Uncertainty Quantification and Conjugate Heat Transfer: A Stochastic Analysis

Abstract

Conjugate heat transfer is gaining acceptance for predicting the thermal loading in high pressure nozzles. Despite the accuracy nowadays of numerical solvers, 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 simulated is the high pressure nozzle of an F-type Mitsubishi Heavy Industries gas turbine. The complete coolant system is included: 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 a 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. 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 deg, the metal temperature at midspan can change up to 30%. The impact of turbulence level and thermal barrier coating thickness is 1 order of magnitude less important.

Uncertainty quantification and race car aerodynamics

“…The model used in this paper has been fully validated in [7,5,14]. The code has been validated against Monte Carlo Simulations in several applications, from multi-physics problems [5] to turbulence closures uncertainty [14] and geometrical uncertainty [4].…”

“…The code has been validated against Monte Carlo Simulations in several applications, from multi-physics problems [5] to turbulence closures uncertainty [14] and geometrical uncertainty [4]. Table 1 shows the variations which were considered in this work and the number of simulations required to build the stochastic space: The Uncertainty Quantification comparison gives to the designer the probability to achieve higher downforce under random variations of the car position.…”

“…These errors are random and only stochastic methodologies, known as Uncertainty Quantification methods [3], can be used to account their effects. These methods have been developed in the aerospace sector to evaluate the impact of manufacturing errors on the life of the components [4][5].…”

Uncertainty Quantification, Rare Events, and Mission Optimization: Stochastic Variations of Metal Temperature During a Transient

“…CFD is moving gradu ally toward high fidelity models [5][6][7][8], and this demands the introduction of uncertainties in such models using uncertainty quantification (UQ) techniques [9][10][11]. CFD is moving gradu ally toward high fidelity models [5][6][7][8], and this demands the introduction of uncertainties in such models using uncertainty quantification (UQ) techniques [9][10][11].…”

Uncertainty Quantification of Leakages in a Multistage Simulation and Comparison With Experiments

“…The study of Bunker [18], for example, was based on a flat plate assumption. More recently some studies have considered the impact or real geometries [19,[21][22][23][24][25][26][27]. However it is not clear how uncertainty is propagating in a flow.…”