An Inverse Inviscid Method for the Design of Quasi-Three-Dimensional Turbomachinery Cascades

1993 ◽  
Vol 115 (1) ◽  
pp. 121-127 ◽  
Author(s):  
E. Bonataki ◽  
P. Chaviaropoulos ◽  
K. D. Papailiou
Keyword(s):  
Differential Equation ◽  
Three Dimensional ◽  
Test Cases ◽  
Elliptic Type ◽  
Flow Angle ◽  
Blade Shape ◽  
Closure Conditions ◽  
Type Boundary ◽  
Absolute Frame ◽  
The Given

The calculation of the blade shape, when the desired velocity distribution is imposed, has been the object of numerous investigations in the past. The object of this paper is to present a new method suitable for the design of turbomachinery stator and rotor blade sections, lying on an arbitrary axisymmetric stream-surface with varying streamtube width. The flow is considered irrotational in the absolute frame of reference and compressible. The given data are the streamtube geometry, the number of blades, the inlet flow conditions and the suction and pressure side velocity distributions as functions of the normalized arc-length. The output of the computation is the blade shape that satisfies the above data. The method solves an elliptic type partial differential equation for the velocity modulus with Dirichlet and periodic type boundary conditions on the (potential function, stream function)-plane (Φ, Ψ). The flow angle field is subsequently calculated solving an ordinary differential equation along the iso-Φ or iso-Ψ lines. The blade coordinates are, finally, computed by numerical integration. A set of closure conditions has been developed and discussed in the paper. The method is validated on several test cases and a discussion is held concerning its application and limitations.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

Performance enhancement of Savonius wind turbine by blade shape and twisted angle modifications

2021 ◽  
pp. 095765092098794
Author(s):  
Ahmed M Nagib Elmekawy ◽  
Hassan A Hassan Saeed ◽  
Sadek Z Kassab
Keyword(s):  
Wind Turbine ◽  
Performance Enhancement ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Vertical Axis ◽  
Cfd Simulations ◽  
Sliding Mesh ◽  
Blade Shape ◽  
Rotor Shape ◽  
Twisting Angle

Three-dimensional CFD simulations are carried out to study the increase of power generated from Savonius vertical axis wind turbines by modifying the blade shape and blade angel of twist. Twisting angle of the classical blade are varied and several proposed novel blade shapes are introduced to enhance the performance of the wind turbine. CFD simulations have been performed using sliding mesh technique of ANSYS software. Four turbulence models; realizable k -[Formula: see text], standard k - [Formula: see text], SST transition and SST k -[Formula: see text] are utilized in the simulations. The blade twisting angle has been modified for the proposed dimensions and wind speed. The introduced novel blade increased the power generated compared to the classical shapes. The two proposed novel blades achieved better power coefficients. One of the proposed models achieved an increase of 31% and the other one achieved 32.2% when compared to the classical rotor shape. The optimum twist angel for the two proposed models achieved 5.66% and 5.69% when compared with zero angle of twist.

scholarly journals From Stress to Shape: Equilibrium of Cloister and Cross Vaults

2021 ◽  
Vol 11 (9) ◽  
pp. 3846
Author(s):  
Andrea Montanino ◽  
Carlo Olivieri ◽  
Giulio Zuccaro ◽  
Maurizio Angelillo
Keyword(s):  
Error Function ◽  
Membrane Surface ◽  
Equilibrium Analysis ◽  
Test Cases ◽  
Order Partial Differential Equation ◽  
Negative Semidefinite ◽  
Historical Heritage ◽  
Masonry Vaults ◽  
Membrane Shape ◽  
The Given

The assessment of the equilibrium and the safety of masonry vaults is of high relevance for the conservation and restoration of historical heritage. In the literature many approaches have been proposed for this tasks, starting from the 17th century. In this work we focus on the Membrane Equilibrium Analysis, developed under the Heyman’s theory of Limit Analysis. Within this theory, the equilibrium of a vault is assessed if it is possible to find at least one membrane surface, between the volume of the vaults, being in equilibrium under the given loads through a purely compressive stress field. The equilibrium of membranes is described by a second order partial differential equation, which is definitely elliptic only when a negative semidefinite stress is assigned, and the shape is the unknown of the problem. The proposed algorithm aims at finding membrane shapes, entirely comprised between the geometry of the vault, in equilibrium with admissible stress fields, through the minimization of an error function with respect to shape parameters of the stress potential, and then, with respect to the boundary values of the membrane shape. The application to two test cases shows the viability of this tool for the assessment of the equilibrium of existing masonry vaults.

scholarly journals Automatized Evaluation of Students’ CAD Models

2021 ◽  
Vol 11 (4) ◽  
pp. 145
Author(s):  
Nenad Bojcetic ◽  
Filip Valjak ◽  
Dragan Zezelj ◽  
Tomislav Martinec
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Computer Application ◽  
Test Cases ◽  
Cad Model ◽  
Computer Solution ◽  
3D Cad ◽  
Computer Aided ◽  
Cad Models ◽  
Aided Design

The article describes an attempt to address the automatized evaluation of student three-dimensional (3D) computer-aided design (CAD) models. The driving idea was conceptualized under the restraints of the COVID pandemic, driven by the problem of evaluating a large number of student 3D CAD models. The described computer solution can be implemented using any CAD computer application that supports customization. Test cases showed that the proposed solution was valid and could be used to evaluate many students’ 3D CAD models. The computer solution can also be used to help students to better understand how to create a 3D CAD model, thereby complying with the requirements of particular teachers.

The Influence of Static Response of Super Tall Building Mega-Frame Structure Caused by Changes of Frame Rigidities

2012 ◽  
Vol 166-169 ◽  
pp. 277-281
Author(s):  
Xiang Dong Xie ◽  
Xuan Wang ◽  
Li Qin
Keyword(s):  
Differential Equation ◽  
Analytical Approach ◽  
Three Dimensional ◽  
Tall Building ◽  
Frame Structure ◽  
Thin Wall ◽  
Static Response ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Frame Rigidity

The superstructure and its foundation of a super tall building mega-frame structure are simplified equivalently and continuously to a stiffened-thin-wall tube on semi-infinite elastic subgrade. And the influences of static response on super tall building mega-frame structure caused by changes of frame rigidity are computed and analyzed with the three-dimensional model by semi-analytical approach based on ODE(Ordinary Differential Equation) Solver, considering the interactions of subgrade, foundation and superstructure. Then some valuable conclusions are obtained through analyzing the reasonable results of the numerical example.

Experimental Studies of Leading Edge Contouring Influence on Secondary Losses in Transonic Turbines

2012 ◽  
Author(s):  
Ranjan Saha ◽  
Jens Fridh ◽  
Torsten Fransson ◽  
Boris I. Mamaev ◽  
Mats Annerfeldt
Keyword(s):  
Gas Turbine ◽  
Guide Vane ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Leading Edge ◽  
Secondary Flows ◽  
Noticeable Effect ◽  
Flow Angle ◽  
Wide Range ◽  
Contour Plots

An experimental study of the hub leading edge contouring using fillets is performed in an annular sector cascade to observe the influence of secondary flows and aerodynamic losses. The investigated vane is a three dimensional gas turbine guide vane (geometrically similar) with a mid-span aspect ratio of 0.46. The measurements are carried out on the leading edge fillet and baseline cases using pneumatic probes. Significant precautions have been taken to increase the accuracy of the measurements. The investigations are performed for a wide range of operating exit Mach numbers from 0.5 to 0.9 at a design inlet flow angle of 90°. Data presented include the loading, fields of total pressures, exit flow angles, radial flow angles, as well as profile and secondary losses. The vane has a small profile loss of approximately 2.5% and secondary loss of about 1.1%. Contour plots of vorticity distributions and velocity vectors indicate there is a small influence of the vortex-structure in endwall regions when the leading edge fillet is used. Compared to the baseline case the loss for the filleted case is lower up to 13% of span and higher from 13% to 20% of the span for a reference condition with Mach no. of 0.9. For the filleted case, there is a small increase of turning up to 15% of the span and then a small decrease up to 35% of the span. Hence, there are no significant influences on the losses and turning for the filleted case. Results lead to the conclusion that one cannot expect a noticeable effect of leading edge contouring on the aerodynamic efficiency for the investigated 1st stage vane of a modern gas turbine.

scholarly journals Nonlocal Symmetry, Painlevé Integrable and Interaction Solutions for CKdV Equations

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1268
Author(s):  
Yarong Xia ◽  
Ruoxia Yao ◽  
Xiangpeng Xin ◽  
Yan Li
Keyword(s):  
Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Dynamical Evolution ◽  
Symmetry Transformation ◽  
Nonlocal Symmetry ◽  
Similarity Reduction ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
Dependent Variables

In this paper, we provide a method to construct nonlocal symmetry of nonlinear partial differential equation (PDE), and apply it to the CKdV (CKdV) equations. In order to localize the nonlocal symmetry of the CKdV equations, we introduce two suitable auxiliary dependent variables. Then the nonlocal symmetries are localized to Lie point symmetries and the CKdV equations are extended to a closed enlarged system with auxiliary dependent variables. Via solving initial-value problems, a finite symmetry transformation for the closed system is derived. Furthermore, by applying similarity reduction method to the enlarged system, the Painlevé integral property of the CKdV equations are proved by the Painlevé analysis of the reduced ODE (Ordinary differential equation), and the new interaction solutions between kink, bright soliton and cnoidal waves are given. The corresponding dynamical evolution graphs are depicted to present the property of interaction solutions. Moreover, With the help of Maple, we obtain the numerical analysis of the CKdV equations. combining with the two and three-dimensional graphs, we further analyze the shapes and properties of solutions u and v.

Performance study of twisted Darrieus hydrokinetic turbine with novel blade design

2021 ◽  
pp. 1-37
Author(s):  
Mabrouk Mosbahi ◽  
Mouna Derbel ◽  
Mariem Lajnef ◽  
Bouzid Mosbahi ◽  
Zied Driss ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Maximum Power ◽  
Power Coefficient ◽  
Speed Ratio ◽  
Small Scale ◽  
Performance Study ◽  
Hydrokinetic Turbine ◽  
Blade Shape ◽  
Water Turbine ◽  
Water Canals

Abstract Twisted Darrieus water turbine is receiving growing attentiveness for small-scale hydropower generation. Accordingly, the need for raised water energy conversion incentivizes researchers to focalise on the blade shape optimization of twisted Darrieus turbine. In view of this, an experimental analysis has been performed to appraise the efficiency of a spiral Darrieus water rotor in the present work. To better the performance parameters of the studied water rotor with twisted blades, three novel blade shapes, namely U-shaped blade, V-shaped blade and W-shaped blade, have been numerically tested using a computational fluid dynamics three-dimensional numerical model. Maximum power coefficient of Darrieus rotor reaches 0.17 at 0.63 tip-speed ratio using twisted blades. Using V-shaped blades, maximum power coefficient has been risen up to 0.185. The current study could be practically applied to provide more effective employment of twisted Darrieus turbines and to improve the generated power from flowing water such as river streams, tidal currents, or other man made water canals.

Short Helical Combustor: Flow Control in a Combustion System With Angular Air Supply

2017 ◽  
Author(s):  
Behdad Ariatabar ◽  
Rainer Koch ◽  
Hans-Jörg Bauer
Keyword(s):  
Temperature Field ◽  
Angular Momentum ◽  
Three Dimensional ◽  
The Novel ◽  
Combustion System ◽  
Flow Angle ◽  
Air Supply ◽  
Inhomogeneous Flow ◽  
Generic Design ◽  
Industrial Optimization

The concept of the novel Short Helical Combustor (SHC) was investigated in our previous work [1, 2]. Based on the insight gained from these previous investigations, we propose a generic design improvement to address the tremendous loss of initial angular momentum as well as inhomogeneous flow and temperature field at the outlet of the SHC. In the present paper, the main features of this design are introduced. It is shown that a three-dimensional shaping of the sidewalls, the dome, and the liners can effectively counteract the suboptimal interaction of the swirl flames with these surrounding walls. As a result, the flow at the outlet of the combustor features a high angular momentum and exhibits a uniform flow angle and temperature field. The insight gained from these generic investigations, and the resulting design optimization provides a useful framework for further industrial optimization of the SHC.

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