Throughflow Method for Turbomachines Applicable for All Flow Regimes

1995 ◽  
Author(s):  
S. V. Damle ◽  
T. Q. Dang ◽  
D. R. Reddy
Keyword(s):  
Body Force ◽  
Equations Of Motion ◽  
Tangential Velocity ◽  
Matrix Methods ◽  
Streamline Curvature ◽  
Time Stepping ◽  
Viscous Losses ◽  
Blade Shape ◽  
Flow Quantity ◽  
Analysis Mode

A new axisymmetric throughflow method for analyzing and designing turbomachines is proposed. This method utilizes body-force terms to represent blade forces and viscous losses. The resulting equations of motion, which include these body-force terms, are casted in terms of conservative variables and are solved using a finite-volume time-stepping scheme. In the inverse mode, the swirl schedule in the bladed regions (i.e. the radius times the tangential velocity rVθ) is the primary specified flow quantity, and the corresponding blade shape is sought after. In the analysis mode, the blade geometry is specified and the flow solution is computed. The advantages of this throughflow method compared to the current family of streamline curvature and matrix methods are that the same code can be used for subsonic/transonic/supersonic throughflow velocities, and the proposed method has a shock capturing capability. This method is demonstrated for designing a supersonic throughflow fan stage and a transonic throughflow turbine stage.

Throughflow Method for Turbomachines Applicable for All Flow Regimes

1997 ◽  
Vol 119 (2) ◽  
pp. 256-262 ◽  
Author(s):  
S. V. Damle ◽  
T. Q. Dang ◽  
D. R. Reddy
Keyword(s):  
Body Force ◽  
Equations Of Motion ◽  
Tangential Velocity ◽  
Matrix Methods ◽  
Streamline Curvature ◽  
Time Stepping ◽  
Viscous Losses ◽  
Blade Shape ◽  
Flow Quantity ◽  
Analysis Mode

A new axisymmetric throughflow method for analyzing and designing turbomachines is proposed. This method utilizes body-force terms to represent blade forces and viscous losses. The resulting equations of motion, which include these body-force terms, are cast in terms of conservative variables and are solved using a finite-volume time-stepping scheme. In the inverse mode, the swirl schedule in the bladed regions (i.e., the radius times the tangential velocity rVθ) is the primary specified flow quantity, and the corresponding blade shape is sought after. In the analysis mode, the blade geometry is specified and the flow solution is computed. The advantages of this throughflow method compared to the current family of streamline curvature and matrix methods are that the same code can be used for subsonic/transonic/supersonic throughflow velocities, and the proposed method has a shock capturing capability. This method is demonstrated for designing a supersonic throughflow fan stage and a transonic throughflow turbine stage.

scholarly journals Inverse Method for Turbomachine Blades Using Existing Time-Marching Techniques

1994 ◽  
Author(s):  
T. Dang ◽  
V. Isgro
Keyword(s):  
Euler Equations ◽  
Inverse Method ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Tangential Velocity ◽  
Steady State Solution ◽  
Slip Boundary ◽  
Time Stepping ◽  
Time Marching ◽  
Blade Geometry

A newly-developed inverse method for the design of turbomachine blades using existing time-marching techniques for the numerical solutions of the unsteady Euler equations is proposed. In this inverse method, the pitch-averaged tangential velocity (or the blade loading) is the specified quantity, and the corresponding blade geometry is Iteratively sought after. The presence of the blades are represented by a periodic array of discrete body forces which are included in the equations of motion. A four-stage Runge-Kutta time-stepping scheme is used to march a finite-volume formulation, of the unsteady Euler equations to a steady-state solution. Modification of the blade geometry during this time marching process is achieved using the slip boundary conditions on the blade surfaces. This method is demonstrated for the design of infinitely-thin cascaded blades in the subsonic, transonic, and supersonic flow regimes. Results are validated using an Euler analysis method and are compared against those obtained using a similar inverse method. Excellent agreement in the results are obtained between these different approaches.

Pure Design Method for Aerofoils in Cascade

1969 ◽  
Vol 11 (5) ◽  
pp. 454-467 ◽  
Author(s):  
K. Murugesan ◽  
J. W. Railly
Keyword(s):  
Exact Solution ◽  
Velocity Distribution ◽  
Design Problem ◽  
Design Method ◽  
Tangential Velocity ◽  
Surface Velocity ◽  
Normal Velocity ◽  
Blade Design ◽  
Blade Shape

An extension of Martensen's method is described which permits an exact solution of the inverse or blade design problem. An equation is derived for the normal velocity distributed about a given contour when a given tangential velocity is imposed about the contour and from this normal velocity an initial arbitrarily chosen blade shape may be successively modified until a blade is found having a desired surface velocity distribution. Five examples of the method are given.

Closed Form Solution for Outflow Between Corotating Disks

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Closed Form ◽  
Stokes Equations ◽  
Closed Form Solution ◽  
Tangential Velocity ◽  
Form Solution ◽  
Navier Stokes ◽  
Published Data ◽  
Rotational Inertia ◽  
Viscous Losses ◽  
Present Solution

Mathematical expressions are derived for flow velocities and pressure distributions for a laminar flow in the gap between two rotating concentric disks. Fluid enters the gap between disks at the center and diverges to the outer periphery. The Navier–Stokes equations are linearized in order to get closed-form solution. The present solution is applicable to the flow between corotating as well as contrarotating disks. The present results are in agreement with the published data of other investigators. The tangential velocity is less for contrarotating disks than for corotating disks in core region of the radial channel. The flow is influenced by rotational inertia and convective inertia both. Dominance of rotational inertia over convective inertia causes backflow. Pressure depends on viscous losses, convective inertia, and rotational inertias. Effect of viscous losses on pressure is high at small throughflow Reynolds number. The convective and rotational inertia influence pressure significantly at high throughflow and rotational Reynolds numbers. Both favorable and unfavorable pressure gradients can be found simultaneously depending on a combination of parameters.

Unilateral Impact and Contact of Elastic Structures Using Lagrangian Multipliers

2011 ◽  
Author(s):  
Sebastian Tatzko
Keyword(s):  
Equations Of Motion ◽  
Structural Equations ◽  
Contact Forces ◽  
Integration Scheme ◽  
Lagrangian Multiplier ◽  
Elastic Structures ◽  
Lagrangian Multipliers ◽  
Linear Elastic ◽  
Time Stepping ◽  
Numerical Effort

This paper deals with linear elastic structures exposed to impact and contact phenomena. Within a time stepping integration scheme contact forces are computed with a Lagrangian multiplier approach. The main focus is turned on a simplified solving method of the linear complementarity problem for the frictionless contact. Numerical effort is reduced by applying a Craig-Bampton transformation to the structural equations of motion.

Investigation of the Fluid Flow in a Rotor-Stator Cavity With Inward Through-Flow

2009 ◽  
Author(s):  
Bjo¨rn-Christian Will ◽  
Friedrich-Karl Benra
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Flow Model ◽  
Equations Of Motion ◽  
Tangential Velocity ◽  
Layer Model ◽  
Practical Applications ◽  
The Core ◽  
Through Flow ◽  
Core Rotation

The present paper covers fluid flow in rotor-stator cavities with inward through-flow. First, a general introduction into the physics of the cavity boundary layer flow is given. The structure of the flow is very complex and depends on different dimensionless parameters. For practical applications, simple and robust calculation procedures are crucial for design purposes. Two basic modelling approaches are compared (3 layer model of Kurokawa [14] and “one layer” approach of Mo¨hring [17]) with experimental data from the literature. The flow models are classified in context of the simplified equations of motion by emphasizing the main assumptions and simplifications in their derivation. Further on, for the one layer model, the use of the logarithmic law for the velocity distribution close to the wall is proposed instead of the classic 1/7 power law. The modified flow model is validated against experimental data for different parameter combinations, yielding better agreement for moderate inlet rotation. Finally numerical simulations have been performed in order to investigate the discrepancies between measured and calculated core rotation distributions for strong inlet swirl. It is supposed that the assumption of radial equilibrium in the core region is not necessarily appropriate for evaluation of the core rotation. Further on, it is clarified in which situations the tangential velocity component of the absolute velocity at the impeller outlet can be used as a boundary condition for the flow model.

scholarly journals QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

2008 ◽  
Vol 1 (1) ◽  
pp. 187-241
Author(s):  
P. D. Williams ◽  
T. W. N. Haine ◽  
P. L. Read ◽  
S. R. Lewis ◽  
Y. H. Yamazaki
Keyword(s):  
Laboratory Experiments ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Fluids ◽  
Stochastic Forcing ◽  
Internal Interface ◽  
Time Stepping ◽  
Beta Effect ◽  
Fluid Layers ◽  
Special Case

Abstract. QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

Ice Mass Motions Near an Offshore Structure

1987 ◽  
Vol 109 (2) ◽  
pp. 206-210 ◽  
Author(s):  
M. Isaacson
Keyword(s):  
Equations Of Motion ◽  
Diffraction Theory ◽  
Offshore Structure ◽  
Drift Motion ◽  
Time Stepping ◽  
Drag Forces ◽  
Added Masses ◽  
Wave Drift Forces ◽  
Wave Induced ◽  
Typical Design

The present paper treats the motions of an ice mass up to the instant of impact with a large fixed offshore structure, and describes a numerical method for predicting these motions taking account of the interaction between the ice mass and structure. In general an ice mass will undergo wave-induced oscillatory motions as well as drift motion. The former are calculated by linear diffraction theory applied to bodies of arbitrary shape so that interaction effects are fully accounted for. The drift motion is calculated by a time-stepping procedure applied to the drift equations of motion which involve zero frequency added masses, drag forces and wave drift forces. As an example of the methods application, results are presented for a typical design situation which illustrate the nature of the hydrodynamic interaction between the ice mass and structure.

A Fast Numerical Procedure to Solve the Meridional Equations of Motion in a Multistage Axial Flow Turbomachine

1981 ◽  
Author(s):  
A. Kündig
Keyword(s):  
Equations Of Motion ◽  
Computing Time ◽  
Axial Flow ◽  
Numerical Procedure ◽  
Flow Conditions ◽  
Compressor Blades ◽  
Streamline Curvature ◽  
Downstream Flow ◽  
Real Flow ◽  
End Wall

A new numerical procedure has been developed to solve the meridional equations of motion in an axial flow turbomachine. It is based on the so-called streamline-curvature method. The primary aim of this project was to reduce the computing-time of existing programs. The procedure has been tested. The new program is coupled with a program for the calculation of end-wall-boundary layers on axial flow compressors. This combination makes the simulation of real flow conditions possible. The pitch wise deviation angles and blade-row efficiencies are generally given as input. For compressor blades of the NACA-65-family they can be called from stored empirical data as function of geometry and the upstream and downstream flow conditions. The paper presents an exact description of the numerical procedure and a computed example.

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