Effect of Input Variability on the Performance of Turbine Blade Thermal Design Using Monte Carlo Simulation: An Exploratory Study

A probabilistic approach to the thermal design and analysis of cooled turbine blades is presented. Various factors that affect the probabilistic performance of the blade thermal design are grouped into categories and a select number of factors known to be significant, for which the variability could be assessed are modeled as random variables. The variability data for these random variables were generated from separate Monte Carlo simulations (MCS) of the combustor and the upstream stator and secondary air system. The oxidation life of the blade is used as a measure to evaluate the thermal design as well as to evaluate validity of the methods. Two approaches have been explored to simulate blade row life variability and compare it with the field data. Field data from several engine removals are used for investigating the approach. Additionally a response surface approximation technique has been explored to expedite the simulation process. The results indicate that the conventional approach of a worst-case analysis is overly conservative and analysis based on nominal values could be very optimistic. The potential of a probabilistic approach in predicting the actual variability of the blade row life is clearly evident in the results. However, the results show that, in order to predict the blade row life variability adequately, it is important to model the operating condition variability. The probabilistic techniques such as MCS could become very practical when approximation techniques such as response surface modeling are used to represent the analytical model.

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Probabilistic Lifetime Analysis for Turbine Blades Based on a Combined Direct Monte Carlo and Response Surface Approach

Volume 6: Turbo Expo 2004 ◽

10.1115/gt2004-53439 ◽

2004 ◽

Cited By ~ 6

Author(s):

Matthias Voigt ◽

Roland Mu¨cke ◽

Konrad Vogeler ◽

Michael Oevermann

Keyword(s):

Monte Carlo ◽

Response Surface ◽

Turbine Blades ◽

Probabilistic Approach ◽

Computational Effort ◽

Life Assessment ◽

Direct Monte Carlo Simulation ◽

Gas Turbine Blades ◽

Lifetime Analysis ◽

Analysis Models

The paper addresses a probabilistic approach to lifetime prediction of cooled gas turbine blades. Variations of load and material parameters are taken into account by a combination of a direct Monte Carlo Simulation and a Response Surface Method. The proposed approach allows a reduction in the number of finite element analyses especially for problems with low failure probability. Therefore, the computational effort becomes acceptable even for full-scale 3D and 2D analysis models. Results of a probabilistic life assessment are shown for two cooled turbine blades. The probability of failure and the sensitivity of material and loading parameters are presented.

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Robust Thermal Design for Power Device Package Using Response Surface Method and Monte Carlo Simulation

Journal of Thermal Science and Technology ◽

10.1299/jtst.3.452 ◽

2008 ◽

Vol 3 (3) ◽

pp. 452-460 ◽

Cited By ~ 1

Author(s):

Yasuyuki YOKONO ◽

Katsumi HISANO ◽

Kenji HIROHATA

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Response Surface ◽

Response Surface Method ◽

Thermal Design ◽

Power Device ◽

Surface Method

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FP/FIFO scheduling: coexistence of deterministic and probabilistic QoS guarantees

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.407 ◽

2007 ◽

Vol Vol. 9 no. 1 (Distributed Computing and...) ◽

Author(s):

Pascale Minet ◽

Steven Martin ◽

Leila Azouz Saidane ◽

Skander Azzaz

Keyword(s):

Response Time ◽

Probabilistic Approach ◽

Worst Case Analysis ◽

Deterministic Approach ◽

Worst Case ◽

Qos Guarantee ◽

High Resource ◽

Qos Guarantees ◽

International Audience

Distributed Computing and Networking International audience In this paper, we focus on applications having quantitative QoS (Quality of Service) requirements on their end-to-end response time (or jitter). We propose a solution allowing the coexistence of two types of quantitative QoS garantees, deterministic and probabilistic, while providing a high resource utilization. Our solution combines the advantages of the deterministic approach and the probabilistic one. The deterministic approach is based on a worst case analysis. The probabilistic approach uses a mathematical model to obtain the probability that the response time exceeds a given value. We assume that flows are scheduled according to non-preemptive FP/FIFO. The packet with the highest fixed priority is scheduled first. If two packets share the same priority, the packet arrived first is scheduled first. We make no particular assumption concerning the flow priority and the nature of the QoS guarantee requested by the flow. An admission control derived from these results is then proposed, allowing each flow to receive a quantitative QoS guarantee adapted to its QoS requirements. An example illustrates the merits of the coexistence of deterministic and probabilistic QoS guarantees.

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Tolerances: Their Analysis and Synthesis

Journal of Engineering for Industry ◽

10.1115/1.2899553 ◽

1990 ◽

Vol 112 (2) ◽

pp. 113-121 ◽

Cited By ~ 86

Author(s):

Woo-Jong Lee ◽

T. C. Woo

Keyword(s):

Reliability Index ◽

Cost Minimization ◽

Probabilistic Approach ◽

Convex Polytope ◽

Random Variable ◽

Structural Safety ◽

Worst Case Analysis ◽

Manufacturing Cost ◽

Worst Case ◽

Tolerance Synthesis

Tolerance, representing a permissible variation of a dimension in an engineering drawing, is synthesized by considering assembly stack-up conditions based on manufacturing cost minimization. A random variable and its standard deviation are associated with a dimension and its tolerance. This probabilistic approach makes it possible to perform trade-off between performance and tolerance rather than the worst case analysis as it is commonly practiced. Tolerance (stack-up) analysis, as an inner loop in the overall algorithm for tolerance synthesis, is performed by approximating the volume under the multivariate probability density function constrained by nonlinear stack-up conditions with a convex polytope. This approximation makes use of the notion of reliability index [10] in structural safety. Consequently, the probabilistic optimization problem for tolerance synthesis is simplified into a deterministic nonlinear programming problem. An algorithm is then developed and is proven to converge to the global optimum through an investigation of the monotonic relations among tolerance, the reliability index, and cost. Examples from the implementation of the algorithm are given.

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Robust Thermal Design for Power Device Package Using Response Surface Method and Monte Carlo Simulation

ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference, Volume 2 ◽

10.1115/ht2007-32168 ◽

2007 ◽

Cited By ~ 9

Author(s):

Yasuyuki Yokono ◽

Katsumi Hisano ◽

Kenji Hirohata

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Thermal Resistance ◽

Response Surface ◽

Response Surface Method ◽

Thermal Conduction ◽

Thermal Design ◽

Power Device ◽

Design Parameters ◽

Surface Method

In the present study, the robust thermal design of a power device package was accomplished using thermal conduction calculation, design of experiment, response surface method and Monte Carlo simulation. Initially, the effects of the design parameters on the solder strain were examined in terms of the thermal expansion difference as a result of unsteady thermal conduction simulation. From the factorial effects of design parameters, the design proposals were screened. Then, robustness of the thermal resistance was evaluated for the three design proposals obtained. The thermal resistances were calculated by solving the steady thermal conduction equation under the design of experiment conditions. The solder thickness, the substrate thickness, and the cooling fin performance were considered as the fluctuation factors, assuming the error associated with manufacturing process. Using a response surface method, the values of thermal resistance were expressed as a function of the design variables. The variances of the thermal resistance were examined based on Monte Carlo simulations. Related to the cooling fin design, the Pareto line showing the trade-off relation between the fin dimension and the fan velocity was obtained. By repeating the Monte Carlo simulations, the Pareto solution was calculated so that the thermal resistances satisfy the criteria in the position of 95 percrntile of the thermal resistance variation. Under the same flow velocity conditions, the fin dimensions become about 10% higher compared to the case where the manufacturing error was not taken into account. By carrying out the thermal design following this Pareto line, even if the manufacturing error was taken into consideration, the thermal resistance could satisfy the desired value.

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Thermal Robustness and Mass Optimization of Heat Pipe Shape for Spacecraft Panel Using a Combination of Response Surface Methodology and Monte Carlo Simulation

Volume 2: 28th Design Automation Conference ◽

10.1115/detc2002/dac-34055 ◽

2002 ◽

Cited By ~ 3

Author(s):

Takashi Kobayashi ◽

Takehide Nomura ◽

Masaki Kamifuji ◽

Akira Yao ◽

Tetsurou Ogushi

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Response Surface Methodology ◽

Heat Pipe ◽

Response Surface ◽

Thermal Control ◽

Optimization Method ◽

Thermal Design ◽

Design Parameters ◽

Short Time

A commercial spacecraft should survive on orbit for more than 10 years under the severe circumstances without any maintenance. To realize this subject, not only performance but also other design factors such as reliability, mass, robustness, cost, etc. should be taken into consideration. From point of the thermal design, it is very important to obtain the robust thermal control subsystem with matrix heat pipe layout while minimizing the mass (weight). A new thermal optimization method without compromising the thermal robustness and the mass of thermal subsystem is highly anticipated. This paper proposes a robust thermal design approach for optimizing the heat pipe shape to minimize the mass of the spacecraft panel. We apply a combination of Design of Experiments (DOE), Response Surface Methodology (RSM) and Monte Carlo Simulation to determine the robust design parameters that minimize the mass of the heat pipe structure. Dimensions of the heat pipe design parameters were determined with rationally in a short time and practical robust optimization method was established.

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Why simple quadrature is just as good as Monte Carlo

Monte Carlo Methods and Applications ◽

10.1515/mcma-2020-2055 ◽

2020 ◽

Vol 26 (1) ◽

pp. 1-16

Author(s):

Kevin Vanslette ◽

Abdullatif Al Alsheikh ◽

Kamal Youcef-Toumi

Keyword(s):

Monte Carlo ◽

Random Sampling ◽

Bayesian Probability ◽

Independent Factor ◽

Worst Case ◽

Statistical Equivalence ◽

Deterministic Sampling ◽

Quadrature Methods ◽

Quadrature Sampling ◽

Simple Quadrature

AbstractWe motive and calculate Newton–Cotes quadrature integration variance and compare it directly with Monte Carlo (MC) integration variance. We find an equivalence between deterministic quadrature sampling and random MC sampling by noting that MC random sampling is statistically indistinguishable from a method that uses deterministic sampling on a randomly shuffled (permuted) function. We use this statistical equivalence to regularize the form of permissible Bayesian quadrature integration priors such that they are guaranteed to be objectively comparable with MC. This leads to the proof that simple quadrature methods have expected variances that are less than or equal to their corresponding theoretical MC integration variances. Separately, using Bayesian probability theory, we find that the theoretical standard deviations of the unbiased errors of simple Newton–Cotes composite quadrature integrations improve over their worst case errors by an extra dimension independent factor {\propto N^{-\frac{1}{2}}}. This dimension independent factor is validated in our simulations.

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