Machine Learning for Turbulence Model Development Using a High-Fidelity HPT Cascade Simulation

The validity of the Boussinesq approximation in the wake behind a high-pressure turbine blade is explored. We probe the mathematical assumptions of such a relationship by employing a least-squares technique. Next, we use an evolutionary algorithm to modify the anisotropy tensor a priori using highly resolved LES data. In the latter case we build a non-linear stress-strain relationship. Results show that the standard eddy-viscosity assumption underpredicts turbulent diffusion and is theoretically invalid. By increasing the coefficient of the linear term, the farwake prediction shows minor improvement. By using additional non-linear terms in the stress-strain coupling relationship, created by the evolutionary algorithm, the near-wake can also be improved upon. Terms created by the algorithm are scrutinized and the discussion is closed by suggesting a tentative non-linear expression for the Reynolds stress, suitable for the wake behind a high-pressure turbine blade.

Large-Eddy and Unsteady Reynolds-Averaged Navier-Stokes Simulations of an Axial Flow Pump for Cardiac Support

The use of implantable pumps for cardiac support (Ventricular Assist Devices) has proven to be a promising option for the treatment of advanced heart failure. Avoiding blood damage and achieving high efficiencies represent two main challenges in the optimization process. To improve VADs, it is important to understand the turbulent flow field in depth in order to minimize losses and blood damage. The application of the Large-eddy simulation (LES) is an appropriate approach to simulate the flow field because turbulent structures and flow patterns, which are connected to losses and blood damage, are directly resolved. The focus of this paper is the comparison between an LES and an Unsteady Reynolds-Averaged Navier-Stokes simulation (URANS) because the latter one is the most frequently used approach for simulating the flow in VADs. Integral quantities like pressure head and efficiency are in a good agreement between both methods. Additionally, the mean velocity fields show similar tendencies. However, LES and URANS show different results for the turbulent kinetic energy. Deviations of several tens of percent can be also observed for a blood damage parameter, which depend on velocity gradients. Possible reasons for the deviations will be investigated in future works.

Towards High-Order Large Eddy Simulation of Aero-Thermal Flows for Turbomachinery Applications

The solution accuracy and computational efficiency of high order Large Eddy Simulation (LES) solvers are evaluated on two benchmark open literature blade cascade problems. The first problem concerns wake development in the T106A low pressure turbine cascade [1]. The second problem examines the effect of free-stream turbulence on heat transfer from the VKI first stage high pressure turbine vane [2]. The calculations are performed with two independently developed high order LES solvers using completely different numerical algorithms. The first solver FDL3Di [3] was originally developed at the Airforce Research Laboratory (AFRL) and employs structured overset grids. It uses a sixth order compact finite difference scheme in space along with an implicit Beam-Warming scheme for time marching. The second solver, hpMusic, is developed at the University of Kansas [4]. This is a variable order (up to sixth order) unstructured grid solver employing a discontinuous formulation known as flux reconstruction (FR) / correction procedure via reconstruction (CPR) [5]. The computational grids used are independently tuned for each application. The solvers are benchmarked against experimental data for wake development and blade heat transfer coefficient. Further physical insights in to the test cases are also obtained, filling gaps in experimental results, especially for the VKI problem.

Integrated Large Eddy Simulation of Combustor and Turbine Interactions: Effect of Turbine Stage Inlet Condition

To study the effects of combustion chamber dynamics on a turbine stage aerodynamics and thermal loads, an integrated Large-Eddy Simulation of the FACTOR combustion chamber simulator along with its high pressure turbine stage is performed and compared to a standalone turbine stage computation operated under the same mean conditions. For this specific configuration, results illustrate that the aerodynamic expansion of the turbine stage is almost insensitive to the inlet turbulent conditions. However, the temperature distribution in the turbine passages as well as on the stator vane and rotor blade walls are highly impacted by these inlet conditions: underlying the importance of inlet conditions in turbine stage computations and the potential of integrated combustion chamber / turbine simulations in such a context.

Experimental and Numerical Investigation of Transition Effects on a Low Reynolds Number Airfoil

Low speed, small scale turbomachinery operates at low Reynolds number with transition phenomena occurring. In small consumer product applications, high efficiency and low noise are key performance metrics. Transition behaviour will partly determine the state of the boundary layer at the trailing edge; whether it is laminar, turbulent or separated impacts aerodynamic and acoustic performance. This study aimed to evaluate a commercially available CFD transition model on a low Reynolds number Eppler E387 airfoil and identify whether it was able to correctly model the boundary layer transition, and at what expense. CFD was carried out utilising the ANSYS Shear Stress Transport (SST) k-ω γ-Reθ transition model. The CFD progressed from 2D in Fluent v150, through to single cell thickness 3D (pseudo 2D) in CFX v172. An Eppler E387 low Reynolds number airfoil, for which experimental data was readily available from literature at Re = 200,000 was used as the validation case for the CFD, with results computed at numerous incidence angles and mesh densities. Additionally, experimental surface oil flow visualisation was undertaken in a wind tunnel using a scaled E387 airfoil for the zero incidence case at Re = 50,000. The flow visualisation exhibited the expected key features of transition in the breakdown of the boundary layer from laminar to turbulent, and was used as a validation case for the CFD transition model. The comparison between the results from the CFD transition model and the experimental data from literature suggested varying levels of agreement based on the mesh density and CFD solver in the starting location of the laminar separation bubble, with higher disparity for the position of the reattachment point. Whether 2D or 3D, the prediction accuracy was seen to worsen at high incidence angles. Finally, the location of the laminar separation bubble between CFD and oil flow visualisation had good agreement and a set of guidelines on the mesh parameters which can be applied to low Reynolds number turbomachinery simulations was determined.

An Implicit Off-Design Deviation Angle Correlation of Axial Flow Compressor Blade Elements

This paper applies a new analytical/empirical method to formulate the off-design deviation angle correlation of axial flow compressor blade elements. An implicit function of deviation angle is used to map off-design deviation curves into linear correlations (minimum linear correlation coefficient R = 0.959 in this paper). Solution of the coefficients in the correlation is given through the study of classical theories and statistical analysis of the experimental data. The off-design deviation angle can be calculated numerically. The approach requires only knowledge of the blade element geometry. The comparison among 2 classical correlations and the new correlation proposed in this paper shows the new correlation has minimum error over the entire range of incidence angle while classical correlations show high reliability only in a limited range. Experimental data in this paper is collected from NASA’s open technical reports. Rotors and stators are studied together. Considering there is significant deviation angle variation along spanwise direction, only data at 50% span is studied, if possible. The error among experimental data, statistical regressions of the experimental data, and numerical results based on the new correlation is discussed. It has to be noted that the influence of the flow condition other than incidence angle is only being discussed but with less break through.

An Approach for Efficient CFD Simulations of an Ejector Air Injection System for Active Aerodynamic Compressor Stabilization

The Institute of Jet Propulsion at the University of the German Federal Armed Forces Munich has developed and patented a novel concept of air injection systems for active aerodynamic stabilization of turbo compressors. This so-called Ejector Injection System (EIS) utilizes the ejector effect to enhance efficiency and impact of the aerodynamic stabilization of the Larzac 04 two-spool turbofan engine’s LPC. The EIS design manufactured recently has been subject to CFD and experimental pre-investigations in which the expected ejector effect performance has been proven and the CFD set-up has been validated. Subsequently, optimization of the EIS ejector geometry comes into focus in order to enhance its performance. In this context, CFD parameter studies on the influence of in total 16 geometric and several aerodynamic parameters on the ejector effect are required. However, the existing and validated CFD set-up of the EIS comprises not only the mainly axisymmetric ejector geometry but also the highly complex 3D supply components upstream of the ejector geometry. This is hindering large scale CFD parameter studies due to the numerical effort required for these full 3D CFD simulations. Therefore, an approach to exploit the overall axissymmetry of the ejector geometry is presented within this paper which reduces the numerical effort required for CFD simulations of the EIS by more than 90%. This approach is verified by means of both experimental results as well as CFD predictions of the full 3D set-up. The comprehensive verification data set contains wall pressure distributions and the mass flow rates involved at various Aerodynamic Operating Points (AOP). Furthermore, limitations of the approach are revealed concerning its suitability e.g. to judge the response of the attached compressor of future EIS designs concerning aerodynamic stability or cyclic loading.

Large Eddy Simulation of Transitional Flow in a Compressor Cascade

At off-design conditions, when the blade Reynolds number is low, a significant part of the blade boundary layer can be transitional. Then, standard RANS models are unable to predict the flows correctly but explicit transition modeling provides some improvement. Since large eddy simulations (LES) are improvements on RANS, the performance of LES was examined by simulating a flow through a linear, compressor cascade for which experimental data are available — specifically at the Reynolds number of 210,000 based on blade chord when transition processes occur over a significant extent of the suction surface. The LES were performed with an explicit filtering approach, applying a low-pass filter to achieve sub-grid-scale modeling. Explicit 8th-order difference formulas were used to obtain high resolution spatial derivative terms. An O-grid was wrapped around the blade with suitable clustering for the boundary layer and regions of large changes along the blade. Turbulent in-flow was provided from a precursor simulation of homogeneous, isotropic turbulence. Two LES and a DNS were performed. The second LES refines the grid in the vicinity of the separation bubble on the suction surface, and along the span. Surface pressure distributions from all simulations agree closely with experiment, thus providing a much better prediction than even transition-sensitive RANS computations. Wall normal profiles of axial velocity and fluctuations also agree closely with experiment. Differences between LES and DNS are small, but the refined grid LES is closer to the DNS almost everywhere. This monotonic convergence, expected of the LES method used, demonstrates its reliability. The pressure surface undergoes transition almost immediately downstream of the leading edge. On the suction surface there are streaks as expected for freestream-turbulence-induced transition, but spots do not appear. Instead, a separating shear layer rolls up and breaks down to turbulence at re-attachment. Both LES capture this process. Skin friction distribution reveals the transition near the re-attachment to occur over an extended region, and subsequent relaxation is slower in the LES. The narrower transition zone in the DNS is indicative of the essential role of smaller scales during transition that should not be neglected in LES. Simulation data also reveal that an assumption of laminar kinetic energy transition models that Reynolds shear stress remains small in the pre-transitional region is supported. The remaining differences in the predictions of such models is thus likely to be the separation-induced transition which preempts the spot formation.

Total Temperature Based Correction of the Turbulence Production in Hot Jets

Comparisons with experiments have shown that RANS models tend to underpredict the mixing process in shear layers with strong temperature gradients. In the modeling of jet engine’s exhaust systems this leads to an overpredicted potential core length and underestimated turbulence intensity in the free jet. In addition, the calculated efficiency gain is lower than indicated by measurements in mixed turbofan engines. Based on the findings from scale-resolving simulations a correction to the turbulence production term is proposed and compared with two NASA-experiments on hot jets. This correction is implemented in a Reynolds-stress and a k-ε model. The results are in very good agreement with the experimental data.

Correlation Between Pressure Recovery of Highly Loaded Annular Diffusers and Integral Stage Design Parameters

Exhaust diffusers significantly enhance the available power output and efficiency of gas and steam turbines by allowing for lower turbine exit pressures. The residual dynamic pressure of the turbine outflow is converted into static pressure, which is referred to as pressure recovery. Since total pressure losses as well as construction costs increase drastically with diffuser length, it is more than favourable to design shorter diffusers with rather steep opening angles. However, those designs are more susceptible to boundary layer separation. In this paper, the stabilising properties of tip leakage vortices generated in the last rotor row and their effect on the boundary layer characteristics are examined. Based on analytical considerations, for the first time a correlation between the pressure recovery of the diffuser and integral rotor parameters of the last stage, namely the loading coefficient, flow coefficient and reduced frequency, is established. Both, experimental data and scale resolving simulations, carried out with the SST-SAS method, show excellent agreement with the correlation. Blade tip vortex strength predominantly depends on the amount of work performed in the rotor, which in turn is described by the non-dimensional loading coefficient. The flow coefficient influences mainly the orientation of the vortex, which affects the interaction between vortex and boundary layer. The induced velocity field accelerates the boundary layer, essentially reducing the thickness of the separated layer or even locally preventing separation.