on its adjacent nodes, removes the unphysical pressure oscillation with small size of the physical time step but leads to divergence with the pseudo-time step as well. As a remedy for the pseudo-time step, such methods are recommended as implicit methods and the local-time step method with a proposed modification of the time-marching MIM preventing accuracy loss due to very large time step size. Numerical experiments support the theoretical analyses and show the validity of the time-marching MIM proposed.

Cavitation Mechanism of Oil-Film Bearing and Development of a New Gaseous Cavitation Model Based on Air Solubility

Cavitation phenomenon in lubricants significantly influences the performance of associated machinery. In this paper, the cavitation mechanism of an oil-film bearing is attributed to gaseous cavitation, and a new gaseous cavitation model based on air solubility in the lubricant is presented. The model is validated using the Reynolds equation algorithm for fixed-geometry oil-film journal bearing, and the predicted results at different eccentricity ratios show good agreement with published data. The analyses show that gaseous mechanism can explain the cavitation phenomena that occur in the bearing except for very heavy load cases. In particular, this new model is compatible with the Jakobsson–Floberg–Olsson condition. Therefore, the new model has an explicit physical meaning, can produce good results, can identify whether vaporous cavitation occurs, and more importantly, can provide a novel means of developing cavitation models for low-vapor-pressure lubricants.

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.

Performance Prediction and Analysis of a Three-Shaft Gas Turbine Supported by Turbine Cooling Model

Performance prediction method of the modern gas turbine is an important tool for the engine design and performance analysis. This paper integrates a hybrid cooling model to the previous research of gas turbine performance prediction method which is applied to predict the multi-shaft gas turbine performance. The cooling model, combined with the semi-empirical model and analytical model, had been originally proposed for the investigation of turbine convective cooling or film cooling performance. The aim of the work is to apply the hybrid model to effectively estimate the coolant requirement in the gas turbine performance prediction, therefore to improve the reliability of the analysis in the innovative gas turbine cycle.The analysis involved a three-shaft gas turbine. Experiments were carried out on the engine, and the effectiveness of the prediction method is validated by the experiment. Consequently detailed performance characteristic of the engine is investigated under different stagger angles of the variable-angle nozzle, revealing how the stagger angle of the variable-angle nozzle and the turbine inlet temperature affect the gas turbine performance. The analysis is considered valuable for the engine operation and components optimization.Copyright

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