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 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

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

"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

Uncertainty quantification and conjugate heat transfer: A stochastic analysis

Conjugate Heat Transfer studies are a common method to predict the thermal loading in high pressure nozzles. Despite the accuracy of nowadays tools, it is not clear how to include the uncertainties associated to the turbulence level, the temperature distribution or the thermal barrier coating thickness in the numerical simulations. All these parameters are stochastic even if their value is commonly assumed to be deterministic. For the first time, in this work a stochastic analysis is used to predict the metal temperature in a real high pressure nozzle. The domain is the complete high pressure nozzle of F-type Mitsubishi Heavy Industries gas turbine with impingement, film and trailing edge cooling. The stochastic variations are included by coupling Uncertainty Quantification Methods and Conjugate Heat Transfer. Two Uncertainty Quantification methods have been compared: a Probabilistic Collocation Method (PCM) and a Stochastic Collocation Method (SCM). The stochastic distribution of thermal barrier coating thickness, used in the simulations, has been measured at the midspan. A Gaussian distribution for the turbulence intensity and hot core location has been assumed. By using PCM and SCM, the probability to obtain specific metal temperature at midspan is evaluated. The two methods predict the same distribution of temperature with a maximum difference of 0.6% and the results are compared with the experimental data measured in the real engine. The experimental data are inside the uncertainty band associated to the CFD predictions except near at the trailing edge on the pressure side, This work shows that one of the most important parameters affecting the metal temperature uncertainty is the pitch-wise location of the hot core. Assuming a probability distribution for this location, with a standard deviation of 1.7 degrees, the metal temperature at midspan can change up to 30%. The impact of turbulence level and thermal barrier coating thickness is one order of magnitude less important. Copyright © 2012 by ASME

Uncertainty quantification and conjugate heat transfer: A stochastic analysis

Conjugate Heat Transfer studies are a common method to predict the thermal loading in high pressure nozzles. Despite the accuracy of nowadays tools, it is not clear how to include the uncertainties associated to the turbulence level, the temperature distribution or the thermal barrier coating thickness in the numerical simulations. All these parameters are stochastic even if their value is commonly assumed to be deterministic. For the first time, in this work a stochastic analysis is used to predict the metal temperature in a real high pressure nozzle. The domain is the complete high pressure nozzle of F-type Mitsubishi Heavy Industries gas turbine with impingement, film and trailing edge cooling. The stochastic variations are included by coupling Uncertainty Quantification Methods and Conjugate Heat Transfer. Two Uncertainty Quantification methods have been compared: a Probabilistic Collocation Method (PCM) and a Stochastic Collocation Method (SCM). The stochastic distribution of thermal barrier coating thickness, used in the simulations, has been measured at the midspan. A Gaussian distribution for the turbulence intensity and hot core location has been assumed. By using PCM and SCM, the probability to obtain specific metal temperature at midspan is evaluated. The two methods predict the same distribution of temperature with a maximum difference of 0.6% and the results are compared with the experimental data measured in the real engine. The experimental data are inside the uncertainty band associated to the CFD predictions except near at the trailing edge on the pressure side, This work shows that one of the most important parameters affecting the metal temperature uncertainty is the pitch-wise location of the hot core. Assuming a probability distribution for this location, with a standard deviation of 1.7 degrees, the metal temperature at midspan can change up to 30%. The impact of turbulence level and thermal barrier coating thickness is one order of magnitude less important. Copyright © 2012 by ASME