scholarly journals Mathematical model of centrifugal compressor vaneless diffuser based on CFD calculations

2020 ◽  
Vol 178 ◽  
pp. 01014
Author(s):  
Olga Solovyeva ◽  
Aleksandr Drozdov
Keyword(s):  
Mathematical Model ◽  
Centrifugal Compressor ◽  
Similarity Criteria ◽  
Relative Width ◽  
Inlet Flow ◽  
Flow Angle ◽  
Gas Dynamic ◽  
Modelling Method ◽  
Vaneless Diffusers ◽  
The Mathematical Model

The approximate engineering techniques based on mathematical modelling are used in centrifugal compressor design. One of such methods is the well-proven Universal Modelling Method, developed in the scientific and research laboratory “Gas dynamics of turbo machines”, SPbPU. In the modern version of the compressor model, vaneless diffusers mathematical model was applied based on a generalization of the CFD calculations. The mathematical model can be used for vaneless diffusers with a relative width in the range of 1.4 – 10.0%, with a radial length up to 2.0, in the range of inlet flow angles 10 to 90 degrees, the inlet velocity coefficient in the range of 0.39 – 0.82, Reynolds number varying from 87 500 to 1 030 000. The model was also used for calculating low-flow-rate model stages with narrow diffusers with diffusers’ relative width in the range of 0.5 – 2.0%. The mathematical model showed lesser accuracy. To widen the model applicability, new series of CFD-calculations were executed. A series of vaneless diffusers was designed with relative width in the range of 0.6 – 1.2%, The gas-dynamic characteristics of loss coefficients and outlet flow angle versus inlet flow angle of diffuser were calculated. Regression analysis was used to process the calculated data. System of algebraic equations linking geometric, gas-dynamic parameters and similarity criteria was developed. The obtained equations are included in a new mathematical model of the Universal Modelling Method.

CFD-model of Vaneless Diffuser of Centrifugal Compressor

2021 ◽  
pp. 109-130
Author(s):  
О.А. Solovyeva ◽  
А.А. Drozdov ◽  
E.Yu. Popova ◽  
K.V. Soldatova
Keyword(s):  
Mathematical Model ◽  
Centrifugal Compressor ◽  
Dynamic Characteristics ◽  
Modeling Method ◽  
Relative Width ◽  
Vaneless Diffuser ◽  
Flow Angle ◽  
Flow Parameters ◽  
Gas Dynamic ◽  
Vaneless Diffusers

The centrifugal compressor design involves the use of approximate engineering techniques based on mathematical modeling. One of such techniques is the universal modeling method, which proves to be practically applicable. Having generalized a series of CFD calculations, we used a mathematical model in the latest version of the compressor model to calculate flow parameters in vaneless diffusers. The diffuser model was identified based on the results of experimental studies of average-flow model stages carried out at SPbPU. The model is also used to calculate Clark low-flow centrifugal compressor stages with narrow diffusers with a relative width in the range of 0.5--2.0 %. For these stages, the developed mathematical model showed insufficient efficiency, since the dimensions of the diffusers go beyond the limits of its applicability. To solve this problem, we calculated a series of vaneless diffusers with a relative width in the range of 0.6--1.2 % in the ANSYS CFX software package. Relying on the results of CFD calculations, we plotted the gas dynamic characteristics of the loss coefficients and changes in the flow angle depending on the flow angle at the inlet to the vaneless diffuser. To process the calculated data, the method of regression analysis was applied, with the help of which a system of algebraic equations was developed that connects geometric, gas-dynamic parameters and similarity criteria. The obtained equations are included in a new mathematical model of the universal modeling method for calculating the flow parameters of vaneless diffusers. Comparison of the calculated gas-dynamic characteristics according to the new model with experimental data showed the average error of modeling the calculated (maximum) efficiency equal to 1.08 %

Simulating Characteristics of Vaneless Diffusers Using Neural Networks

2020 ◽  
pp. 29-42
Author(s):  
Y.B. Galerkin ◽  
A.G. Nikiforov ◽  
O.A. Solovyeva ◽  
E.Y. Popova
Keyword(s):  
Neural Networks ◽  
Mathematical Models ◽  
Dynamic Characteristics ◽  
Flow Direction ◽  
Similarity Criteria ◽  
Relative Width ◽  
Flow Angle ◽  
Gas Dynamic ◽  
Vaneless Diffusers ◽  
Two Parameters

To calculate flow parameters of a vaneless diffuser of the centrifugal compressor stage, it is sufficient to determine the loss coefficient and the flow direction at the outlet. The paper presents the results of modeling the characteristics of these two parameters using neural networks and CFD methods. To obtain mathematical models, ANSYS calculation data was used for vaneless diffusers with a relative width of 0.014–0.1, relative outlet diameter of 1.4–2.0, inlet flow angle of 10–90° and velocity coefficient of 0.39–0.82, with the Reynolds number being in the range of 87 500–1 030 000. A comparison with the theory showed the regularity of gas-dynamic characteristics, and comparison with well-known experiments showed the correspondence of the flow structure. In order to improve the accuracy of simulation using neural networks, various recommendations on the preparation and processing of the initial data were collected and tested: identification of conflict examples and outliers, data normalization, improving the quality of the neural network training under the insufficient amount of sampling, etc. The application of the aforementioned recommendations significantly improved the accuracy of simulation. A simulation experiment based on neural models for studying the influence of dimensions, diffuser shape and similarity criteria on the diffuser gas dynamic characteristics made it possible to verify physical adequacy of the mathematical models, obtain new data on energy conversion processes and produce a set of recommendations on the optimal design of vaneless diffusers.

Primary Design of Vaneless Diffusers of Centrifugal Compressor Stages by the Universal Modeling Method

2021 ◽  
pp. 39-52
Author(s):  
O.A. Solovyeva ◽  
K.V. Soldatova ◽  
Y.B. Galerkin ◽  
A.F. Rekstin
Keyword(s):  
Continuous Flow ◽  
Design Method ◽  
Modeling Method ◽  
Inlet Section ◽  
Relative Width ◽  
Design Practice ◽  
Main Section ◽  
Flow Angle ◽  
Gas Dynamic ◽  
Vaneless Diffusers

Vaneless diffusers of industrial centrifugal compressors most often consist of a tapered inlet section and a parallel-walled main section. The study proposes to choose such a width of the main section, at which the flow in the diffuser remains unseparated at the surge limit. To implement the primary design method, an empirical formula was obtained to determine the minimum continuous flow angle depending on the relative width of the diffuser. The primary design of eighteen stages was completed, covering a practically important range of parameters. The corresponding gas-dynamic characteristics were calculated by the universal modeling method, the dimensions and angles of the flow were analyzed. The proposed primary design method is integrated into the universal modeling method and is used in design practice.

Effects of Inlet Flow Field Conditions on the Performance of Centrifugal Compressor Diffusers: Part 2 — Straight-Channel Diffuser

1998 ◽  
Author(s):  
Sabri Deniz ◽  
Edward M. Greitzer ◽  
Nicholas A. Cumpsty
Keyword(s):  
Mach Number ◽  
Flow Field ◽  
Centrifugal Compressor ◽  
Axial Flow ◽  
Rotating Stall ◽  
Pressure Recovery ◽  
Straight Channel ◽  
Inlet Flow ◽  
Flow Angle ◽  
Operating Range

This is Part 2 of an examination of influence of inlet flow conditions on the performance and operating range of centrifugal compressor vaned diffusers. The paper describes tests of straight-channel type diffuser, sometimes called a wedge-vane diffuser, and compares the results with those from the discrete-passage diffusers described in Part 1. Effects of diffuser inlet Mach number, flow angle, blockage, and axial flow non-uniformity on diffuser pressure recovery and operating range are addressed. The straight-channel diffuser investigated has 30 vanes and was designed for the same aerodynamic duty as the discrete-passage diffuser described in Part 1. The ranges of the overall pressure recovery coefficients were 0.65–0.78 for the straight-channel diffuser and 0.60–0.70 for the discrete-passage diffuser; the pressure recovery of the straight-channel diffuser was roughly 10% higher than that of the discrete-passage diffuser. Both types of the diffusers showed similar behavior regarding the dependence on diffuser inlet flow angle and the insensitivity of the performance to inlet flow field axial distortion and Mach number. The operating range of the straight-channel diffuser, as for the discrete-passage diffusers was limited by the onset of rotating stall at a fixed momentum-averaged flow angle into the diffuser, which was for the straight-channel diffuser, αcrit = 70° ±0.5°. The background, nomenclature and description of the facility and method are all given in Part 1.

scholarly journals Physical modeling of a skip pneumatic winder

2021 ◽  
pp. 64-73
Author(s):  
Aleksandr Leontiev ◽  
Keyword(s):  
Mathematical Model ◽  
Physical Modeling ◽  
Aerodynamic Characteristics ◽  
Volumetric Efficiency ◽  
Similarity Criteria ◽  
Experimental Sample ◽  
Point Analysis ◽  
Analytical Phase ◽  
The Mathematical Model ◽  
Parameters Calculation

Introduction. The analytical phase of research on mine skip pneumatic winders has been passed, so the theoretical provisions have to be tested by the methods of physical modeling which is aimed at confirming the mathematical model adequacy and assessing the effectiveness of different types of sealing devices. Research methods. Physical modeling phases have been formulated, including modeling by geometric and aerodynamic similarity criteria, constructing aerodynamic characteristics of the installation, carrying out experiments with non-contacting and combined seals, and calculating the values of the installation volumetric efficiency based on the experimental data obtained. Research results. The lifting time of the skip model with different masses of material and seal types has been determined. The installation working points in the “flow rate–pressure” coordinate system have been identified, and the values of the volumetric efficiency have been calculated for each working point. Analysis of the results. A satisfactory convergence of calculated and experimental parameters of the physical model has been established. The model's volumetric efficiency has reached a technically acceptable level. The expected value of the experimental model’s volumetric efficiency has been calculated according to the similarity constants. Conclusions. The model's study revealed the convergence of the experimentally obtained volumetric efficiency of the model with its calculated values and proved the applicability of the mathematical model to experimental sample parameters calculation. The volumetric efficiency of the installation with both non-contacting and combined seals is quite high allowing to recommend the studied sealing devices for mine pneumatic winders.

scholarly journals Analysis of the non-stationary mathematical model of a simple hydraulic network with a centrifugal pump

Vestnik IGEU ◽  
2020 ◽  
pp. 64-70
Author(s):  
V.A. Naumov
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Centrifugal Pump ◽  
Similarity Criteria ◽  
Dimensionless Form ◽  
Maximum Volume ◽  
Stationary Flows ◽  
Variable Level ◽  
Hydraulic Network ◽  
The Mathematical Model

Simple hydraulic networks with a centrifugal pump are not only part of complex networks, but are also widely used in Autonomous water supply and Sewerage systems. The mathematical model of simple networks taking into account the variable level of liquid in reservoirs includes the well-known Bernoulli equation for non-stationary flows. Published works on this problem do not take into account the non-stationary nature of the flow due to the variable liquid level. The conditions for using the quasi-stationary model are not discussed. Similarity criteria for the issue were not found. The purpose of the study is to analyze the non-stationary mathematical model of the object, including the definition of criteria for similarity of the problem and their impact on the solution. The well-known equations of fluid quantity balance and Bernoulli for non-stationary flows with smoothly changing characteristics were used as a mathematical model of a simple hydraulic network. The pressure characteristic of a centrifugal pump is approximated by a well-established dependence in the form of a square three-member. The system of differential equations was reduced to a dimensionless form. Analytical and numerical methods were used to solve the problem. The analysis of the mathematical model of pumping liquid by a centrifugal pump in a hydraulic network with a variable level was carried out. The dimensionless form of the system of equations allowed us to determine three similarity criteria for the problem, including the analog of the Struhal number Str. The analytical solution to the Cauchy problem is found in the quasi-stationary formulation (Str = 0). The solution of the problem in the full statement is obtained by the numerical method. The results of the study of the influence of similarity criteria on the solution are presented. The dimensionless flow rate of the liquid decreases with increasing Str values. In this case, the maximum volume of liquid and the time to reach it increases. Increasing the values of the other two criteria leads to an increase in both the flow rate and the maximum volume of the liquid. The analytical solution in the quasi-rational formulation can be used only for Str < 0,1. The results obtained can be used in the design of Autonomous Water supply and Sewerage systems. Further research for the non-self-similar area of hydraulic resistance and for variable fluid viscosity is promising.

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