Improving a Hospital Trayline through the Application of Lean Techniques

Design Optimization of Gas Turbine Blade Internal Cooling ChannelsNarasimha R. Nagaiah and Christopher D. Geiger

Department of Industrial Engineering and Management SystemsUniversity of Central Florida4000 Central Florida BlvdOrlando, FL 32816-2993USA2013 IIE Industrial & Systems Engineering Research ConferenceSan Juan, Puerto RicoMay 19-22, 2013BackgroundPower GenerationTurbines for Power GenerationMotivation of Research InvestigationProposed Design Optimization ApproachComputational StudyProblem Formulation and Parameter SettingExperimental ResultsSummary and Conclusions Future Research DirectionsOutline

2BackgroundPower GenerationGlobal Energy DemandExxonMobil projects that global energy demand will grow by 1.2% annually, on average, between 2008 to 2035 - resulting in about a 30% increase from 2008 to 2035Turbines for Power GenerationTurbines, in general, are the heart of almost all of the world's electric power generating systems. (Source: National Energy Technology Laboratory (NETL))

Approximately 5000+ power plants in the world

Turbines are involved in generation of about 98% of all electricity added to US Grid (IBISWorld Report 2009)

-In 2008 power generation revenue is US$112 billion in the U.S. alone, which is a 12% increase in energy consumption compared to 2005, which generated revenue of US$100 billion (IBISWorld, 2008).

-It is estimated that over the next 25 years, the worlds energy consumption will grow by 50 percent

3BackgroundTurbines are classified based on the driving fluidSteam, Gas, Water and Wind

Focus of this study: Gas TurbinesUsed for power generationAlso used for transportation

Why Gas Turbines?

High efficiency: > 60% CCGT

Multi-fuel capabilities: Coal, Natural gas, gasoline, propane, diesel, and kerosene as well as renewable fuels such as E85, biodiesel and biogas.

4BackgroundTheir Working Principle and Critical Components of Gas TurbinesGENERATOR

INTAKEEXHAUSTCOMPRESSIONCOMBUSTIONEXPANSIONCOMPRESSORTURBINEFUEL1234Turbine Inlet Temperature (TIT)Courtesy: Dr.Sommai Priprem, Khon Kaen University

Figure: Vane or NozzleFigure: Blade

Courtesy: www.me.umn.edu

Figure: Gas turbine Critical ComponentsCourtesy: http://www.turbocare.com/gas_turbine_parts.html

The gas turbine is an internal combustion engine that uses air and fuel (hot gas) mixture as the working fluid.The engine extracts chemical energy from fuel and converts it to mechanical energy using the gaseous energy of the working fluid (air) to drive the engine and propeller, which, in turn, propel the airplane.Intake of air (and possibly fuel).Compression of the air (and possibly fuel).Combustion, where fuel is injected (if it was not drawn in with the intake air) and burned to convert the stored energy.Expansion and exhaust, where the converted energy is put to use.

In the turbine engine, however, these four steps occur at the same time but in different places. As a result of this fundamental difference, the turbine has engine sections called:The inlet sectionThe compressor sectionThe combustion section (the combustor)The turbine (and exhaust) section.

The turbine section of the gas turbine engine has the task of producing usable output shaft power to drive the propeller. In addition, it must also provide power to drive the compressor and all engine accessories.It does this by expanding the high temperature, pressure, and velocity gas and converting the gaseous energy to mechanical energy in the form of shaft power.A large mass of air must be supplied to the turbine in order to produce the necessary power. This mass of air is supplied by the compressor, which draws the air into the engine and squeezes it to provide high-pressure air to the turbine.The compressor does this by converting mechanical energy from the turbine to gaseous energy in the form of pressure and temperature.5BackgroundGas Turbine Internal Cooling SystemHot gas path components are cooled by a small percentage of compressed air that is extracted from the compressor by a cooling supply system

Turbine Inlet Temperature (TIT) has greatest influence on core power and thermal efficiencyTIT reaches metal melting point temperatures (2200 F to 2600 F)

Where only the first stage needs cooling, 4% to 5% of the mainstream flow.

Several stages needs cooling, then cooling air flow can be as high as 25% to 30% of the mainstream flow.

One of the most important parameters for measuring and assessing the cooling performance of a blade is the cooling effectiveness

The advances in the blade cooling and material technology have enabled the life of the blade to be increased in spite of high TIT. The cooling effectiveness is influenced by many variables such as the blade design, arrangement of cooling channels, design configuration of ribs and the mass flow rate of cooling air used.6BackgroundBlade Internal Cooling System ConfigurationFocus is rib-configured internal cooling channels

Ribs increase air flow turbulence, thereby increasing heat transfer

Ribs decrease air flow pressure, thereby decreasing core power output

Therefore, important to balance cooling effectiveness (heat transfer) and cooling air flow pressure

Figure :The schematic of a modern gas turbine blade with common cooling techniques [obtained from Han (2004)]

Zone 1: leading edge Film cooling, and Impingement coolingZone 2: Pressure surface and suction surfaces Film cooling and internal Channel coolingZone 3: Blade tip Film cooling

Film cooling depends on mass flow rate and flow velocity of the coolant rib configuration in the internal cooling passages7MotivationTraditional mechanical component design optimization uses numerical simulation and experimental methods to test new, pre-specified designsPotential designs are limited in numberTime and cost prohibitive to validate all possible designs

Blade internal cooling channel design should simultaneously satisfy two primary objectives:Maximize the cooling effectiveness () (or, heat transfer coefficient (h))Minimize the pressure drop (p) in the internal cooling channel

8Previous ResearchMultiobjective Optimization in Internal Cooling System Design Design of the cooling channel is extensively studied by Kim and Kim (2002), who consider the optimization of internal cooling channel withthe shape of the ribs (Kim and Kim, 2001). straight rectangular ribs (Kim and Kim, 2004),V-shaped ribs (Kim and Lee, 2007b)

Two objectives considered in their study are heat transfer coefficient and pressure dropHowever, these two objectives are combined to form a composite function using a vector of weights. The other approach was to solve each objective separately and map solutions.Selection of the weights is based on designers experience, which could lead to errors in optimization if the factors are not carefully selected.

Proposed ApproachDesign Optimization of Gas Turbine Blade Internal Cooling Channels Set of Input Data:{Periodic Segment Dimensions, Boundary Conditions, Objective Functions, Design Variables and Initial Values, Optimizing Procedure Control Parameters}Solve Governing Equations Enforce Boundary Conditions and ConstraintsGenerate Mesh of Geometric ModelGenerate Geometric Model of the Periodic Segment of the Component Using Design ValuesUpdate the Set of Candidate Design ValuesTermination Criteria Met?Report Set of Final Design ValuesPerturb the Set of Design Variable Values

YesNoOptimizerSolution Evaluation (Simulator)Set of Design Variable Values andCorresponding Objective Function Values

Compute Objective Function Values

Proposed ApproachOptimization of Gas Turbine Blade Internal Cooling Channels Set of Input Data:{Periodic Segment Dimensions, Boundary Conditions, Objective Functions, Design Variables and Initial Values, Optimizing Procedure Control Values}Solve Governing Equations Enforce Boundary Conditions and ConstraintsGenerate Mesh of Geometric ModelGenerate Geometric Model of the Periodic Segment of the Component Using Design ValuesUpdate the Set of Candidate Design Variable ValuesTermination Criteria Met?Report Set of Final Design ValuesPerturb the Set of Design Variable Values

YesNoOptimizerSolution Evaluation (Simulator)Set of Design Variable Values andCorresponding Objective Function Values

Compute Objective Function Values

Finite Difference Method 1. Introduced by Euler in the 18th century. 2. Governing equations in differential form domain with grid replacing the partial derivatives by approximations in terms of node values of the functions one algebraic equation per grid node linear algebraic equation system.temperature, pressure, velocity, and an error 3. Applied to structured grids Finite Volume Method 1. Governing equations in integral form solution domain is subdivided into a finite number of contiguous control volumes conservation equation applied to each CV. 2. Computational node locates at the centroid of each CV. 3. Applied to any type of grids, especially complex geometries 4. Compared to FD, FV with methods higher than 2nd order will be difficult, especially for 3D. Finite Element Method (not covered in this lecture-COMSOL is FEM) 1. Similar to FV 2. Equations are multiplied by a weight function before integrated over the entire domain.

During the iterations, the iterations will stop when error value is 10-3

11Proposed ApproachOptimization of Gas Turbine Blade Internal Cooling Channels 12COMSOL Multiphysics, a Finite Element Analysis Simulation Software is selectedNon-dominated Sorting Genetic Algorithm II (NSGA-II) MOEA is Used

CrossoverMutation010110010011111010Parent

Child010111010011110010010110010011111010Parents

Children1111122233f2f1f1f2ii+1i-1F1F2F3Rank and Crowding Distance Solution PerturbationReproduction/Selection

Proposed ApproachOptimization of Gas Turbine Blade Internal Cooling Channels Rank Solutions Based on Objective Function ValuesPerturb Set of Good Solutions to Generate New Set of Candidate Design Solutions (Design Variable Values)New Set of Candidate Design Variable Values

To Solution Evaluation From Solution EvaluationSelect and Store Good Solutions Based on Objective Function ValuesSet of Input Data:{Periodic Segment Dimensions, Boundary Conditions, Objective Functions, Design Variables and Initial Values, Optimizing Procedure Control Values}Solve Governing Equations Enforce Boundary Conditions and ConstraintsGenerate Mesh of Geometric ModelGenerate Geometric Model of the Periodic Segment of the Component Using Design ValuesUpdate the Set of Candidate Design Variable ValuesTermination Criteria Met?Report Set of Final Design ValuesPerturb the Set of Design Variable Values

YesNoOptimizerSolution Evaluation (Simulator)Set of Design Variable Values andCorresponding Objective Function Values

Compute Objective Function Values

Non-dominated Sorting Genetic Algorithm II (NSGA-II) MOEA is Used

Computational StudyProblem Formulation Gas turbine blade rib-based internal cooling channel geometric model with a:Length L,Height H,Pitch P,Angle of Attack of the Rib , andRib Width e

ObjectivesMaximize Heat Transfer Coefficient (h)Minimize Pressure Drop (p)Figure: Typical coolant channels in turbine blade and internal rib arrangement (Han et al., 2000)

Courtesy: http://kimerius.com

Figure: Sectional top view of blade

Computational StudyProblem Formulation - Design Variables (for Periodic Segment)Consider a periodic segment due:Replicates throughout channelSave computational time

Design variablesRib radiiR1, R2Fillet radii R3, R4, R5 and R6H

R2R1LWR3R4R5R6

R3R1R4Periodic SegmentRib 1Fillet

Without FilletsWith Fillets

Computational StudyParameter Setting CFD Simulation ParametersTable 1: Design variables and value ranges

Table 2: Initial subdomain conditions used for the COMSOL numerical simulationTable 3: Initial boundary conditions used for the CFD simulation

(Source: Han et al.)Number of Elements Triangular: 5080Quadrilateral: 388Total:5468Number of Boundary Elements460Minimum Element Quality0.8Table: Mesh statistics

Computational StudyParameter Setting - Optimizer (MOEA) Parameters (via Pilot Study)Control ParameterValuesPopulation (Pop){10, 25, 50}Generations (Genmax){100}Crossover Probability (c){80%, 90%, 95%}Mutation Probability (m){5%, 10%}Total Number of Combinations18Population size (Pop) = 50Generations (Genmax) =100Crossover (c) = 90%Mutation Probability (m) = 10%

Computational StudyResults Single Objective: Heat Transfer Coefficient (h)2 Design Variables4 Design Variables6 Design Variables

Initial Avg. value = 13.3949 W/m2.K

Best Avg. value = 15.4253 W/m2.K

15.15 % increase in h

Initial Avg. value = 13.7239 W/m2.K

Best Avg. value = 16.2793 W/m2.K

18.62 % increase in h and 5.53% more thantwo design variables case

Initial Avg. value = 13.9687 W/m2.K

Best Avg. value = 17.8476 W/m2.K

27.75 % increase in h and 9.63% more thanfour design variable case and 15.70% more than two design variables case

Computational StudyResults 2Objectives, 2 Design Variables

(b) After 25 gens(d) After 100 gens (a) Initial solutions(c) After 50 gens

Computational StudyInterpretation of Results

Computational StudyResults 2Objectives,4 Design Variables (b) After 25 gens(d) After 100 gens (a) Initial solutions(c) After 50 gens

Computational StudyResults 2Objectives,6 Design Variables (b) After 25 gens(d) After 100 gens (a) Initial solutions(c) After 50 gens

Summary and ConclusionsInvestigation undertaken is an attempt to bridge gap between multiobjective optimization and numerical simulation to automate the mechanical component design process

No researcher has tried to simultaneously optimize two or more equally-weighted design objectives for mechanical components

Proposed framework can reduce time and cost requirements depending upon the nature of the design under consideration

Future Research DirectionsReduce the computational effort: parallel processing

Introduce other objectives, variables and features to cooling optimization problem:Increase the number design variables and number of generations until the solution convergesIncrease the number objective functionsOptimize different rib configurations

Thank You!Questions?