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.

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 II—Assessment

1990 ◽  
Vol 112 (3) ◽  
pp. 328-337 ◽  
Author(s):  
R. P. Dring ◽  
G. C. Oates
Keyword(s):  
Total Pressure ◽  
Present Formulation ◽  
Dominant Effect ◽  
Blockage Factor ◽  
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 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 throughflow 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.

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 Prediction of Performance of a Variable-Pitch Axial Fan with Forward-Skewed Blades

Energies ◽  
2019 ◽  
Vol 12 (12) ◽  
pp. 2353 ◽  
Author(s):  
Xuemin Ye ◽  
Fuwei Fan ◽  
Ruixing Zhang ◽  
Chunxi Li
Keyword(s):  
Total Pressure ◽  
Pressure Rise ◽  
Separation Flow ◽  
Axial Fan ◽  
Point Change ◽  
Variable Pitch ◽  
Tip Leakage ◽  
Through Flow ◽  
Efficiency Increase ◽  
Blade Pitch Angle

For a single-stage variable-pitch axial fan, the aerodynamic performance and through flow with and without blade skewing are examined numerically. Simulated results show that the total pressure rise and efficiency increase by 2.99% and 0.16%, respectively, with the best forward-skewed angle of θ = 3° at the design conditions. At the blade pitch angles of β = 29° and 35°, the total pressure rises and efficiency of the fan with θ = 3.0° under the highest efficiency point change by −0.55%, −0.53% and 1.39%, 2.11%, respectively. At design and off-design conditions, the forward-skewed blades mitigate tip leakage and delay the emergence of separation flow at the blade root, these benefits are higher at the higher blade pitch angle. The θ = 3.0° forward skew effectively raises the stage performance of the impeller and guide vanes.

Mass Flow and Thrust Performance of Nozzles With Mixed and Unmixed Nonuniform Flow

1995 ◽  
Vol 117 (4) ◽  
pp. 617-622 ◽  
Author(s):  
Reiner Decher
Keyword(s):  
Mass Flow ◽  
Total Pressure ◽  
Nonuniform Flow ◽  
Flow Properties ◽  
One Dimensional ◽  
Flow Equations ◽  
Design Variables ◽  
Analytic Expressions ◽  
The One ◽  
Thrust Performance

The calculated thrust and mass flow rate of a nozzle depend on the uniformity of the entering flow. The one-dimensional flow equations are extended to arrive at analytic expressions for the predicted performance of a nozzle processing two streams whose properties are determined ahead of the throat. The analysis approach forms the basis for the understanding of flows which have more complex distributions of total pressure and temperature. The uncertainty associated with mixing is examined by the consideration of the two limiting cases: compound flow with no mixing and completely mixed flow. Nozzle discharge and velocity coefficients accounting for non-uniformity are derived. The methodology can be extended to experimentally measured variations of flow properties so that proper geometric design variables may be obtained.

Oxy-Fuel Turbine Through-Flow Design

2014 ◽  
Author(s):  
Majed Sammak ◽  
Srikanth Deshpande ◽  
Magnus Genrup
Keyword(s):  
Mach Number ◽  
Total Pressure ◽  
Tangential Velocity ◽  
Flow Angle ◽  
Power Turbine ◽  
Through Flow ◽  
The Mean ◽  
Line Design ◽  
Reaction Degree ◽  
Relative Flow

The objective of the paper is to present the through-flow design of a twin-shaft oxy-fuel turbine. The through-flow design is the subsequent step after the turbine mean-line design. The through-flow phase analyses the flow in both axial and radial directions, where the flow is computed from hub to tip and along streamlines. The parameterization of the through-flow is based on the mean-line results, so principal features such as blade angles at the mean-line into the through-flow phase should be retained. Parameters such as total inlet pressure and temperature, mass flow, rotation speed and turbine geometries are required for the through-flow modelling. The through-flow study was performed using commercial software — AxCent(™) from Concepts NREC. The rotation speed of the twin-shaft power turbine was set to 7200 rpm, while the power turbine was set to 4800 rpm. The mean-line design determined that the twin-shaft turbine should be designed with two compressor turbine stages and three power turbine stages. The through-flow objective was to study the variations in the thermodynamic parameters along the blade. The power turbine last-stage design was studied because of the importance of determining exit Mach number distribution of the rotor tip. The last stage was designed with damped forced condition. The term ‘damped’ is used because the opening from the tip to the hub is limited to a certain value rather than maintaining the full concept of forced vortex. The study showed the parameter distribution of relative Mach number, total pressure and temperature, relative flow angle and tangential velocity. Through-flow results at 50% span and mean-line results showed reasonable agreement between static pressure, total pressure, reaction degree and total efficiency. Other parameters such as total temperature and relative Mach number showed some difference which can be attributed to working fluid in AxCent being pure CO2. The relative tip Mach number at rotor exit was 1.03, which is lower than the maximum typically allowed value of 1.2. The total pressure distribution was smooth from hub to tip which minimizes the spanwise gradient of total pressure and thus reduces the strength of secondary vortices. The reaction degree distribution was presented in the paper and no problems were revealed in the reaction degree at the hub. Rotor blades were designed to produce a smooth exit relative flow angle distribution. The relative flow angle varied by approximately 5° from hub to tip. The tangential velocity distribution was proportional to blade radius, which coincided with forced vortex design. Through-flow design showed that the mean-line design of a twin-shaft oxy-fuel turbine was suitable.

Impacts of tandem configurations on the aerodynamic performance of an axial supersonic through-flow fan cascade

2021 ◽  
pp. 1-25
Author(s):  
Shijun Sun ◽  
Jiaqi Hao ◽  
Jutao Yang ◽  
Ling Zhou ◽  
Lucheng Ji
Keyword(s):  
Pressure Loss ◽  
Total Pressure ◽  
Threshold Value ◽  
Total Pressure Loss ◽  
System Structure ◽  
Pressure Loss Coefficient ◽  
Through Flow ◽  
Shock System ◽  
The Impact ◽  
Total Pressure Loss Coefficient

Abstract In the current study, the tandem blade technology is applied to an STFF tandem cascade for the first time, and a 2D STFF tandem cascade is preliminarily designed. Through the modification design of the tandem airfoils and their configuration (axial overlap, AO and percent pitch, PP), the coefficients of total pressure loss and loading are reduced by 4% and 8.58%, respectively. Furtherly, the impact of tandem configurations on the performance is parametrically investigated by numerical simulations. The results indicate that compared with AO, the performance under design incidence is more sensitive to PP except for the cases with PP exceeding a threshold value (1.15). PP dominates the loss and load by controlling the evolution of the FB wake and the shock structure of FB and RB, while AO mainly adjusts the entire shock system structure through the change of virtual shape, resulting in the variation in load distribution between FB and RB. It is worth noting that the overall loading and the total loss remain unchanged with increasing AO except for the tandem configurations (PP=1.05, AO≤−0.01), which make the flow structure in the gap region undergo a fundamental change. With the optimal tandem configuration (PP=1.05, AO=−0.01) and the modified tandem blades (The ratios of chord length and camber for FB over RB is 0.67 and 0.5, respectively), the total pressure loss coefficient is further reduced by 19.7% in comparison with the preliminary tandem design.

A Finite-Element Method for Through Flow Calculations in Turbomachines

1976 ◽  
Vol 98 (3) ◽  
pp. 403-414 ◽  
Author(s):  
Ch. Hirsch ◽  
G. Warzee
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Axisymmetric Flow ◽  
Axial Flow ◽  
The Finite Element Method ◽  
Flow Equations ◽  
Through Flow ◽  
Method Of Solution ◽  
Element Technique ◽  
Element Method

A new method for the numerical solution of the meridional through-flow equations in an axial flow machine is presented based on the finite-element method. A rigorous derivation of the pitch-averaged flow equations is presented and the assumption of axisymmetric flow leads, with the introduction of a stream function, to the equation to be solved. A description is given of the finite-element technique which is applied in this problem. The method of solution allows the calculation of transonic stages. Numerical results are compared with experimental data and show very satisfactory agreement. This method appears, therefore, to compare very favorably with the other methods used up to now. Although the present results pertain to axial flow machines, the method is easily applicable to radial flow machines as well and the way of solution for this case is indicated.

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