Numerical and experimental investigation of a new film cooling geometry with high P/D ratio

In order to improve the coolant surface coverage, in the past years new geometries have been proposed with higher lateral fan-shaped angle and/or greater inter-hole pitch distance (P/D). Unfortunately it is not possible to increase the fan angle or the pitch distance even further without inducing a coolant separation and a drop in the overall effectiveness. This study proposes an innovative design which improves the lateral coverage and reduces the jet lift off. The results have been validated by a combination of numerical and experimental analyses: the experimental work has been assessed on a flat plate using thermo chromic liquid crystals and the results have been confirmed numerically by the CFD with the same conditions. The CFD simulations have been carried out considering a stochastic distribution for the free stream Mach number and the coolant blowing ratio. The experimental and computational results show that the inducing lateral pressure gradients there is a minimum increase in lateral averaged adiabatic effectiveness of +30% than the baseline case until a distance downstream of 20 times the coolant diameter. © 2013 Elsevier Ltd. All rights reserved

Uncertainty quantification of leakages in a multistage simulation and comparison with experiments

The present paper presents a numerical study of the impact of tip gap uncertainties in a multistage turbine. It is well known that the rotor gap can change the gas turbine efficiency but the impact of the random variation of the clearance height has not been investigated before. In this paper the radial seals clearance of a datum shroud geometry, representative of steam turbine industrial practice, was systematically varied and numerically tested. By using a Non-Intrusive Uncertainty Quantification simulation based on a Sparse Arbitrary Moment Based Approach, it is possible to predict the radial distribution of uncertainty in stagnation pressure and yaw angle at the exit of the turbine blades. This work shows that the impact of gap uncertainties propagates radially from the tip towards the hub of the turbine and the complete span is affected by a variation of the rotor tip gap. This amplification of the uncertainty is mainly due to the low aspect ratio of the turbine and a similar behavior is expected in high pressure turbines

The benefit of high-conductivity materials in film cooled turbine nozzles

This study presents an experimental and numerical investigation of the beneficial effect of higher conductivity materials in HP turbine nozzles. Most of the literature studies focus on the maximum temperature that a nozzle can withstand, whereas the effect of thermal gradients is often neglected. However thermal gradients have higher influence on the life of the components and they have to be given careful consideration. In this work it is shown that thermal gradients are reduced by using high conductivity materials and, as a consequence, the nozzles life is appreciably increased. A representative film cooled leading edge with an internal impingement plate was studied experimentally at Texas AM University. Two materials were used, namely polycarbonate and stainless steel, in order to highlight the impact of conduction on coolant effectiveness. Numerically conjugate heat transfer simulations have been carried out with an in house solver to analyse in detail the impact of conduction and internal convection. Both experimental and numerical results show that by increasing the conductivity in the solid region, the thermal gradients are strongly reduced. Numerically it is shown that using inserts of nickel-aluminide alloys in nozzles may reduce the thermal gradients from 3 to 4 times if compared to nowadays design. © 2012 Elsevier Inc

Surrogate modelling and uncertainty quantification based on multi-fidelity deep neural network

To reduce training costs, several Deep neural networks (DNNs) that can learn from a small set of HF data and a sufficient number of low-fidelity (LF) data have been proposed. In these established neural networks, a parallel structure is commonly proposed to separately approximate the non-linear and linear correlation between the HF- and LF data. In this paper, a new architecture of multi-fidelity deep neural network (MF-DNN) was proposed where one subnetwork was built to approximate both the non-linear and linear correlation simultaneously. Rather than manually allocating the output weights for the paralleled linear and nonlinear correction networks, the proposed MF-DNN can autonomously learn arbitrary correlation. The prediction accuracy of the proposed MF-DNN was firstly demonstrated by approximating the 1-, 32- and 100-dimensional benchmark functions with either the linear or non-linear correlation. The surrogating modelling results revealed that MF-DNN exhibited excellent approximation capabilities for the test functions. Subsequently, the MF DNN was deployed to simulate the 1-, 32- and 100-dimensional aleatory uncertainty propagation progress with the influence of either the uniform or Gaussian distributions of input uncertainties. The uncertainty quantification (UQ) results validated that the MF-DNN efficiently predicted the probability density distributions of quantities of interest (QoI) as well as the statistical moments without significant compromise of accuracy. MF-DNN was also deployed to model the physical flow of turbine vane LS89. The distributions of isentropic Mach number were well-predicted by MF-DNN based on the 2D Euler flow field and few experimental measurement data points. The proposed MF-DNN should be promising in solving UQ and robust optimization problems in practical engineering applications with multi-fidelity data sources

"Uncertainty Quantification and Film Cooling"

In gas turbine cooling, hundreds of ducts are fed by common plena connected to small channels. The inlet stagnation pressure, temperature and turbulence levels are unknown in the ducts and subjected to a strong variability, due to the uncertainty associated with operating conditions and/or manufacturing defects. Despite the uncertainty level in boundary values, it is a common practice to use deterministic values. In this work, a Monte Carlo Method Lattice Sampling (MCMLS) and a Probabilistic Collocation Method (PCM) are used to assess the uncertainty quantification problem in film cooling. By assuming Gaussian distributions for the inlet total pressures, 242 CFD simulations have been performed for MCMLS and the probabilistic distribution of the adiabatic effectiveness is obtained. It provides the average value for the stochastic output and the level of confidence related to that value. The results show that 20% variation in the stochastic inputs provides a variation of the adiabatic effectiveness of about 100%, and reduces the blade life by more than 5 times. The MCMLS is two orders of magnitude less computational expensive than a standard MCM, robust and accurate but still computationally expensive for everyday design. Therefore, using the MCMLS as baseline, an innovative technique has been proposed: the Probabilistic Collocation Method (PCM), in order to both reduce the number of simulations and obtain accurate results. The developed PCM methodology is 10 times faster than the MCMLS with negligible differences in the results and three orders of magnitude faster than standard MCM. This work shows that in nowadays design, computational fluid dynamics must use stochastic methods and it is possible to integrate probabilistic analysis in the design phase to investigate the robustness by using PCM and MCMLS

Deep Neural Network and Monte Carlo Tree Search applied to Fluid-Structure Topology Optimization

This paper shows the application of Deep Neural Network algorithms for Fluid-Structure Topology Optimization. The strategy offered is a new concept which can be added to the current process used to study Topology Optimization with Cellular Automata, Adjoint and Level-Set methods. The design space is described by a computational grid where every cell can be in two states: fluid or solid. The system does not require human intervention and learns through an algorithm based on Deep Neural Network and Monte Carlo Tree Search. In this work the objective function for the optimization is an incompressible fluid solver but the overall optimization process is independent from the solver. The test case used is a standard duct with back facing step where the optimizer aims at minimizing the pressure losses between inlet and outlet. The results obtained with the proposed approach are compared to the solution via a classical adjoint topology optimization code

Uncertainty quantification and race car aerodynamics

Car aerodynamics are subjected to a number of random variables which introduce uncertainty into the downforce performance. These can include, but are not limited to, pitch variations and ride height variations. Studying the effect of the random variations in these parameters is important to predict accurately the car performance during the race. Despite their importance the assessment of these variations is difficult and it cannot be performed with a deterministic approach. In the open literature, there have been no studies dealing with this uncertainty in car racing aerodynamics modelling the complete car and assessing the probability of a competitive advantage introduced by a new geometry. A stochastic method is used in this work in order to predict the car downforce under stochastic variations and the probability of obtaining a better performance with a new diffuser geometry. A probabilistic collocation method is applied to an innovative diffuser design to prove its performance with stochastic geometrical variations. The analysis is conducted using a complete three-dimensional computational fluid dynamics simulation with a k-ω turbulence closure, allowing the performance of the physical diffuser to be more accurately represented in a stochastic real environment. The random variables included in the analysis are the pitch variations and the ride height variations in different speed conditions. The mean value and the standard deviation of the car downforce are evaluated. © IMechE 2014

Film-cooling performance in supersonic flows: Effect of shock impingement

High pressure turbine stages work in transonic regimes and then shock waves, shed by the trailing edge, impinge on the suction side modifying the flow structures. Gas turbine entry temperature is much higher than the allowable material limit and the hot components can survive only using advanced film-cooling systems. Unfortunately these systems are designed without taking into account the interaction with the shock waves and this article would like to address this problem and to evaluate if this assumption is correct or not. A correct prediction and understanding of the interaction between the ejected coolant and the shock waves is crucial in order to achieve an optimal distribution of the coolant and to increase the components life. In this work, the numerical investigation of a film-cooling test case, investigated experimentally by the University of Karlsruhe, is shown. An in-house computational fluid dynamics solver is used for the numerical analysis. The test rig consists of a converging-diverging nozzle that accelerates the incoming flow up to supersonic conditions and an oblique shock is generated at the nozzle exit section. Three cases have been studied, where the cooling holes have been positioned before, near and after the shock impingement. The results obtained considering four blowing ratios are presented and compared with the available experimental data. The local adiabatic effectiveness is affected by the shock-coolant interaction and this effect has been observed for all the blowing ratios investigated. A similar trend is observed in the experimental data even if the numerical simulations over-predict the impact of the interaction. © IMechE 2013

The response of an elastic-plastic clamped beam to transverse pressure loading

This study presents a new analytical model to predict the response of elastic-plastic, fully clamped beams to transverse pressure loading. The model accounts for travelling elastic flexural waves, stationary and travelling plastic hinges, elastic-plastic stretching and plastic shear deformation. The predictions of the model are validated by detailed Finite Element simulations. The model is used to construct deformation mechanism maps and design charts