The Inverse Design of Internally Cooled Turbine Blades

1985 ◽  
Vol 107 (1) ◽  
pp. 123-126 ◽  
Author(s):  
S. R. Kennon ◽  
G. S. Dulikravich
Keyword(s):  
Heat Flux ◽  
Cross Section ◽  
Turbine Blades ◽  
Design Procedure ◽  
Coolant Flow ◽  
Surface Shape ◽  
Inverse Design ◽  
Flow Passage ◽  
Hollow Blade ◽  
Internally Cooled

A methodology is developed for the inverse design and/or analysis of interior coolant flow passage shapes in internally cooled configurations with particular applications to turbine cascade blade design. The user of this technique may specify the temperature (or heat flux) distribution along the blade outer fixed surface shape and the unknown interior coolant/blade interface. The numerical solution of the outer gas flow field determines the remaining unspecified blade outer surface quantity—surface heat flux if temperature was originally specified or vice versa. Along the unknown coolant flow passage shape the designer has the freedom to specify the desired temperature distribution. The hollow blade wall thickness distribution is then found from the solution of Laplace’s equation governing the temperature field within the solid portion of the hollow blade, while satisfying both boundary conditions of temperature and heat flux at the fixed outer blade surface, and the specified temperature boundary condition on the evolving inner surface. A first order panel method, coupled with Newton’s N-dimensional interation scheme, is used for the iterative solution of the unknown coolant/blade interface shape. Results are shown for a simple eccentrical bore pipe cross section and a realistic turbine blade cross section. The inverse design procedure is shown to be efficient and stable for all configurations that have been tested.

Inverse Design of Coolant Flow Passage Shapes With Partially Fixed Internal Geometries

1985 ◽  
Author(s):  
Stephen R. Kennon ◽  
George S. Dulikravich
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Turbine Blade ◽  
Outer Boundary ◽  
Turbine Blades ◽  
Design Procedure ◽  
Coolant Flow ◽  
Inverse Design ◽  
Original Design ◽  
Flow Passage

A method is described for the inverse design of complex coolant flow passage shapes in internally cooled turbine blades. This method is a refinement and extension of a method developed by the authors for designing a single coolant hole in turbine blades. The new method allows the turbine designer to specify the number of holes the turbine blade is to have. In addition, the turbine designer may specify that certain portions of the interior coolant flow passage geometry are to remain fixed (eg. struts, surface coolant ejection channels, etc.). Like the original design method, the designer must specify the outer blade surface temperature and heat flux distribution and the desired interior coolant flow passage surface temperature distributions. This solution procedure involves satisfying the dual Dirichlet and Neumann specified boundary conditions of temperature and heat flux on the outer boundary of the airfoil while iteratively modifying the shapes of the coolant flow passages using a least squares optimization procedure that minimizes the error in satisfying the specified Dirichlet temperature boundary condition on the surface of each of the evolving interior holes. Portions of the inner geometry that are specified to be fixed are not modified. A first order panel method is used to solve Laplace’s equation for the steady heat conduction within the solid portions of the hollow blade, making the inverse design procedure very efficient and applicable to realistic geometries. Results are presented for a realistic turbine blade design problem.

Inverse Design of Composite Turbine Blade Circular Coolant Flow Passages

1986 ◽  
Author(s):  
Ting-Lung Chiang ◽  
George S. Dulikravich
Keyword(s):  
Heat Flux ◽  
Turbine Blade ◽  
Flux Distribution ◽  
Turbine Blades ◽  
Unconstrained Minimization ◽  
Coolant Flow ◽  
Inverse Design ◽  
Blade Surface ◽  
Heat Flux Distribution ◽  
Linear Temperature

An inverse design and optimization method is developed to determine the proper size and location of the circular shaped holes (coolant flow passages) in a composite turbine blade. The temperature distributions specified on the outer blade surface and on the surfaces of the inner holes can be prescribed a priori. In addition, heat flux distribution on the outer blade surface can be prescribed and iteratively enforced using optimization procedures. The prescribed heat flux distribution on the outer surface is iteratively approached by using the Sequential Unconstrained Minimization Technique (SUMT) to adjust the sizes and locations of the initially guessed circular holes. During each optimization iteration, a two-dimensional heat conduction equation is solved using direct Boundary Element Method (BEM) with linear temperature singularity distribution. For manufacturing purposes the additional constraints are enforced assuring the minimal prescribed blade wall thickness and spacing between the walls of two neighboring holes. The method is applicable to both single material (homogeneous) and coated (composite) turbine blades. Three different cases were tested to prove the feasibility and the accuracy of the method.

Inverse Design of Composite Turbine Blade Circular Coolant Flow Passages

1986 ◽  
Vol 108 (2) ◽  
pp. 275-282 ◽  
Author(s):  
T.-L. Chiang ◽  
G. S. Dulikravich
Keyword(s):  
Heat Flux ◽  
Turbine Blade ◽  
Flux Distribution ◽  
Turbine Blades ◽  
Coolant Flow ◽  
Inverse Design ◽  
Blade Surface ◽  
Heat Flux Distribution ◽  
Linear Temperature ◽  
Circular Holes

An inverse design and optimization method is developed to determine the proper size and location of the circular holes (coolant flow passages) in a composite turbine blade. The temperature distributions specified on the outer blade surface and on the surfaces of the inner holes can be prescribed a priori. In addition, heat flux distribution on the outer blade surface can be prescribed and iteratively enforced using optimization procedures. The prescribed heat flux distribution on the outer surface is iteratively approached by using the Sequential Unconstrained Minimization Technique (SUMT) to adjust the sizes and locations of the initially guessed circular holes. During each optimization iteration, a two-dimensional heat conduction equation is solved using direct Boundary Element Method (BEM) with linear temperature singularity distribution. For manufacturing purposes the additional constraints are enforced assuring the minimal prescribed blade wall thickness and spacing between the walls of two neighboring holes. The method is applicable to both single material (homogeneous) and coated (composite) turbine blades. Three different cases were tested to prove the feasibility and the accuracy of the method.

Inverse Design and Active Control Concepts in Strong Unsteady Heat Conduction

1988 ◽  
Vol 41 (6) ◽  
pp. 270-277 ◽  
Author(s):  
George S. Dulikravich
Keyword(s):  
Thermal Conditions ◽  
Coolant Flow ◽  
Geometric Constraints ◽  
Inverse Design ◽  
Optimal Time ◽  
Design And Optimization ◽  
Design Engineers ◽  
Thermal Boundary Conditions ◽  
Internally Cooled ◽  
Unsteady Heat Conduction

A summary of recent research in the field of inverse design and optimization of coolant flow passages in the internally cooled configurations is presented. The methodology allows design engineers to prescribe desired surface temperature and heat flux distributions and to fix portions of the multiply connected realistically shaped configurations. The shapes of the resulting coolant flow passages can be arbitrarily or circularly shaped with a capability to maintain certain manufacturing geometric constraints. Unsteady cooling of organs and tissues in bioengineering is demonstrated by determining optimal time variation of thermal boundary conditions on the walls of the cooling container while maintaining the geometry and size of the configuration. Another concept suggests that components subjected to strong unsteady cooling or heating can be optimized for the desired time dependent overspecified surface thermal conditions by determining the corresponding instantaneous temperatures of the coolant flow passages. This effect can be achieved by applying optimal control of distributed coolant flow rates in each flow passage.

Minimization of Coolant Mass Flow Rate in Internally Cooled Gas Turbine Blades

1999 ◽  
Author(s):  
Thomas J. Martin ◽  
George S. Dulikravich ◽  
Zhen-Xue Han ◽  
Brian H. Dennis
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Mass Flow Rate ◽  
Turbine Blade ◽  
Flow Rate ◽  
Design Variable ◽  
Turbine Blades ◽  
Dimensional System ◽  
One Dimensional ◽  
Internally Cooled

This paper presents a coupled aerodynamic and thermal study of computer-automated design and optimization of internally cooled turbine blades. The turbine blade, thermal barrier coating, coolant passages and struts were developed from a set of design variables, including β-splines for the coolant wall thickness distribution. The turbine inlet temperature, mass flow rate, and coolant wall roughness were also incorporated into the design variable set. The maximum temperature in the metal blade was enforced with equality or inequality constraint functions. Because the coolant flow rate was a design variable, this function could not be explicitly minimized. Instead, three different thermal objective functions were studied: uniform temperature, heat flux extremum, and minimum coolant ejection temperature. Results have shown that it is possible to increase or maintain high turbine inlet temperatures while decreasing the turbine blade coolant requirements. A new constrained hybrid optimization algorithm was developed and used to modify the turbine blade designs until an optimum design was found. This evolutionary optimization package incorporated four popular algorithms (steepest descent, genetic, simplex, and simulated annealing) with automatic switching among them. A computational heat conduction analysis, using the boundary element method (BEM), was iteratively coupled to an unstructured finite volume Reynolds-averaged Navier-Stokes CFD analysis for turbulent hot gas flow. A quasi-one-dimensional system with heat addition and friction was iteratively coupled to the BEM heat conduction via heat flux for the simulation of the airflow in the serpentine coolant passages. This quasi-one-dimensional system yielded correlations for the heat convection coefficients on the coolant passage walls. The coolant passage pressure loss was one of the quantities arising from the quasi-one-dimensional analysis.

Cooling Efficiency Enhancement Using Impingement Cooling Technique for Turbine Blades

2013 ◽  
Author(s):  
Keerthivasan Rajamani ◽  
Madhu Ganesh ◽  
Karthikeyan Paramanandam ◽  
Chandiran Jayamurugan ◽  
Sridharan R. Narayanan ◽  
...  
Keyword(s):  
Dead Zone ◽  
Turbine Blades ◽  
Leading Edge ◽  
Coolant Flow ◽  
Base Case ◽  
Surface Cooling ◽  
Flow Passage ◽  
Impingement Cooling ◽  
First Case ◽  
Cooling Passage

The effect of impingement cooling on the internal surface (cooling passage) of the leading edge region in a commercial turbine high pressure first stage rotor blade is investigated using Computational Fluid Dynamics (CFD) simulations. The flow domain is obtained by stretching the middle cross section (50% span) of the above mentioned blade. The simulations are performed for 3 different profiles in the cooling flow passage. In all the cases, the nozzle position and Mach number of cooling fluid is kept constant at E/D = 4.32 and 0.4 respectively. In the first case, the suction side profile is modified to facilitate shift in the vortex. This may reduce the crossflow effect, which will enhance the Nuavg. However, simulation results showed that Nuavg is reduced by 2% when compared to base case. In the second case, the coolant flow passage is smoothened at the apex to reduce dead zone and to enhance spreading of the jet. In this case, a 3% increase in Nuavg is obtained. Based on the analysis of velocity contours in the second case, the coolant flow passage in the third case is further modified to improve the spreading of flow. This resulted in 5% increase in the Nuavg when compared to base case.

Laminar Natural Convection About Downward Facing Heated Blunt Bodies to Liquid Metals

1976 ◽  
Vol 98 (2) ◽  
pp. 208-212 ◽  
Author(s):  
G. M. Harpole ◽  
I. Catton
Keyword(s):  
Heat Flux ◽  
Surface Temperature ◽  
Series Expansion ◽  
Surface Heat Flux ◽  
Liquid Metals ◽  
Surface Heat ◽  
Surface Shape ◽  
Boundary Layer Equations ◽  
Stagnation Points ◽  
Shape Dependence

The laminar boundary layer equations for free convection over bodies of arbitrary shape (i.e., a three-term series expansion) and with arbitrary surface heat flux or surface temperature are solved in local Cartesian coordinates. Both two-dimensional bodies (e.g., horizontal cylinders) and axisymmetric bodies (e.g., spheres) with finite radii of curvature at their stagnation points are considered. A Blasius series expansion is applied to convert from partial to ordinary differential equations. An additional transformation removes the surface shape dependence and the surface heat flux or surface temperature dependence of the equations. A second-order-correct, finite-difference method is used to solve the resulting equations. Tables of results for low Prandtl numbers are presented, from which local Nusselt numbers can be computed.

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