A Robust Implementation of a Reynolds Stress Model for Turbomachinery Applications in a Coupled Solver Environment

In the industrial simulation of flow phenomena, turbulence modeling is of prime importance. Due to their low computational cost, Reynolds-averaged methods (RANS) are predominantly used for this purpose. However, eddy viscosity RANS models are often unable to adequately capture important flow physics, specifically when strongly anisotropic turbulence and vortex structures are present. In such cases the more costly 7-equation Reynolds stress models often lead to significantly better results. Unfortunately, these models are not widely used in the industry. The reason for this is not mainly the increased computational cost, but the stability and convergence issues such models usually exhibit. In this paper we present a robust implementation of a Reynolds stress model that is solved in a coupled manner, increasing stability and convergence speed significantly compared to segregated implementations. In addition, the decoupling of the velocity and Reynolds stress fields is addressed for the coupled equation formulation. A special wall function is presented that conserves the anisotropic properties of the model near the walls on coarser meshes. The presented Reynolds stress model is validated on a series of semi-academic test cases and then applied to two industrially relevant situations, namely the tip vortex of a NACA0012 profile and the Aachen Radiver radial compressor case.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

The Feasibility of an Euler-Lagrange Approach for the Modelling of Wet Steam

This study investigates the applicability of an Euler-Lagrange approach for the calculation of nucleation and condensation of steam flows. Supersonic nozzles are used as generic validation cases, as their high expansion rates replicate the flow conditions in real turbines. Experimental and numerical validation data for these nozzles are provided by the International Wet Steam Modelling Project of Starzmann et al. (2018). In contrast to most participants of that project, an Euler-Lagrange approach is utilized for this study. Therefore, the classical nucleation theory with corrections and different droplet growth laws is incorporated into the Discrete Phase Model of ANSYS Fluent. Suggestions for an efficient implementation are presented. The Euler-Lagrange results show a good agreement with the experimental and numerical validation data. The sensitivities of the Euler-Lagrange approach to modelling parameters are analysed. Finally, an optimal parameter set for the calculation of nucleation and condensation is proposed.

Analysis of Transonic Bladerows With Non-Uniform Geometry Using Spectral Method

Turbomachinery blade rows can have non-uniform geometries due to design intent, manufacture errors or wear. When predictions are sought for the effect of such non-uniformities, it is generally the case that whole assembly calculations are needed. A spectral method is used in this paper to approximate the flow fields of the whole assembly but with significantly less computation cost. The method projects the flow perturbations due to the geometry non-uniformity in an assembly in Fourier space, and only one passage is required to compute the flow perturbations corresponding to a certain wave-number of geometry variation. The performance of this method on transonic blade rows is demonstrated on a modern fan assembly. Low engine order and high engine order geometry non-uniformity (e.g. “saw-tooth” pattern) are examined. The non-linear coupling between the flow perturbations and the passage-averaged flow field is also demonstrated. Pressure variations on the blade surface and the potential flow field upstream of the leading edge from the proposed spectral method and the direct whole assembly solutions are compared. Good agreement is observed on both quasi-3D and full 3D cases. A lumped approach to compute deterministic fluxes is also proposed to further reduce the computational cost of the spectral method. The spectral method is formulated in such a way that it can be easily implemented into an existing harmonic flow solver by adding an extra source term, and can be potentially used as an efficient tool for aeromechanical and aeroacoustics design of turbomachinery blade rows.

Analysis of the Exit Flow Angle and Characteristics of Flow in Axial Turbine Cascades

Despite a wealth of sophisticated CFD-methods, most designs are still based on one-dimensional and two-dimensional inviscid analytical tools. In such methods, realistic loss and angle assessment are indeed critical in order to arrive at correct loading, flow coefficient and reaction. The selected values are normally retained through the detailed design sequence for each iteration. This means that the throat sizing and hence the gauge angle is largely based on the early design work within the through-flow environment. Even one-degree error in angle estimation will turn into a rather large capacity error. For most designs, the exchange rate between capacity and gauge angle is on the order of 3–5 percent, per degree exit angle. In a previous publication, a methodology and equations were presented to assess the exit flow in an axial turbine blade row by Mamaev in Russian nomenclature and the tangential coordinate system. The approach, provided a unified and flow-physics based method for assessing exit angles from the geometry features like gauge angle, uncovered turning and flow features like Laval number, etc. Analysis of those formulas showed good agreement with physical flow pattern in real cascades for sub and transonic blade cascades. In this work, the same basic principal procedure is followed by employing the more international agreed nomenclature of blades such as an axial reference plane and Mach number. In the current work, the one-dimensional analysis results were compared with the three dimensional numerical modelling of a full annulus two-stage turbine. Analysis of the results showed the inherent unsteadiness specially outside the rotor blade cascades, however, comparison of the mass averaged exit angle with the one dimensional analysis showed satisfactory agreement.

On the Development of a Synchronized Harmonic Balance Method for Multiple Frequencies and its Application to LPT Flows

The aim of this paper is to describe the development and application of a multi-frequency harmonic balance solver for GPUs, particularly suitable for the simulation of periodic unsteadiness in nonlinear turbomachinery flows comprised of a few dominant frequencies, with an unsteady multistage coupling that bolsters the flow continuity across the rotor/stator interface. The formulation is addressed with the time-domain reinterpretation, where several non-equidistant time instants conveniently selected are solved simultaneously. The set of required frequencies in each row is driven into the governing equations with the help of almost-periodic Fourier transforms for time derivatives and time shifted boundary conditions. The spatial repetitiveness inside each row can be exploited to perform single-passage simulations and the relative circumferential positioning of the rotors or stators and the different blade or vane counts is tackled by means of adding fictitious frequencies referring to non-adjacent rows therefore taking into account clocking and indexing effects. Existing multistage row coupling techniques of harmonic methods rely on the use of non-reflecting boundary conditions, based on linearizations, or time interpolation, which may lead to Runge phenomenon with the resulting numerical instabilities and non-preserving flux exchange. Different sets of time instants might be selected in each row but the interpolation in space and time across their interfaces gives rise to robustness issues due to this phenomenon. The so-called synchronized approach, developed in this work, consist of having the same time instances among the whole ensemble of rows, ensuring that flux transfer at sliding planes is applied more robustly. The combination of a set of shared non-equidistant time instances plus the use of unequal frequencies (real and fictitious) may spoil the Fourier transforms conditioning but this can be dramatically improved with the help of oversampling and instants selection optimization. The resulting multistage coupling naturally addresses typical numerical issues such as flow that might reverse locally across the row interfaces by means of not using boundary conditions but a local flux conservation scheme in the sliding planes. Some examples will be given to illustrate the ability of this new approach to preserve accuracy and robustness while resolving them. A brief analysis of results for a fan stage and a LPT multi-row case is presented to demonstrate the correctness of the method, assessing the impact in the modeling accuracy of the present approach compared with a time-domain conventional analysis. Regarding the computational performance, the speedup compared to a full annulus time-domain unsteady simulation is a factor of order 30 combining the use of single-passage rows and time spectral accuracy.

Prediction of Tip Leakage Vortex Dynamics in an Axial Compressor Cascade Using RANS Analyses

The tip leakage flow in turbine and compressor blade rows is responsible for a relevant fraction of the total loss. It contributes to unsteadiness, and have an important impact on the operability range of compressor stages. Experimental investigations and, more recently, scale-resolving CFD approaches have helped in clarifying the flow mechanism determining the dynamics of the tip leakage vortex. Due to their continuing fundamental role in design verifications, it is important to establish whether RANS/URANS approaches are able to reproduce the effects of such a flow feature, in order to correctly drive the design of the next generation of turbomachinery. Base studies are needed in order to accomplish this goal. In the present work the tip leakage flow in axial compressor rotor blade cascade have been studied. The cascade was tested experimentally in Virginia Tech Low Speed Cascade Wind Tunnel in both stationary and moving endwall configurations. Numerical analyses were performed using the TRAF code, a state-of-the-art in-house-developed 3D RANS/URANS flow solver. The impact of the numerical framework was investigated selecting different advection schemes including a central scheme with artificial dissipation and a high-resolution upwind strategy. In addition, two turbulence models have been used, the Wilcox linear k–ω model and a non-linear eddy viscosity model (Realizable Quadratic Eddy Viscosity Model), which accounts for turbulence anisotropy. The numerical results are scrutinized using the available measurements. A detailed discussion of the vortex evolution inside the blade passage and downstream of the blade trailing edge is presented in terms of streamwise velocity, streamwise vorticity, and turbulent kinetic energy contours. The purpose is to identify guidelines for obtaining the best representation of the vortex dynamics, with the methodologies usually employed in routine design iterations and, at the same time, evidence their weak aspects that need further modelling efforts.

Reynolds Number and Roughness Effects on Turbocompressor Performance: Numerical Calculations and Measurement Data Evaluation

Further validation of an analytic method to calculate the influence of changes in Reynolds number, machine size and roughness on the performance of axial and radial turbocompressors is presented. The correlation uses a dissipation coefficient as a basis for scaling the losses with changes in relative roughness and Reynolds number. The original correlation from Dietmann and Casey [6] is based on experimental data and theoretical models. Evaluations of five numerically calculated compressor stages at different flow coefficients are presented to support the trends of the correlation. It is shown that the sensitivity of the compressor performance to Reynolds and roughness effects is highest for low flow coefficient radial stages and steadily decreases as the design flow coefficient of the stage and the hydraulic diameter of the flow channels increases.

The Effect of Blade Count on Body Force Model Performance for Axial Fans

Body force models enable inexpensive numerical simulations of turbomachinery. The approach replaces the blades with sources of momentum/energy. Such models capture a “smeared out” version of the blades’ effect on the flow, reducing computational cost. The body force model used in this paper has been widely used in aircraft engine applications. Its implementation for low speed, low solidity (few blades) turbomachines, such as automotive cooling fans, enables predictions of cooling flows and component temperatures without calibrated fan curves. Automotive cooling fans tend to have less than 10 blades, which is approximately 50% of blade counts for modern jet engine fans. The effect this has on the body force model predictions is unknown and the objective of this paper is to quantify how varying blade count affects the accuracy of the predictions for both uniform and non-uniform inflow. The key findings are that reductions in blade metal blockage combined with spanwise flow redistribution drives the body force model to more accurately predict work coefficient as the blade count decreases, and that reducing the number of blades is found to have negligible impacts on upstream influence and distortion transfer in non-uniform inflow until extremely low blade counts (such as 2) are applied.

Evaluation of the Rotor Temperature Distribution of an Automotive Turbocharger Under Hot Gas Conditions Including Indirect Experimental Validation

While turbocharging is a key technology for improving the performance and efficiency of internal combustion engines, the operating behavior of the turbocharger is highly dependent on the rotor temperature distribution as it directly modifies viscosity and clearances of the fluid film bearings. Since a direct experimental identification of the rotor temperature of an automotive turbocharger is not feasible at an acceptable expense, a combination of numerical analysis and experimental identification is applied to investigate its temperature characteristic and level. On the one hand, a numerical conjugate heat transfer (CHT) model of the automotive turbocharger investigated is developed using a commercial CFD-tool and a bidirectional, thermal coupling of the CFD-model with thermohydrodynamic lubrication simulation codes is implemented. On the other hand, experimental investigations of the numerically modelled turbocharger are conducted on a hot gas turbocharger test rig for selected operating points. Here, rotor speeds range from 64.000 to 168.000 rpm. The turbine inlet temperature is set to 600°C and the lubricant is supplied at a pressure of 300 kPa with 90°C to ensure practically relevant boundary conditions. Comparisons of measured and numerically predicted local temperatures of the turbocharger components indicate a good agreement between the analyses. The calorimetrically determined frictional power loss of the bearings as well as the floating ring speed are used as additional validation parameters. Evaluation of heat flow of diabatic simulations indicates a high sensitivity of local temperatures to rotor speed and load. A cooling effect of the fluid film bearings is present. Consequently, results confirm the necessity of the diabatic approach to the heat flow analysis of turbocharger rotors.