Hierarchical Development of Three Direct-Design Methods for Two-Dimensional Axial-Turbomachinery Cascades

1993 ◽  
Vol 115 (2) ◽  
pp. 314-324 ◽  
Author(s):  
T. Korakianitis
Keyword(s):  
High Performance ◽  
Direct Method ◽  
Thickness Distribution ◽  
Leading Edge ◽  
Design Methods ◽  
Blade Design ◽  
Two Dimensional ◽  
The Third ◽  
Direct Design ◽  
Turbomachinery Cascades

The direct and inverse blade-design iterations for the selection of isolated airfoils and gas turbine blade cascades are enormously reduced if the initial blade shape has performance characteristics near the desirable ones. This paper presents the hierarchical development of three direct blade-design methods of increasing utility for generating two-dimensional blade shapes. The methods can be used to generate inputs to the direct- or inverse-blade-design sequences for subsonic or supersonic airfoils for compressors and turbines, or isolated airfoils. The examples included for illustration are typical modern turbine cascades, and they have been designed by the direct method exclusively. The first method specifies the airfoil shapes with analytical polynomials. It shows that continuous curvature and continuous slope of curvature are necessary conditions to minimize the possibility of flow separation, and to lead to improved blade designs. The second method specifies the airfoil shapes with parametric fourth-order polynomials, which result in continuous-slope-of-curvature airfoils, with smooth Mach number and pressure distributions. This method is time consuming. The third method specifies the airfoil shapes by using a mixture of analytical polynomials and mapping the airfoil surfaces from a desirable curvature distribution. The third method provides blade surfaces with desirable performance in very few direct-design iterations. In all methods the geometry near the leading edge is specified by a thickness distribution added to a construction line, which eliminates the leading edge overspeed and laminar-separation regions. The blade-design methods presented in this paper can be used to improve the aerodynamic and heat transfer performance of turbomachinery cascades, and they can result in high-performance airfoils in very few iterations.

Prescribed-Curvature-Distribution Airfoils for the Preliminary Geometric Design of Axial-Turbomachinery Cascades

1992 ◽  
Author(s):  
Theodosios Korakianitis
Keyword(s):  
Turbine Blade ◽  
High Performance ◽  
Direct Method ◽  
Thickness Distribution ◽  
Turbine Blades ◽  
Leading Edge ◽  
Design Parameters ◽  
Blade Design ◽  
Curvature Distribution ◽  
Stagger Angle

Blade surfaces with continuous curvature and continuous slope of curvature minimize the possibility of flow separation, lead to improved blade designs, and reduce the direct and inverse blade-design iterations for the selection of isolated airfoils and gas-turbine-blade cascades. A method for generating two-dimensional blade shapes is presented. The geometry near the trailing edge is specified by an analytic polynomial, the main portion of the blade surface is mapped using as input a prescribed surface-curvature distribution, and the leading edge is specified as a thickness distribution added to a construction line. This procedure is similar for the suction and pressure surfaces, and by specification it constructs continuous slope-of-curvature surfaces that result in smooth surface-Mach-number and surface-pressure distributions. The method can be used to generate subsonic or supersonic airfoils for compressors and turbines, or isolated airfoils. The resulting geometric shapes can be used as inputs to various blade-design sequences. It is shown that, with other cascade-design parameters being equal, increasing the stagger angle of turbine blades results in more-front-loaded and thinner blades, and that there is an optimum stagger angle resulting in minimum wake thickness. The subsonic axial-turbine blade rows included for discussion in this paper have been designed by iterative modifications of the blade geometry to obtain a desirable velocity distribution. The blade-design method can be used to improve the aerodynamic and heat transfer performance of turbine cascades, and it can result in high-performance airfoils, even if using the direct method exclusively, in very few iterations.

Prescribed-Curvature-Distribution Airfoils for the Preliminary Geometric Design of Axial-Turbomachinery Cascades

1993 ◽  
Vol 115 (2) ◽  
pp. 325-333 ◽  
Author(s):  
T. Korakianitis
Keyword(s):  
Turbine Blade ◽  
High Performance ◽  
Direct Method ◽  
Thickness Distribution ◽  
Turbine Blades ◽  
Leading Edge ◽  
Design Parameters ◽  
Blade Design ◽  
Curvature Distribution ◽  
Stagger Angle

Blade surfaces with continuous curvature and continuous slope of curvature minimize the possibility of flow separation, lead to improved blade designs, and reduce the direct and inverse blade-design iterations for the selection of isolated airfoils and gas-turbine-blade cascades. A method for generating two-dimensional blade shapes is presented. The geometry near the trailing edge is specified by an analytic polynomial, the main portion of the blade surface is mapped using as input a prescribed surface-curvature distribution, and the leading edge is specified as a thickness distribution added to a construction line. This procedure is similar for the suction and pressure surfaces, and by specification it constructs continuous slope-of-curvature surfaces that result in smooth surface-Mach-number and surface-pressure distributions. The method can be used to generate subsonic or supersonic airfoils for compressors and turbines, or isolated airfoils. The resulting geometric shapes can be used as inputs to various blade-design sequences. It is shown that, with other cascade-design parameters being equal, increasing the stagger angle of turbine blades results in more front-loaded and thinner blades, and that there is an optimum stagger angle resulting in minimum wake thickness. The subsonic axial-turbine blade rows included for discussion in this paper have been designed by iterative modifications of the blade geometry to obtain a desirable velocity distribution. The blade-design method can be used to improve the aerodynamic and heat transfer performance of turbine cascades, and it can result in high-performance airfoils, even if using the direct method exclusively, in very few iterations.

scholarly journals Development of an Aerostructural Analysis Tool for a Low-Sweep Parametric Wing

2021 ◽  
Author(s):  
Julian Bardin
Keyword(s):  
Boundary Layer ◽  
Direct Method ◽  
Three Dimensional ◽  
Beam Theory ◽  
Leading Edge ◽  
Analysis Tool ◽  
Two Dimensional ◽  
Viscous Boundary Layer ◽  
Drag Forces ◽  
Displacement Thickness

An aerostructural analysis program was developed to predict the aerodynamic performance of a non-rigid, low-sweep wing. The wing planform was geometrically defined to have a rectangular section, and a trapezoidal section. The cross-section was further set to an airfoil shape which was consistent across the entire wingspan. Furthermore, to enable the inclusion of this multidisciplinary analysis module into an optimization scheme, the wing geometry was defined by a series of parameters: root chord, taper ratio, leading-edge sweep, semi-span length, and the kink location. Aerodynamic analysis was implemented through the quasi-three-dimensional approach, including a three-dimensional inviscid solution and a sectional two-dimensional viscous solution. The inviscid analysis was provided through the implementation of the vortex ring lifting surface method, which modelled the wing about its mean camber surface. The viscous aerodynamic solution was implemented through a sectional slicing of the wing. For each section, the effective angle of attack was determined and provided as an input to a two-dimensional airfoil solver. This airfoil solution was comprised of two subcomponents: a linear-strength vortex method inviscid solution, and a direct-method viscous boundary layer computation. The converged airfoil solution was developed by adjusting the effective airfoil geometry to account for the boundary layer displacement thickness, which in itself required the inviscid tangential speeds to compute. The structural solution was implemented through classical beam theory, with a torsion and bending calculator included. The torque and bending moment distribution along the wing were computed from the lift distribution, neglecting the effects of drag, and used to compute the twist and deflection of the wing. Interdisciplinary coupling was achieved through an iterative scheme. With the developed implementation, the inviscid lift loads were used to compute the deformation of the wing. This deformation was used to update the wing mesh, and the inviscid analysis was run again. This iteration was continued until the lift variation between computations was below 0.1%. Once the solution was converged upon by the inviscid and structural solutions, the viscous calculator was run to develop the parasitic drag forces. Once computation had completed, the aerodynamic lift and drag forces were output to mark the completion of execution.

A Non-Dimensional Quasi-3D Blade Design Approach With Respect to Aerodynamic Criteria

2008 ◽  
Author(s):  
Amit Kumar Dutta ◽  
Peter Michael Flassig ◽  
Dieter Bestle
Keyword(s):  
Design Process ◽  
High Performance ◽  
Thickness Distribution ◽  
Computational Effort ◽  
Design Flow ◽  
Computational Time ◽  
Design Parameters ◽  
Angle Distribution ◽  
Blade Design ◽  
Additional Increase

The competition between aero-engine manufacturers has increased dramatically in the last decades. Saving computational time within the design process, which is equivalent to saving money, is of major importance for the industry. Talking about the aerodynamic compressor blading process, it becomes indispensable to go for new or alternative ways in designing blades in order to fulfill raised performance demands. The focus of this paper, therefore, is to propose a quasi-3D aerodynamic design concept with extended and improved parameterization of the aerofoil in order to support the industrial blading process. A Be´zier-surface is selected to parameterize the non-dimensional camber-line angle distribution along the blade chord from leading to trailing edge over the entire blade height in radial direction. Starting from scratch, the geometric blade build-up is completed by superposing the resulting camber-line with a given thickness distribution. For additional increase of design freedom, Be´zier-curves are used to radially parameterize blade inlet and outlet angles in their dimensionless form. The chosen parameterization of these distributions guarantees smooth blade shapes and geometry distributions with a minimum of design parameters. For optimization purpose it is essential to get performance information on the entire blade, however, with minimal computational effort. Facing this challenge, aerodynamic blade performance is evaluated by a two-dimensional blade-to-blade flow solver for specific sections on different radial blade heights. In order to speed up the blade design process, the flow calculations are realized by a distributed computing concept on a Linux high-performance cluster. All investigations are carried out for highly loaded controlled diffusion blades which are taken from an existing industrial research application. Since selected criteria such as mean loss at design point conditions and working range for off-design flow conditions represent contradicting design goals, the blade design problem is solved by means of a multi-objective problem formulation and a stochastic optimization algorithm. As a result Pareto-optimal trade-off solutions between conflicting design goals are shown where the design engineer can choose from according to his specific preferences.

Indirect and Direct Design Methods for Design of Reinforced Concrete Pipe

2020 ◽  
Vol 2674 (9) ◽  
pp. 575-585
Author(s):  
Josh Beakley ◽  
Steven J. DelloRusso ◽  
Margarita Takou
Keyword(s):  
Applied Load ◽  
Pipe Wall ◽  
Design Method ◽  
Direct Method ◽  
Method Comparison ◽  
Design Procedure ◽  
Design Methods ◽  
Concrete Members ◽  
Direct Design ◽  
Concrete Pipe

There are currently two acceptable methods by which concrete pipe may be designed per the AASHTO Bridge Design Specifications: the direct design method and the indirect design method. The evaluation of applied load is similar for both methods, however, evaluation of the pipe’s capacity to resist applied load differs between the two methods. The indirect design method uses physical three edge bearing (TEB) testing at the production facility based on a relationship between the forces in the pipe wall in the installed condition compared with forces in the pipe wall from the TEB test. The direct design method follows the conventional design procedure for concrete members where demand versus capacity is determined using load and resistance factors to account for variability in applied loads and resistant capacity of the structure. Because of advances in computer technology, the direct method has become easier to apply than it was in the past. However, the indirect method, which has been used for approximately 70 years, has demonstrated conservatism and is a proven design method. Comparison of similar installations using the two methods has resulted in disagreements with respect to the minimum required reinforcement, however, both methods are adequately conservative, and each may have its place depending on the size and strength of the pipe. This paper presents the fundamental differences between the two design methods and offers some guidance on when to use each of them.

scholarly journals High Order Projection Plane Method for Evaluation of Supersingular Curved Boundary Integrals in BEM

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Miao Cui ◽  
Wei-zhe Feng ◽  
Xiao-wei Gao ◽  
Kai Yang
Keyword(s):  
Direct Method ◽  
Three Dimensional ◽  
High Order ◽  
Two Dimensional ◽  
Boundary Integrals ◽  
Third Order ◽  
Curved Boundary ◽  
Plane Method ◽  
The Third ◽  
Projection Plane

Boundary element method (BEM) is a very promising approach for solving various engineering problems, in which accurate evaluation of boundary integrals is required. In the present work, the direct method for evaluating singular curved boundary integrals is developed by considering the third-order derivatives in the projection plane method when expanding the geometry quantities at the field point as Taylor series. New analytical formulas are derived for geometry quantities defined on the curved line/plane, and unified expressions are obtained for both two-dimensional and three-dimensional problems. For the two-dimensional boundary integrals, analytical expressions for the third-order derivatives are derived and are employed to verify the complex-variable-differentiation method (CVDM) which is used to evaluate the high order derivatives for three-dimensional problems. A few numerical examples are given to show the effectiveness and the accuracy of the present method.

scholarly journals Development of an Aerostructural Analysis Tool for a Low-Sweep Parametric Wing

2021 ◽  
Author(s):  
Julian Bardin
Keyword(s):  
Boundary Layer ◽  
Direct Method ◽  
Three Dimensional ◽  
Beam Theory ◽  
Leading Edge ◽  
Analysis Tool ◽  
Two Dimensional ◽  
Viscous Boundary Layer ◽  
Drag Forces ◽  
Displacement Thickness

An aerostructural analysis program was developed to predict the aerodynamic performance of a non-rigid, low-sweep wing. The wing planform was geometrically defined to have a rectangular section, and a trapezoidal section. The cross-section was further set to an airfoil shape which was consistent across the entire wingspan. Furthermore, to enable the inclusion of this multidisciplinary analysis module into an optimization scheme, the wing geometry was defined by a series of parameters: root chord, taper ratio, leading-edge sweep, semi-span length, and the kink location. Aerodynamic analysis was implemented through the quasi-three-dimensional approach, including a three-dimensional inviscid solution and a sectional two-dimensional viscous solution. The inviscid analysis was provided through the implementation of the vortex ring lifting surface method, which modelled the wing about its mean camber surface. The viscous aerodynamic solution was implemented through a sectional slicing of the wing. For each section, the effective angle of attack was determined and provided as an input to a two-dimensional airfoil solver. This airfoil solution was comprised of two subcomponents: a linear-strength vortex method inviscid solution, and a direct-method viscous boundary layer computation. The converged airfoil solution was developed by adjusting the effective airfoil geometry to account for the boundary layer displacement thickness, which in itself required the inviscid tangential speeds to compute. The structural solution was implemented through classical beam theory, with a torsion and bending calculator included. The torque and bending moment distribution along the wing were computed from the lift distribution, neglecting the effects of drag, and used to compute the twist and deflection of the wing. Interdisciplinary coupling was achieved through an iterative scheme. With the developed implementation, the inviscid lift loads were used to compute the deformation of the wing. This deformation was used to update the wing mesh, and the inviscid analysis was run again. This iteration was continued until the lift variation between computations was below 0.1%. Once the solution was converged upon by the inviscid and structural solutions, the viscous calculator was run to develop the parasitic drag forces. Once computation had completed, the aerodynamic lift and drag forces were output to mark the completion of execution.

Co-planar two-dimensional Metal-Insulator-Semiconductor Capacitor: Numerical study of the device electrostatics.

2017 ◽  
Author(s):  
Varun Bheemireddy
Keyword(s):  
Space Charge ◽  
High Performance ◽  
Numerical Study ◽  
2D Materials ◽  
Space Charge Density ◽  
Two Dimensional ◽  
Short Channel ◽  
Metal Insulator ◽  
Metal Insulator Semiconductor ◽  
New Family

The two-dimensional(2D) materials are highly promising candidates to realise elegant and e cient transistor. In the present letter, we conjecture a novel co-planar metal-insulator-semiconductor(MIS) device(capacitor) completely based on lateral 2D materials architecture and perform numerical study of the capacitor with a particular emphasis on its di erences with the conventional 3D MIS electrostatics. The space-charge density features a long charge-tail extending into the bulk of the semiconductor as opposed to the rapid decay in 3D capacitor. Equivalently, total space-charge and semiconductor capacitance densities are atleast an order of magnitude more in 2D semiconductor. In contrast to the bulk capacitor, expansion of maximum depletion width in 2D semiconductor is observed with increasing doping concentration due to lower electrostatic screening. The heuristic approach of performance analysis(2D vs 3D) for digital-logic transistor suggest higher ON-OFF current ratio in the long-channel limit even without third dimension and considerable room to maximise the performance of short-channel transistor. The present results could potentially trigger the exploration of new family of co-planar at transistors that could play a signi significant role in the future low-power and/or high performance electronics.<br>

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