scholarly journals Merging and splitting flows in a tee: the Pavlovsky method

Vestnik MGSU ◽  
2020 ◽  
pp. 1546-1555
Author(s):  
Mihail R. Petrichenko ◽  
Ol’ga A. Solov’yova
Keyword(s):  
Flow Rate ◽  
Flow Separation ◽  
Rate Coefficient ◽  
Mechanical Power ◽  
Head Losses ◽  
Increase Flow Rate ◽  
Split Flow ◽  
Flow Rate Coefficient ◽  
External Power Source ◽  
External Power

Introduction. The Pavlovsky method is employed to consider the flows that merge and split inside a tee. Materials and methods. The problem of flows, merging and splitting inside a simple straight tee, is reduced to the problem of limits in a theory of functions applied to the characteristic function of a flow. The influence of the geometric parameter of a tee (a module), head losses and an external power source, produced on the flow rate coefficient in a tee, is identified in the work. Results. The co-authors identified a relation between the geometric parameters of a tee and its capacity in case of an isoenergetic flow and an external mechanical power supply. Conclusions. As for practical tasks, it is sufficient to reproduce a pentagon, stylizing a simple straight tee, on a strip having a ledge, while preserving the correspondence of points of polygons. The following conclusions are made: dissipation does not reduce the flow rate coefficient when flows merge, neither does it reduce the flow rate coefficient when flows split; minimum values of flow rate coefficient q = Q0/Q1 in case of merging flows are attained in the absence of dissipation, and they do not exceed the maximum value of the flow rate coefficient in case of splitting flows is attained in the absence of dissipation and it is not less than dissipation in a tee is explained by the flow separation from the vertex of angle B when flows merge and by the flow separation from the vertex of angle C when flows merge. Hydraulic losses do not reduce flow rate coefficient q = q+ when flows merge and do not increase flow rate coefficient q = q– when flows split. flow rate coefficient q+ goes down if a source of external mechanical power (a pump) is connected to a tee when flows merge; if flows split, the flow rate coefficient goes up and varies within the 1 < q– < 2 interval, and it doesn’t go up if q– > 2.

scholarly journals Stator elements optimization of centrifugal compressor intermediate type stage by CFD methods

2020 ◽  
Vol 178 ◽  
pp. 01020 ◽  
Author(s):  
Lyubov Marenina ◽  
Yuri Galerkin ◽  
Alexandr Drozdov
Keyword(s):  
Flow Rate ◽  
Centrifugal Compressor ◽  
Rate Coefficient ◽  
Optimization Problems ◽  
Flow Path ◽  
Loss Coefficient ◽  
Radius Of Curvature ◽  
Intermediate Type ◽  
Flow Rate Coefficient ◽  
Return Channel

Optimal gas-dynamic design is a complex and time-consuming process. Modern CFD methods help in solving optimization problems and reliably calculating characteristics of stator elements of centrifugal compressor stages. To carry out such calculations, it is necessary to create a parametrized model, which facilitates automation of the process of changing the flow path geometry, rebuilding its dimensions and the computational grid. Using the Direct Optimization program of the ANSYS software package, we have optimized the flow path of the stator elements of a centrifugal compressor intermediate type stage consisting of a vaneless diffuser and a return channel. In this paper, the MOGA (Multi-Objective Genetic Algorithm) optimization method was used. The object of the study was stator elements of one of the model stages designed by the Problem Laboratory of Compressor Engineering, SPbPU. The goal was to achieve the minimum value of the loss coefficient of stator elements when changing 5 geometric parameters: the number of vanes, the inlet vane angle, the height of the vane at the inlet to the return channel vane cascade, the radius of curvature of the leading edge and the thickness of the vane profile. For the best variants based on the results of optimization, the characteristics of the loss coefficient depending on the flow rate coefficient were calculated, their characteristics were compared with the initial variant of the stator elements. The best variant in the design mode has a loss coefficient 4.4% lower than the reference model. With a flow rate coefficient of 1.63 times greater than the calculated one, the optimized variant’s loss coefficient is 33% less.

Centrifugal Compressor Stage Design Principles Checking

2015 ◽  
Author(s):  
Y. Galerkin ◽  
A. Drozdov
Keyword(s):  
Optimal Design ◽  
Flow Rate ◽  
Gas Dynamics ◽  
Rate Coefficient ◽  
Computer Programs ◽  
Design Flow ◽  
Flow Coefficient ◽  
Inlet Velocity ◽  
Flow Rate Coefficient ◽  
Performance Curves

Laboratory “Gas dynamics of turbo machines” (LGDTM) has quite effective optimal design computer programs based on theoretic analysis and experimental data. The authors do not share an opinion that 3D impellers are superior in any case. A lot of designed compressors are provided with traditional 2D impellers with cylindrical blades disposed in a radial part of an impeller. The industrial partner tested recently 1:2 scale model of a single stage 32 MWt pipeline compressor. The flow path design is based on the medium specific speed 2D impeller. Good general scheme of the industrial partner, no constrains and profound design optimization have led to maximum efficiency 90% and to excellent performance in a whole. But if a design flow rate coefficient exceeds 0,070 … 0,08 application of 3D impeller is inevitable. Meridian configuration and blade cascade shape of 3D impellers are much more complicated in comparison with 2D impellers. LGDTM has no at its disposal complete information on physical or numerical tests of 3D impeller candidates with different design solutions. Modern trend to apply CFD calculation for investigations to fill the gap seems to be most logical. But the authors’ own experience and published data show that CFD modeling of 3D impeller performance curves is not satisfactory. As a rule calculated performances are shifted to bigger flow rates and work coefficient is 6–9% higher. But the positive moment is that the efficiency at the design flow coefficient is predicted quite accurately. It opens a way to compare stage’s candidates at the design regimes efficiency at the design flow coefficient. The initial design of the stage 3D impeller + vaneless diffuser + return channel with flow rate coefficient 0,105 and loading factor 0,56 is based on general principles of LGDTM: inlet velocity minimization, mean velocity deceleration control, Q-3-D non-viscid velocity diagrams with non-incidence inlet and minimal load at leading edges. CFD calculation has demonstrated necessity to apply a diffuser with tampered initial part, and better shape of the tampered part was defined. The better shape of the crossover was defined by CFD calculations too. The impeller candidates with gas dynamic and geometry principle of blade design, with different degree of flow deceleration, different axial dimension and different exit blade angles were compared. The new 6th version of the optimal design computer programs (Universal modeling was widely presented at the conferences in Japan, Germany, Great Britain, etc.) is tuned on high flow rate stages with 3D impellers. Validation calculations demonstrated good level of performance curves modeling. The program was applied to study series of candidates with different dimensions in meridian plane. As these dimensions influence mean blade load each parameter was studied with different number of blades. Main results are: axial elongation of an impeller does not lead to efficiency grow, optimal leading edge position is at about 25% of meridian distance from an impeller inlet, optimal inlet diameter is 8,5% less that the diameter corresponding to minimal peripheral inlet velocity. The last conclusion is of particular interest and needs additional proof. The comparison of 94 impellers candidates has led to the stage efficiency increase on about 1.5%. The results have verified general principles of design applied in the laboratory “Gas dynamics of turbo machines” and pointed out on some improvements of design principles.

scholarly journals Flow Characteristics of the Nozzle Blade Cascade in the Mode of the Joint Operation with the Radial Diffuser

2021 ◽  
pp. 5-11
Author(s):  
Alexander Lapuzin ◽  
Valery Subotovich ◽  
Yuriy Yudin ◽  
Svetlana Naumenko ◽  
Ivan Malymon
Keyword(s):  
Reynolds Number ◽  
Flow Rate ◽  
Rate Coefficient ◽  
Measurement Data ◽  
Flow Characteristics ◽  
Flow Coefficient ◽  
Blade Cascade ◽  
Flow Rate Coefficient ◽  
Wide Range ◽  
Nozzle Blade

The obtained research data are given for the nozzle cascade used by a small-size gas turbine of an average fanning in combination with the radial diffuser. Aerodynamic characteristics of the nozzle blade cascade were determined in a wide range of a change in the Reynolds number varying from 4∙105 to 106 and the reduced velocity varying in the range of 0.4 to 1.13. The flow rate coefficient of the nozzle cascade was derived for all modes using the integral methods and the drainages behind the cascade. The kinetic energy loss coefficient and the flow angles were calculated using the measurement data of flow parameters in three control modes that were obtained due to the use of orientable pneumometric probes. When the expansion degree of the convergent –divergent annular duct behind the cascade is equal to 1.43 the flow in the narrow section of this duct is “enlocked” in the mode when the reduced velocity behind the cascade is equal to 1.127. At such velocity the Reynolds number 106 is self-similar for the flow rate coefficient. At lower values of Reynolds number, the decrease of it is accompanied by an intensive decrease in the flow rate coefficient for all the values of the reduced velocity. For the Reynolds number lower than 7∙105 an increase in the velocity results in a decreased flow rate coefficient. When this number exceeds 8∙105 an increase in the velocity results in an increase of the flow coefficient up to the moment when the flow is “enlocked” in the nozzle cascade.

scholarly journals Flow rate changes of drippers with dilutions of treated water produced by oil exploration in the Brazilian semiarid region

2021 ◽  
pp. 796-805
Author(s):  
Hudson Salatiel Marques Vale ◽  
Danniely de Oliveira Costa ◽  
Rafael Oliveira Batista ◽  
Luis Cesar de Aquino Lemos Filho ◽  
Mychelle Karla Teixeira de Oliveira ◽  
...  
Keyword(s):  
Flow Rate ◽  
Produced Water ◽  
Rate Coefficient ◽  
Underground Water ◽  
Semiarid Region ◽  
Dilution Technique ◽  
Flow Rate Coefficient ◽  
Brazilian Semiarid ◽  
Liquid Residue ◽  
Plot Design

The liquid residue called “produced water” from the exploitation of oil in the ground and sea is generated in large volumes and has significant polluting potential. In the Brazilian semiarid region, this liquid can be applied to the agricultural lands, if properly treated and applied to the soil by dripping. It is an alternative that can mitigate water scarcity and impacts on the environment. However, the vulnerability of drippers to clogging is a problem and can be mitigated with the dilution technique. The flow rate changes of drippers for the application of dilutions of produced water treated (PW) with underground water (UW) was analyzed. The experiment was conducted in a completely randomized split-split-plot design with three replications. Plots consisted of treatments (D1: 100% of UW, D2: 90% of UW and 10% PW, D3: 80% of UW and 20% of PW, D4: 70% of UW and 30% of PW and D5: 60% of UW and 40% of PW). The split-plots consisted of types of drippers (G1: 1.6 L h-1, G2: - 1.6 L h-1, G3: 1.7 L h-1) and split-split-plots consisted of evaluation times (0, 40, 80, 120 and 160 h). Flow rate (D) and flow rate coefficient of variation (FCV) were taken every 40 hours untill 160 h. The results showed that the G3 emitter was the most resistant to clogging. The dilutions D2 and D3 provided the lowest losses in hydraulic performance in the drip units. The highest rates of clogging occurred in the G2 emitter operating in the D5 dilution

215 Flow-Rate Variation Pressure for Tainter Gates and Resulting Instantaneous Flow-Rate Coefficient

2000 ◽  
Vol 2000 (0) ◽  
pp. 63-64
Author(s):  
Keiko ANAMI ◽  
Ichishi KUSANO ◽  
Noriaki ISHII ◽  
Aknori NAKATA ◽  
Kouji TOKUSHIMA
Keyword(s):  
Flow Rate ◽  
Rate Coefficient ◽  
Rate Variation ◽  
Instantaneous Flow ◽  
Flow Rate Coefficient ◽  
Instantaneous Flow Rate

scholarly journals Non-pressure compensating emitters using treated sewage effluent for irrigation

2017 ◽  
Vol 47 (7) ◽  
Author(s):  
João Alberto Fischer Filho ◽  
Alexandre Barcellos Dalri ◽  
Miquéias Gomes dos Santos ◽  
José Renato Zanini ◽  
Rogério Teixeira de Faria
Keyword(s):  
Flow Rate ◽  
Rate Coefficient ◽  
Irrigation System ◽  
Sewage Treatment ◽  
Sewage Effluent ◽  
Drip Irrigation System ◽  
Relative Flow Rate ◽  
Flow Rate Coefficient ◽  
Treated Sewage ◽  
Treated Sewage Effluent

ABSTRACT: This study aimed to evaluate the obstruction of non-pressure compensating emitters using treated sewage effluent (TSE) for irrigation. A drip irrigation system with six models of emitters (encoded) was installed in level field conditions. TSE coming from a sewage treatment station was used as irrigation water after being filtered through a disc filter (120 mesh). Seven flow rate evaluations of drippers operating at 100kPa were performed (0, 100, 200, 300, 400, 500 and 600h of operation). The experimental design was randomized in a 6×7 factorial arrangement (6 models and 7 times), with four repetitions, and Tukey’s test was used to compare means. Relative flow rate (Qr), the flow rate coefficient of variation (CVQ) and degree of clogging (GE) were determined. There was a reduction in flow rate in five dripper models, which are susceptible to clogging. The model with rated flow stood out against the others, showing a Qr of 100.52%, CVQ of 2.76% and GE of 0.49%. The use of TSE changed the Qr of the drippers after 600h of operation.

scholarly journals Issues of gas dynamic characteristics modeling: a study on a centrifugal compressor model stage

2019 ◽  
Vol 140 ◽  
pp. 06003 ◽  
Author(s):  
Aleksey Borovkov ◽  
Igor Voinov ◽  
Yuri Galerkin ◽  
Aleksandr Nikiforov ◽  
Maksim Nikitin ◽  
...  
Keyword(s):  
Flow Rate ◽  
Centrifugal Compressor ◽  
Rate Coefficient ◽  
Design Flow ◽  
Maximum Efficiency ◽  
Design Parameters ◽  
Gas Dynamic ◽  
Flow Rate Coefficient ◽  
Sst Turbulence Model ◽  
Problem Laboratory

The paper presents the results of CFD-calculations of a centrifugal compressor stage with a high-pressure 3D impeller and a vaneless diffuser. The stage was designed by Prof. A. M. Simonov in the Problem Laboratory of Compressor LPI according to the following design parameters: flow rate coefficient 0.080, loading factor 0.74, and the relative Mach number 0.78. Two design grids were used: 2.4 and 4.4 million cells for the sector with one blade. The entire stage was calculated with a sparser grid. Special “Stage” interface conditions are used to interface the gas-dynamic parameters at the boundary regions. The SST turbulence model was used in the calculations. The results of efficiency characteristics and work coefficient comparison showed the following: in design flow rate all three variants of the calculation overstate the loading factor by 14.3%; the calculated characteristics of polytrophic work coefficient in the staging of 360 degrees are closest to the experimental characteristics, but the absolute value is greater than 12% at a flow rate coefficient of 0.085; the maximum calculated efficiency of a stage (the circle of 360 degrees) is almost equal to the measured maximum efficiency.

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