Through-Flow Models for Mass and Momentum-Averaged Variables

1987 ◽  
Vol 109 (3) ◽  
pp. 362-370 ◽  
Author(s):  
C. Hirsch ◽  
R. P. Dring
Keyword(s):  
Current Practice ◽  
Incompressible Flows ◽  
Flow Data ◽  
Rigorous Derivation ◽  
Flow Equations ◽  
Flow Models ◽  
Axial Compressors ◽  
Blockage Factor ◽  
Through Flow ◽  
Flow Components

The turbomachinery through-flow equations are reformulated for mass and momentum-averaged quantities. The background of this analysis is the need for an improved assessment of the accuracy of through-flow computations. Traditional through-flow analyses are based on density-weighted averaged quantities reducing to an area average in incompressible flows. On the other hand, experimental data are usually evaluated under the form of mass-averaged quantities, particularly with regard to the overall energy balance and efficiency estimations. The transition between these two sets of quantities is usually taken into account by introducing an averaged aerodynamic blockage factor in addition to the blade blockage factor resulting from the density-averaged quantities. The present analysis provides a rigorous derivation for the momentum-averaged flow quantities and shows that some strong assumptions on the nature of the nonaxisymmetric flow components are necessary in order to justify the current practice of introducing aerodynamic blockage. The recent availability of detailed flow data in single and two-stage axial compressors allows a partial validation of these assumptions, by the comparison of the various nonaxisymmetric components.

scholarly journals Through Flow Theory for Nonaxisymmetric Turbomachinery Flow: Part I — Formulation

1989 ◽  
Author(s):  
Robert P. Dring ◽  
Gordon C. Oates
Keyword(s):  
Data Base ◽  
Total Pressure ◽  
Flow Theory ◽  
Present Formulation ◽  
Dominant Effect ◽  
Flow Equations ◽  
Benchmark Data ◽  
Blockage Factor ◽  
Through Flow ◽  
Flow Part

Through flow theory has been limited in its applicability and in its accuracy by the fact that it has not historically been cast in a form which can account for the nonaxisymmetries that naturally arise in turbomachinery flow due to the presence of finite numbers of rotor and stator airfoils. The attempt to circumvent this limitation by the introduction of an aerodynamic blockage factor has been demonstrated in earlier work to produce fundamental inconsistencies in the calculation which lead to significant errors in the regions of the flow where the nonaxisymmetries are severe. The formulation in Part I of the present work is a derivation of a system of through flow equations for nonaxisymmetric flow. A benchmark data base is used in Part II to provide input to the calculation and to help identify the dominant terms. It is demonstrated that the dominant effect of nonaxisymmetry is contained in two terms that relate the total pressure of the averaged flow to the mass averaged total pressure. It is also demonstrated that the present formulation produces a result which is more accurate than that obtained with the historical blockage-based formulation.

Through Flow Theory for Nonaxisymmetric Turbomachinery Flow: Part II — Assessment

1989 ◽  
Author(s):  
Robert P. Dring ◽  
Gordon C. Oates
Keyword(s):  
Data Base ◽  
Total Pressure ◽  
Flow Theory ◽  
Present Formulation ◽  
Dominant Effect ◽  
Flow Equations ◽  
Benchmark Data ◽  
Blockage Factor ◽  
Through Flow ◽  
Flow Part

Through flow theory has been limited in its applicability and in its accuracy by the fact that it has not historically been cast in a form which can account for the nonaxisymmetries that naturally arise in turbomachinery flow due to the presence of finite numbers of rotor and stator airfoils. The attempt to circumvent this limitation by the introduction of an aerodynamic blockage factor has been demonstrated in earlier work to produce fundamental inconsistencies in the calculation which lead to significant errors in the regions of the flow where the nonaxisymmetries are severe. The formulation in Part I of the present work is a derivation of a system of through flow equations for nonaxisymmetric flow. A benchmark data base is used in Part II to provide input to the calculation and to help identify the dominant terms. It is demonstrated that the dominant effect of nonaxisymmetry is contained in two terms that relate the total pressure of the averaged flow to the mass averaged total pressure. It is also demonstrated that the present formulation produces a result which is more accurate than that obtained with the historical blockage-based formulation.

Throughflow Theory for Nonaxisymmetric Turbomachinery Flow: Part I—Formulation

1990 ◽  
Vol 112 (3) ◽  
pp. 320-326 ◽  
Author(s):  
R. P. Dring ◽  
G. C. Oates
Keyword(s):  
Total Pressure ◽  
Present Formulation ◽  
Dominant Effect ◽  
Flow Equations ◽  
Blockage Factor ◽  
Through Flow ◽  
Benchmark Database ◽  
Flow Part

Throughflow theory has been limited in its applicability and in its accuracy by the fact that it has not historically been cast in a form that can account for the non-axisymmetries that naturally arise in turbomachinery flow due to the presence of finite numbers of rotor and stator airfoils. The attempt to circumvent this limitation by the introduction of an aerodynamic blockage factor has been demonstrated in earlier work to produce fundamental inconsistencies in the calculation, which lead to significant errors in the regions of the flow where the nonaxisymmetries are severe. The formulation in Part I of the present work is a derivation of a system of through-flow equations for nonaxisymmetric flow. A benchmark database is used in Part II to provide input to the calculation and to help identify the dominant terms. It is demonstrated that the dominant effect of nonaxisymmetry is contained in two terms that relate the total pressure of the averaged flow to the mass-averaged total pressure. It also is demonstrated that the present formulation produces a result that is more accurate than that obtained with the historical blockage-based formulation.

Gas Temperature Profile Attenuation Through a Multistage Axial-Flow Turbine

2009 ◽  
Author(s):  
Boris I. Mamaev ◽  
Mikhail M. Petukhovskiy
Keyword(s):  
Temperature Profile ◽  
Attenuation Coefficient ◽  
Flow Model ◽  
Axial Flow ◽  
Gas Temperature ◽  
Empirical Coefficient ◽  
Flow Models ◽  
Flow Parameters ◽  
Through Flow ◽  
Full Scale Tests

Nowadays 2D through-flow models are widespread for designing and analysis of a turbine. Unlike 2D calculations, the measurements show that a non-uniform inlet gas temperature profile is strongly attenuated to the outlet of a turbine. This attenuation can be taken into account in through-flow models only using some corrective coefficients. The objective of this work was to find such an empirical coefficient. The results of full-scale tests of several power GTUs and aviation GTEs were employed to obtain values of the temperature profile attenuation coefficient in the through-flow model for various span locations of airfoil rows. During the tests detailed radial-circumferential distributions of the gas temperature upstream of each of rows and downstream of the turbines were measured (in absolute motion for stator and in relative motion for rotor). The values of the attenuation coefficient for airfoil rows of the three front stages were obtained by means comparison of experimental and computed results. The experience shows that the attenuation coefficient is easily incorporated into the 2D gas-dynamic codes. This incorporation allows spanwise distributions of flow parameters to be predicted and the airfoil geometry and cooling mass flow to be chosen more correctly.

An Integrated Design System for Fans, Compressors, and Turbines: Part 4 — Through-Flow Solver

2005 ◽  
Author(s):  
Allen Medlock ◽  
Max J. Miller ◽  
S. Murthy Konan ◽  
Ben Chambers ◽  
Bao Q. Nguyen
Keyword(s):  
Integrated Design ◽  
Design System ◽  
Aerodynamic Design ◽  
Flow Paths ◽  
Flow Solver ◽  
Axial Compressors ◽  
Interactive Interface ◽  
Through Flow ◽  
Design Cycle ◽  
Access Information

A new aerodynamic design system has been developed that includes a through-flow solver for fans, axial compressors and turbines, and radial compressors and turbines. Three earlier papers gave an overview of the system and described the interactive interface and geometry generators. This paper focuses on several special features in the through-flow solver that provide increases in aerodynamic designer productivity. Some of the key features are stations decoupled from flow paths, ability to accept a wide variety of input parameters, use of gas property routines, ability to inject flow non-uniformly with a different composition than the main flow gas composition, ability to access information from several airfoil geometry generator solutions, and clear, comprehensive error handling. These special features and others have provided major savings from productivity improvements and reductions in design cycle time.

Oil flow in plain steadily loaded journal bearings: Realistic predictions using rapid techniques

1998 ◽  
Vol 212 (6) ◽  
pp. 413-425 ◽  
Author(s):  
F. A. Martin
Keyword(s):  
Journal Bearings ◽  
Hydrodynamic Flow ◽  
Operating Conditions ◽  
Flow Data ◽  
Prediction Equations ◽  
Specific Flow ◽  
Flow Equations ◽  
Flow Prediction ◽  
Lubricant Flow ◽  
Wide Range

The aim of the paper is to produce a rapid calculation method for predicting lubricant flow in plain cylindrical journal bearings. Lubricant flow data, already available from rigorous solutions considering the effect of film reformation, are used together with experimental evidence to develop unique graphical aids and flow prediction equations. These equations, although developed from specific flow data, are of a general form and therefore will be applicable to a wide range of different bearing operating conditions. Graphical aids, from which the flow equations are derived, give normalized actual flow as a function of normalized hydrodynamic flow for different groove geometries. The main input parameters, namely a hydrodynamic flow term Qh and a feed pressure flow term Qp, are easy to derive and have been in common use in bearing design techniques over many decades. The new design aids, in chart and equation form, give realistic flow predictions for bearings with an oil hole, a groove opposite the load line, an axial groove at the maximum film thickness position and the commonly used case of a bearing with two axial grooves. The flow prediction equations are supported by experimental data.

scholarly journals APPLYING DUDUCTIONS FROM NAVIER STOKES EQUATION TO FLOW SITUATIONS IN GAS PIPELINE NETWORK SYSTEM

2019 ◽  
Vol 1 (1) ◽  
pp. 10-18
Author(s):  
Mathew Shadrack Uzoma
Keyword(s):  
Stokes Equations ◽  
Optimal Level ◽  
Gas Pipeline ◽  
Navier Stokes ◽  
Network System ◽  
Gas Pipelines ◽  
Navier Stokes Equation ◽  
Flow Equations ◽  
Flow Models ◽  
Energy Equations

Navier Stokes equations are theoretical equations for pressure-flow-temperature problems in gas pipelines. Other well-known gas equations such as Weymouth, Panhandle A and Modified Panhandle B equations are employed in gas pipeline design and operational procedures at a level of practical relevance. Attaining optimality in the performance of this system entails concrete understanding of the theoretical and prevailing practical flow conditions. In this regard, Navier Stoke’s mass, momentum and energy equations had been worked upon subject to certain simplifying assumptions to deduced expressions for flow velocity and throughput in gas pipeline network system. This work could also bridge the link among theoretical, operational and optimal level of performance in gas pipelines. Purpose: The purpose of this research is to build a measure of practical relevance in gas pipeline operational procedures that would ultimately couple the missing links between theoretical flow equations such as Navier Stokes equation and practical gas pipeline flow equations. Such practical gas pipeline flow models are Weymouth, Panhandle A and Modified Panhandle B equations among others.Methodology: The approach in this regard entails reducing Narvier Stoke’s mas, momentum and energy equations to their appropriate forms by applicable practical conditions. By so doing flow models are deduced that could be worked upon by computational approach analytically or numerically to determine line throughput and flow velocity.The reduced forms of the Navier Stokes velocity and throughput equations would be applied to operating gas pipelines in Nigeria terrain. The gas pipelines are ElfTotal Nig. Ltd and Shell Petroleum Development Company (SPDC). This would enable the comparison of these gas pipelines operational data with theoretical results of Navier Stokes equations reduced to their appropriate forms.Findings: The follow up paper would employ theoretical and numerical discretization computational methods to compare theoretical and numerical discretization results to give a clue if these operating gas pipelines are operated at optimal level of performance.Unique contribution to theory, practice and policy: The reduced forms of Nervier Stokes equations applied to physical operating gas pipelines network system is considered by the researcher to be an endeavor of academic excellence that would foster clear cut understanding of theoretical and practical flow situations. It could also open up a measure of understanding to pushing a flow to attaining optical conditions in practical real life flow situations. Operating gas pipelines optimally would reduce the spread of these capital intensive assets and facilities and more so conserving our limited reserves for foreign exchange.

A Semi-Implicit Scheme for Modeling the Interaction Between Biological Cells and Electric Fields

2007 ◽  
Author(s):  
John H. Pierse ◽  
Arturo Ferna´ndez
Keyword(s):  
Fluid Flow ◽  
Electric Field ◽  
Maxwell Equations ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Computational Time ◽  
Biological Cells ◽  
Field Equations ◽  
Flow Equations

A numerical method for computing the simultaneous solution to the fluid flow equations and the electrostatic field equations is described. The methodology focuses on the modeling of biological cells suspended in fluid plasma. The fluid flow is described using the Navier-Stokes equations for incompressible flows. The electric field is computed trough the Maxwell equations neglecting magnetic effects. The effect of the electric field on the fluid flow is accounted for through the Maxwell stresses. The systems are described by a set of partial differential equations where the solution requires the simultaneous computation of the velocity, pressure and electric potential fields. A semi-implicit numerical scheme is proposed. In order to decrease the computational time required, it is proposed to use a semi-implicit splitting scheme where the Navier-Stokes and Maxwell equations are solved sequentially. The method is used to reproduce the response of human leukocytes immersed in a rotating electric field. An agreement between the numerical results and the data from experiments is observed.

Net Mass Flow Components in a Three-Dimensional Unsteady Rotor Inflow Model

2003 ◽  
Author(s):  
Ke Yu ◽  
David A. Peters
Keyword(s):  
Mass Flow ◽  
Three Dimensional ◽  
Legendre Functions ◽  
Skew Angle ◽  
Pressure Potential ◽  
Associated Legendre Functions ◽  
Galerkin Approach ◽  
Flow Equations ◽  
Closed Form Solutions ◽  
Flow Components

Potential flow equations are converted to ordinary differential equations by the Galerkin approach in which velocity and pressure potential functions are expanded in terms of closed-form solutions to Laplace’s Equation. The reduced number of generalized coordinates in a Galerkin approach gives advantages in real-time simulations, preliminary design, and dynamic eigenvalue analysis for aeroelasticity. Net mass injection from rotor sources is expected to occur in some situations, but cannot be treated by previous models. It is included in the present formulation. In this paper, frequency response due to pressure distributions corresponding to net mass flow in both axial and skew-angle flight are given. These results are compared with exact solutions obtained by the approach of a convolution integral. A brief analysis is also included with respect to numerical simulations of the Associated Legendre Functions, in which it demonstrates that net mass flow components are extremely sensitive to the recursive process of seeking Associated Legendre Functions.

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