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Energy Efficiency of Nozzles for Axial Microturbines
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Procedia Engineering 206 (2017) 499–504
International Conference on Industrial Engineering, ICIE 2017 International Conference on Industrial Engineering, ICIE 2017
Energy Efficiency of Nozzles for Axial Microturbines Energy Efficiency of Nozzles for Axial Microturbines Yu.Ya. Fershalova, M.Yu. Fershalovb, A.Yu. Fershalova,* Yu.Ya. Fershalova, M.Yu. Fershalovb, A.Yu. Fershalova,* Far Eastern Federal University, 8, Suhanova St., Vladivostok, 690950, Russia a
b
a V.I.Il`ichev Oceanological Institute, 43, Baltiyskaya Street, Vladivostok, 690041, Russia FarPacific Eastern Federal University, 8, Suhanova St., Vladivostok, 690950, Russia b V.I.Il`ichev Pacific Oceanological Institute, 43, Baltiyskaya Street, Vladivostok, 690041, Russia
Abstract Abstract The work is devoted to solving important problems of applied gas dynamics of turbine stages, concerning the low efficiency of the axial microturbines nozzles not exceed 9 °), operating at supercritical of The nozzle work isapparatus devoted to solving important (angles problemsofofexit applied gas do dynamics of turbine stages, concerning the lowdifferences efficiency of enthalpy, is aimedaxial at increasing the speed ratioofofexit thenozzles nozzle apparatus (the ratio actual downstream speeddifferences of the nozzle the nozzleand apparatus microturbines (angles do not exceed 9 °),ofoperating at supercritical of apparatus to the possible - the theoretical flowof rate) the prediction angleratio downstream it. enthalpy, and is maximum aimed at increasing speed ratio theand nozzle apparatus (the of actual from downstream speed of the nozzle The work to is the based on the results modeling gas-dynamic processes based onfrom the it. of the results of a physical apparatus maximum possibleof- mathematical theoretical flow rate) andofthe prediction angle downstream experiment. presented as a formalized mathematical regression model typeonfunctions the machine nozzle The work is The basedresults on theare results of mathematical modeling of gas-dynamic processes based the of the- results of a physical velocity and flow rate output depending on the followingregression factors - the expansion nozzle; nozzle angle;nozzle angle experiment. The results are therefrom presented angle as a formalized mathematical model type functions - the exit machine of the front theoutput impeller; the theoretical value of the number;factors dimensionless peripheral speed. velocity andedge flowofrate therefrom angle depending on Mach the following - the expansion nozzle; nozzle exit angle; angle Such presentation of impeller; the results not only numerical analysis and physical interpretation of the afront edge of the theallows theoretical valuefor of their the Mach number; dimensionless peripheral speed. of the purpose of a comprehensive assessment of the impact ratio numerical of the nozzle apparatus and the interpretation downstream corner it, studied Such a presentation of the results allows on not the onlyspeed for their analysis and physical of the of purpose of a factors, but also assessment for the performance of theon optimization calculations. comprehensive of the impact the speed ratio of the nozzle apparatus and the downstream corner of it, studied © 2017 but The Authors. Published by Elsevier B.V. factors, for the performance of the optimization calculations. © 2017 Thealso Authors. Published by Elsevier Ltd. committee Peer-review under responsibility of the scientific of the International Conference on Industrial Engineering. © 2017 The under Authors. Published by Elsevier B.V.committee of Peer-review responsibility of the scientific the International Conference on Industrial Engineering Keywords: nozzle; rotorofwheel; Mach number; efficiency. Peer-review undermicroturbine; responsibility the scientific committee of the International Conference on Industrial Engineering. Keywords: nozzle; microturbine; rotor wheel; Mach number; efficiency.
1. Introduction 1. Introduction At the present stage of development of production reserves more economical running of the powerful stationary turbines limited. This not applyoftoproduction turbines operating with limited weight and size characteristics: the gas At theare present stage of does development reserves more economical running of the powerful stationary flow andare rotor speed.This Thedoes turbines of thetolatter species are widely in weight shipbuilding, traction devices, rail turbines limited. not apply turbines operating with used limited and size characteristics: the and gas road decentralized energyofsystems, thermal gas distribution stations, cryogenic flow transport, and rotor speed. The turbines the latter speciesplants, are widely used in shipbuilding, traction engineering, devices, rail and road transport, decentralized energy systems, thermal plants, gas distribution stations, cryogenic engineering, and
* Corresponding author. Tel.: +7-953-217-2164 E-mail address:author. [email protected] * Corresponding Tel.: +7-953-217-2164
E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier B.V. Peer-review the scientific committee 1877-7058 ©under 2017responsibility The Authors. of Published by Elsevier B.V.of the International Conference on Industrial Engineering . Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering .
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.507
500 2
Yu.Ya. Fershalov et al. / Procedia Engineering 206 (2017) 499–504 Yu.Ya. Fershalov, M.Yu. Fershalov, A.Yu. Fershalov / Procedia Engineering 00 (2017) 000–000
manufacturing. Such turbines are used as main engines, drive engines generators, pump aggregates and compressor stations, to boost diesel engines, in the turbo, while the transportation of gas to be used in the process of reducing the latter. They are also used as a motor for a manual air tool, cathodic protection systems, etc. In the future, these turbines are proposed to use for emergency cooling nuclear reactors when disconnected from the power supply [1]. 2. Topicality The relevance of the work is determined by its focus on solving the most important for the economy and industry of the problems associated with the development of highly efficient power plants, the need for an objective selection of the best technical solutions for microturbines used in power engineering. The relevance of research is confirmed by numerous works of various authors in this field [2-7]. Also in these works reflects the application of turbines of this type. 3. Formulation of the problem Turbine with relatively low power often work in conditions of deficiency of gas flow and the power required for the gas should have a high initial pressure and temperature. In this case, the density of the gas increases and the flow area of the nozzle flow is necessary to carry out extremely small. In this case, the turbine is made or partial supply of gas to the impeller or the height of the turbine blades do significantly less than the recommended value. Both options significantly reduce the efficiency of the turbine. Alternative partial turbine stages are in the turbine nozzle outlet angle which is reduced to 5°. This design enables the turbine with a full gas supply at an acceptable height of the flow, which increases the efficiency of microturbines by eliminating the energy losses associated with partial supply, but such turbine elements and their solid parts still insufficiently investigated and have low efficiency. This is due to non-optimal regimes of the gas flow in the channels, as well as relative values with large surface roughness and long inlet and outlet channels, edge thickness and size of gaps. All this causes a relatively "thick" boundary layer flow and increased non-uniformity, which lead to a sharp decrease in efficiency of the turbine. The main direction in which should be addressed to improve the efficiency of microturbines, gas-dynamic is improving nozzles nozzle units, providing a reduction in the kinetic energy of the gas loss, characterized by speed ratio nozzle units. Such a determination of the effectiveness of the nozzle apparatus allows to evaluate and compare its quantified at various variants of embodiment nozzles. In recent years, the decision in the channels and the expiration of the supersonic gas flow problems are of great advances in the theory known as the "Mathematical theory of control physical fields in continuous media." This theory is intensively developing in our country, and abroad. One of the leading places in the world to address this type of control problems for models of continuum mechanics takes scientific group, which under the leadership of G. Alekseev developed a common management tasks for the research method and hydrodynamic models of heat and mass transfer, and developed efficient numerical algorithms for control problems for a number of models of continuum mechanics [8-11]. However, the results obtained on the basis of the aforementioned theoretical investigations do not currently have sufficient accuracy. This is due to the complexity of the mathematical description of the processes occurring during the movement of gas in the flow of the nozzle having a small size and a large three-dimensional non-uniformity of the flow at the exit of them, which is exacerbated by the presence of a rotating impeller. In connection with this investigation, it was decided to carry out on the basis of experimental methods, which not only lost its relevance but has gained prominence with the verification of the adequacy of the results obtained theoretically. The results of the analysis of previous studies have shown that the greatest impact on the efficiency of the turbines has the perfection of the nozzle apparatus [12-13]. In this regard, this article discusses the results of efforts to improve the nozzle apparatus. Besides the direct impact on the design of the nozzle unit of the turbine efficiency at different operating conditions, the value of the static pressure depends on it in the area between the nozzle assembly and the impeller [14-16], which is related to the terms of the impeller [17]. Preliminary design development [18] and studies [19-21] have shown the possibility and prospects of selected areas of work. Furthermore, in [22] presents the results of studying the effect of various factors on the secondary
Yu.Ya. Fershalov et al. / Procedia Engineering 206 (2017) 499–504 Yu.Ya. Fershalov, M.Yu. Fershalov, A.Yu. Fershalov / Procedia Engineering 00 (2017) 000–000
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integral value of the angle of the downstream nozzle. This information should be considered when choosing the optimal value of the installation angle of the leading edge [23]. The result of this work was to solve the following tasks: regression developed mathematical models to describe the speed ratio of the nozzle apparatus (φ) and the angle of the real output of gas from it (α1); clarified the mutual influence of factors on the characteristics studied with the help of simulation based on the developed regression models; optimization studies conducted coefficient φ. 4. Theoretical part The basis of obtaining numerical data for research lay method, not based on the model representation of the three-dimensional structure of the gas flow. It was assumed that a set of parameters, which depend on the flow characteristics, is finite. Among this set of isolated set of independent parameters defining characteristics investigated. Their values are independent of the method by which the system (part of the flow system and gas nozzle) was transferred into a given state. By the nature of relations with the environment adopted type adiabatically isolated system. The physical interpretation of the gas-dynamic phenomena in the flow of the nozzle apparatus and the output of it is based on the provisions of the theory of formation and propagation of shock waves in supersonic flow of bodies taking into account the concept of average velocity of turbulent flow and the possibility of an approximate consideration of the flow in the one-dimensional formulation based on averaging it parameters in cross section. Accounting random velocity fluctuations that characterize the turbulent flow, manifested in the values of the error of measurement results. A solution of tasks based on the experimental data obtained with the use of staging methods of physical and numerical experiments, as well as regulations and laws of gas dynamics, and statistical techniques. Working hypotheses have been put forward before you start: Low-efficiency microturbines due to lack efficacy nozzle units due to the formation of the secondary vortex near the end faces of the nozzles of the nozzle channel relatively low due to the presence of a pressure gradient acting in the transverse direction in the flow core; optimization of nozzle units carried out without regard to their interaction with the impeller does not guarantee the achievement of the maximum speed ratio. The required set of measurements obtained as a result of the model experiment designed to stand [23]. During experimental studies developed formal mathematical models (the definition of the regression coefficient values produced by the method of least squares) ratio nozzle device speed and the angle of the real output of gas from it (1). 5
5
5
b0 bi xi b ji xi x j φ, α1 i 1
(1)
i 1 j i
where:
x 1
x5
f
f 1,91 x2 ; f f exit f min ; 0,91
М с1t
1к
M c1t 2, 261 ; u u a1min u 1,168
1к 7 2
x3 ;
1к
334,83 T0* ; M c1t
1к 11 3
2 Р0* Р1
; x4
k-1
k
u
1
u 0, 22 0, 22
;
k-1 ;
f exit – normal cross-sectional area of the nozzle outlet; f min – the minimum area of the nozzle; 1к – nozzle exit angle (degrees); 1к – angle of the front edge of the impeller (degrees); u – circumferential speed of the impeller at
Yu.Ya. Fershalov et al. / Procedia Engineering 206 (2017) 499–504 Yu.Ya. Fershalov, M.Yu. Fershalov, A.Yu. Fershalov / Procedia Engineering 00 (2017) 000–000
4502
the middle diameter flow (m/s); a1min – speed of sound in the minimum section of the nozzle (m/sec); T0* – hindered temperature gas stream upstream nozzle (K); Р0* – pressure hindered the flow of gas to the nozzles; Р1 – the static the pressure of the nozzles; k – isentrope factor (for air k 1,4 ); f – the expansion nozzle; u – dimensionless peripheral speed. When using the formula (1) be aware that the values should be in the field of – 1 x1 ; x2 ; x3 ; x4 ; x5 1 . The values of the coefficients bi, bji – to calculate φ and α1 shown in Table 1. Table 1. The coefficients of the polynomial to compute φ and α1.
j
0 1 2
φ
α1
i
i
0
1
2
3
4
5
0
1
2
3
4
5
+0,811
-0,058
-0,036
+0,044
-0,032
+0,114
+12,390
-4,819
+4,922
-1,415
+0,843
+12,588
-0,028
+0,042
+0,015
-0,023
+0,149
+0,793
-0,615
-0,175
+0,514
-6,603
+0,041
+0,004
+0,001
-0,057
-0,480
-0,671
+0,152
+3,862
-0,010
-0,007
+0,003
-0,229
+0,085
-0,855
+0,007
+0,062
+0,182
-0,980
3 4 5
-0,169
+9,236
Confirmation of the adequacy of the results obtained using the regression models, the results of the experiment were tested using Fisher's exact test. Besides adequacy was confirmed by comparing the results obtained by the formula (1) with the results of the control samples of the experiment (the experimental points which are not participating in the development of a regression model). To increase rotor speed is suggested to use the results of [25] to translate the microturbine to operate on gaslubricated bearings; Further research is planned to be based on the use of acoustic methods used in other fields of science, especially in medicine. [26]. 5. Practical significance
established an engineering method of designing high-performance nozzle units, operated as part of microturbines; developed regression models to determine the speed ratio of the nozzle devices and the angle of exit gas from them, to be used in gas-dynamic calculations microturbines; developed a method of determining the scale of similarity coefficient for modeling gas-dynamic characteristics of the nozzles to transfer the results of model tests on full-scale nozzle apparatus [24]. This will improve the accuracy of the use of results by taking into account criteria such as the Reynolds number and Euler's criteria, as well as the criterion of the complex obtained on the basis of the conservation of energy equation (without heat
Yu.Ya.Fershalov, FershalovA.Yu. et al. Fershalov / Procedia/Engineering 206 (2017)00 499–504 Yu.Ya. Fershalov, M.Yu. Procedia Engineering (2017) 000–000
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exchange with the environment) and the account number of the impeller blades and nozzles including Strouhal affecting on unsteady flow. 6. Conclusions
Analysis of the results revealed a pattern nozzle device speed ratio changes depending on the factors. 1. The most strongly on the efficiency of the nozzle apparatus having a Mach number calculated from the theoretical parameters, due to the fact that its value depends on the intensity of the shock waves, the formation of which is wasted energy flow. Increasing the Mach number decreases the degree of influence of the impeller blade tips microturbines to gas dynamic characteristics of the gas flow exiting from the nozzles of the nozzle apparatus, caused by an increase of the axial component of flow velocity. This reduces the relative movement speed jump in the flow direction, which prevents separation at the back of the nozzle profile. In addition, the reduced duration of the impact of shocks to the oblique cut of the nozzle unit as a result of increasing the relative velocity jump. It should be noted that an increase in output flow rate from the nozzle device involves increasing its kinetic energy, which reduces the impact on the flow perturbation from the impeller edge. 2. In second place on the effect on the rate coefficient of the nozzle apparatus is such a factor as the expansion nozzles (nozzle area ratio in the output section normal to the minimum area), thanks to which the acceleration of the flow. In the case of the insufficient magnitude of the expansion nozzle the working fluid does not accelerate to the desired speed, with an excessively large magnitude of the expansion nozzle occurs overexpansion flow, accompanied by a decrease in its speed. 3. In the third place on the influence on the speed ratio value of the nozzle apparatus is the installation angle of the leading edge of the impeller blades, despite the fact that it is itself slightly, but the magnitude of the installation angle of the leading edge of the impeller vane determines the direction reflected by the edges of rotor blades percussion waves or simply disturbances, thereby improving or gas flow conditions, or separation. 4. Such factors as the dimensionless peripheral speed are the twofold impact on the ratio of the nozzle unit rate. When it decreases, on the one hand, the movement speed of the shock wave decreases and increases the duration of its effect on the nozzles, which increases the loss, on the other hand, this prevents the occurrence of separation at the back of an oblique cut, which positively in terms of efficiency of the nozzle apparatus. 5. Reducing the nozzle outlet angle increases the sensitivity of the flow coming from the nozzles to the presence of the impeller, especially when the latter rotates. This phenomenon is explained by the fact that the axial component of the flow velocity becomes less than unity and decreases with small nozzle exit corners. Reflected on the impeller blades edge shock wave through the axial velocity component affects the flow, which negatively affects the efficiency of the bevel. References [1] V.A. Yufereva, A.A. Odintsov, Use of a low-power turbine for emergency cooling of the reactor, Scientific session MIFI-2007. 8, 151 p. (in Russ.) [2] Ju.P. Kuznetsov, A.B. Tchouvakov, A Testing device for research of small-size turbine stages, Proceedings of the higher educational institutions, Machine building. 4 (2013) 58–64 (in Russ.) [3] Ju.P. Kuznetsov, Creation of non-autonomous turbo-drives based on the synthesis of high-performance microturbines of various kinematic schemes, dissertation thesis of the doctor of Sience in Engineering, Saint-Peterburg, 1995. (in Russ.) [4] V.L. Himich, Ju.P. Kuznetsov, A.G. Voevodin, A.B. Chuvakov, S.N. Hrunkov, A.A. Kraynov, Experimental stand for the study of microturbines and grinding machines with turbine drive, In the collection: modern technologies in shipbuilding and aviation education, science and production, A collection of reports of the all-Russian scientific-practical conference dedicated to the centenary of the birth of R.E. Alekseeva. (2016) 426–437. (in Russ.) [5] Ju.P. Kuznetsov, V.L. Himich, A.B. Chuvakov, S.N. Hrunkov, A.A. Kraynov, Calculated characteristics of a two-stage radial microturbine, In the collection: modern technologies in shipbuilding and aviation education, science and production. A collection of reports of the all-Russian scientific-practical conference dedicated to the centenary of the birth of R.E. Alekseeva. (2016) 347–359. (in Russ.) [6] V.L. Himich, Ju.P. Kuznetsov, A.G. Voevodin, A.B. Chuvakov, S.N. Hrunkov, A.A. Kraynov, High-speed pneumatic spindles with gasdynamic rotor bearings, In the collection: modern technologies in shipbuilding and aviation education, science and production, A collection of reports of the all-Russian scientific-practical conference dedicated to the centenary of the birth of R.E. Alekseeva. (2016) 417–425. (in Russ.)
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[7] Ju.P. Kuznetsov, V.L. Khimich, S.N. Khrunkov, A.A. Krainov, Radial two-stage microturbine for pneumatic actuation, Russian Aeronautics. 59 (2016) 283–286. [8] G.V. Alekseev, I.S. Vakhitov, O.V. Soboleva, Stability estimates in identification problems for the convection–diffusion–reaction equation, Computational Mathematics and Mathematical Physics. 52 (2012) 1635–1649. [9] G.V. Alekseev, Solvability of inverse extremum problems for stationary equations of heat and mass transfer, Siberian Mathematical Journal. 42 (2001) 811–827. [10] G.V. Alekseev, D.A. Tereshko, On solvability of inverse extremal problem for stationary equations of viscous heat conducting fluid, Journal of Inverse and Ill-Posed Problems. 6 (1998) 521–562. [11] G.V. Alekseev, Inverse extremal problems for stationary equations in mass transfer theory, Computational Mathematics and Mathematical Physics. 42 (2002) 363–376. [12] Yu.Ya. Fershalov, I.N. Han`kovich, A.N. Minaev, B.Ya. Karasteliov, Yu.V. Yakubovskiy, E.I. Konchakov, The influence of design factors on the efficiency of a low-flow turbine stage, Scientific review. 5 (2012) 440–450. (in Russ.) [13] Yu.Ya. Fershalov, I.N. Han`kovich, A.N. Minaev, B.Ya. Karasteliov, Yu.V. Yakubovskiy, E.I. Konchakov, The influence of regime factors on the efficiency of a low-flow turbine stage, Scientific review. 5 (2012) 425–439. (in Russ.) [14] M.Yu. Fershalov, Yu.Ya. Fershalov, G.V. Alekseev, Degree of reactivity of low-flow turbines with small constructive angles of nozzle exit, Scientific review. 1 (2013) 149–153. (in Russ.) [15] M.Y. Fershalov, Y.Y. Fershalov, A.Y. Fershalov, T.V. Sazonov, D.I. Ibragimov, Microturbines degree of reactivity, Applied Mechanics and Materials. 635-637 (2014) 354–357. [16] M.Y. Fershalov, A.Y. Fershalov, Ju.Ya. Fershalov, Calculation reactivity degree for axial low-account turbines with small emergence angles of nozzle devices, Advanced Materials Research. 915-916 (2014) 341–344. [17] A.Y. Fershalov, Y.Y. Fershalov, M.Y. Fershalov, T.V. Sazonov, D.I. Ibragimov, Analysis and optimization of efficiency rotor wheels microturbines, Applied Mechanics and Materials. 635-637 (2014) 76–79. [18] Yu.Ya. Fershalov, T.V. Sazonov, Experimental research of the nozzles, Advanced Materials Research. 915-916 (2014) 345–348. [19] T.V. Sazonov, Y.Y. Fershalov, M.Y. Fershalov, A.Y. Fershalov, D.I. Ibragimov, Experimental installation for the study of nozzles microturbines, Applied Mechanics and Materials. 635-637 (2014) 155–158. [20] Yu.Ya. Fershalov, A.Yu. Fershalov, M.Yu. Fershalov, Influence of the degree of nozzle expansion with a small exit angle on the efficiency of nozzles of low-flow turbines, Shipbuilding. 1 (2012) 39–41. (in Russ.) [21] Yu.Ya. Fershalov, S.V. Chekhranov, Static testing of nozzles with low outlet angle of flow, Shipbuilding. 5 (2005) 54–56. (in Russ.) [22] Yu.Ya. Fershalov, V.M. Akulenko, Angle of exit of the working fluid from nozzle devices of axial low-flow turbines with nozzles of a new design, Scientific review. 4 (2011) 91–96. (in Russ.) [23] Yu.Ya. Fershalov, Modeling, analysis and improvement of gas dynamic characteristics of ship axial low-flow turbine stages, dissertation of the doctor of Sience in Engineering, Far Eastern Federal University, Vladivostok, 2015. (in Russ.) [24] Yu.Ya. Fershalov, Technique for physical simulation of gasodynamic processes in the turbomachine flow passages, Russian Aeronautics. 55 (2012) 424–429. [25] M.V. Gribinichenko, A.V. Kurenskiy, Yu.Ya. Fershalov, Generalized mathematical model of axial bearings with gas lubrication of elements of ship power plants, Marine intelligent technologies. 1 (2011) 21–23. (in Russ.) [26] V.I. Korenbaum, M.A. Rasskazova, I.A. Pochekutova, Y.Y. Fershalov, Mechanisms of sibilant noise formation observed during forced exhalation of a healthy person, Acoustical Physics. 55 (2009) 528–537.
ScienceDirect ScienceDirect
Available online at www.sciencedirect.com Procedia Engineering 00 (2017)000–000 Procedia Engineering 00 (2017)000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 206 (2017) 499–504
International Conference on Industrial Engineering, ICIE 2017 International Conference on Industrial Engineering, ICIE 2017
Energy Efficiency of Nozzles for Axial Microturbines Energy Efficiency of Nozzles for Axial Microturbines Yu.Ya. Fershalova, M.Yu. Fershalovb, A.Yu. Fershalova,* Yu.Ya. Fershalova, M.Yu. Fershalovb, A.Yu. Fershalova,* Far Eastern Federal University, 8, Suhanova St., Vladivostok, 690950, Russia a
b
a V.I.Il`ichev Oceanological Institute, 43, Baltiyskaya Street, Vladivostok, 690041, Russia FarPacific Eastern Federal University, 8, Suhanova St., Vladivostok, 690950, Russia b V.I.Il`ichev Pacific Oceanological Institute, 43, Baltiyskaya Street, Vladivostok, 690041, Russia
Abstract Abstract The work is devoted to solving important problems of applied gas dynamics of turbine stages, concerning the low efficiency of the axial microturbines nozzles not exceed 9 °), operating at supercritical of The nozzle work isapparatus devoted to solving important (angles problemsofofexit applied gas do dynamics of turbine stages, concerning the lowdifferences efficiency of enthalpy, is aimedaxial at increasing the speed ratioofofexit thenozzles nozzle apparatus (the ratio actual downstream speeddifferences of the nozzle the nozzleand apparatus microturbines (angles do not exceed 9 °),ofoperating at supercritical of apparatus to the possible - the theoretical flowof rate) the prediction angleratio downstream it. enthalpy, and is maximum aimed at increasing speed ratio theand nozzle apparatus (the of actual from downstream speed of the nozzle The work to is the based on the results modeling gas-dynamic processes based onfrom the it. of the results of a physical apparatus maximum possibleof- mathematical theoretical flow rate) andofthe prediction angle downstream experiment. presented as a formalized mathematical regression model typeonfunctions the machine nozzle The work is The basedresults on theare results of mathematical modeling of gas-dynamic processes based the of the- results of a physical velocity and flow rate output depending on the followingregression factors - the expansion nozzle; nozzle angle;nozzle angle experiment. The results are therefrom presented angle as a formalized mathematical model type functions - the exit machine of the front theoutput impeller; the theoretical value of the number;factors dimensionless peripheral speed. velocity andedge flowofrate therefrom angle depending on Mach the following - the expansion nozzle; nozzle exit angle; angle Such presentation of impeller; the results not only numerical analysis and physical interpretation of the afront edge of the theallows theoretical valuefor of their the Mach number; dimensionless peripheral speed. of the purpose of a comprehensive assessment of the impact ratio numerical of the nozzle apparatus and the interpretation downstream corner it, studied Such a presentation of the results allows on not the onlyspeed for their analysis and physical of the of purpose of a factors, but also assessment for the performance of theon optimization calculations. comprehensive of the impact the speed ratio of the nozzle apparatus and the downstream corner of it, studied © 2017 but The Authors. Published by Elsevier B.V. factors, for the performance of the optimization calculations. © 2017 Thealso Authors. Published by Elsevier Ltd. committee Peer-review under responsibility of the scientific of the International Conference on Industrial Engineering. © 2017 The under Authors. Published by Elsevier B.V.committee of Peer-review responsibility of the scientific the International Conference on Industrial Engineering Keywords: nozzle; rotorofwheel; Mach number; efficiency. Peer-review undermicroturbine; responsibility the scientific committee of the International Conference on Industrial Engineering. Keywords: nozzle; microturbine; rotor wheel; Mach number; efficiency.
1. Introduction 1. Introduction At the present stage of development of production reserves more economical running of the powerful stationary turbines limited. This not applyoftoproduction turbines operating with limited weight and size characteristics: the gas At theare present stage of does development reserves more economical running of the powerful stationary flow andare rotor speed.This Thedoes turbines of thetolatter species are widely in weight shipbuilding, traction devices, rail turbines limited. not apply turbines operating with used limited and size characteristics: the and gas road decentralized energyofsystems, thermal gas distribution stations, cryogenic flow transport, and rotor speed. The turbines the latter speciesplants, are widely used in shipbuilding, traction engineering, devices, rail and road transport, decentralized energy systems, thermal plants, gas distribution stations, cryogenic engineering, and
* Corresponding author. Tel.: +7-953-217-2164 E-mail address:author. [email protected] * Corresponding Tel.: +7-953-217-2164
E-mail address: [email protected] 1877-7058 © 2017 The Authors. Published by Elsevier B.V. Peer-review the scientific committee 1877-7058 ©under 2017responsibility The Authors. of Published by Elsevier B.V.of the International Conference on Industrial Engineering . Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering .
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the International Conference on Industrial Engineering. 10.1016/j.proeng.2017.10.507
500 2
Yu.Ya. Fershalov et al. / Procedia Engineering 206 (2017) 499–504 Yu.Ya. Fershalov, M.Yu. Fershalov, A.Yu. Fershalov / Procedia Engineering 00 (2017) 000–000
manufacturing. Such turbines are used as main engines, drive engines generators, pump aggregates and compressor stations, to boost diesel engines, in the turbo, while the transportation of gas to be used in the process of reducing the latter. They are also used as a motor for a manual air tool, cathodic protection systems, etc. In the future, these turbines are proposed to use for emergency cooling nuclear reactors when disconnected from the power supply [1]. 2. Topicality The relevance of the work is determined by its focus on solving the most important for the economy and industry of the problems associated with the development of highly efficient power plants, the need for an objective selection of the best technical solutions for microturbines used in power engineering. The relevance of research is confirmed by numerous works of various authors in this field [2-7]. Also in these works reflects the application of turbines of this type. 3. Formulation of the problem Turbine with relatively low power often work in conditions of deficiency of gas flow and the power required for the gas should have a high initial pressure and temperature. In this case, the density of the gas increases and the flow area of the nozzle flow is necessary to carry out extremely small. In this case, the turbine is made or partial supply of gas to the impeller or the height of the turbine blades do significantly less than the recommended value. Both options significantly reduce the efficiency of the turbine. Alternative partial turbine stages are in the turbine nozzle outlet angle which is reduced to 5°. This design enables the turbine with a full gas supply at an acceptable height of the flow, which increases the efficiency of microturbines by eliminating the energy losses associated with partial supply, but such turbine elements and their solid parts still insufficiently investigated and have low efficiency. This is due to non-optimal regimes of the gas flow in the channels, as well as relative values with large surface roughness and long inlet and outlet channels, edge thickness and size of gaps. All this causes a relatively "thick" boundary layer flow and increased non-uniformity, which lead to a sharp decrease in efficiency of the turbine. The main direction in which should be addressed to improve the efficiency of microturbines, gas-dynamic is improving nozzles nozzle units, providing a reduction in the kinetic energy of the gas loss, characterized by speed ratio nozzle units. Such a determination of the effectiveness of the nozzle apparatus allows to evaluate and compare its quantified at various variants of embodiment nozzles. In recent years, the decision in the channels and the expiration of the supersonic gas flow problems are of great advances in the theory known as the "Mathematical theory of control physical fields in continuous media." This theory is intensively developing in our country, and abroad. One of the leading places in the world to address this type of control problems for models of continuum mechanics takes scientific group, which under the leadership of G. Alekseev developed a common management tasks for the research method and hydrodynamic models of heat and mass transfer, and developed efficient numerical algorithms for control problems for a number of models of continuum mechanics [8-11]. However, the results obtained on the basis of the aforementioned theoretical investigations do not currently have sufficient accuracy. This is due to the complexity of the mathematical description of the processes occurring during the movement of gas in the flow of the nozzle having a small size and a large three-dimensional non-uniformity of the flow at the exit of them, which is exacerbated by the presence of a rotating impeller. In connection with this investigation, it was decided to carry out on the basis of experimental methods, which not only lost its relevance but has gained prominence with the verification of the adequacy of the results obtained theoretically. The results of the analysis of previous studies have shown that the greatest impact on the efficiency of the turbines has the perfection of the nozzle apparatus [12-13]. In this regard, this article discusses the results of efforts to improve the nozzle apparatus. Besides the direct impact on the design of the nozzle unit of the turbine efficiency at different operating conditions, the value of the static pressure depends on it in the area between the nozzle assembly and the impeller [14-16], which is related to the terms of the impeller [17]. Preliminary design development [18] and studies [19-21] have shown the possibility and prospects of selected areas of work. Furthermore, in [22] presents the results of studying the effect of various factors on the secondary
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integral value of the angle of the downstream nozzle. This information should be considered when choosing the optimal value of the installation angle of the leading edge [23]. The result of this work was to solve the following tasks: regression developed mathematical models to describe the speed ratio of the nozzle apparatus (φ) and the angle of the real output of gas from it (α1); clarified the mutual influence of factors on the characteristics studied with the help of simulation based on the developed regression models; optimization studies conducted coefficient φ. 4. Theoretical part The basis of obtaining numerical data for research lay method, not based on the model representation of the three-dimensional structure of the gas flow. It was assumed that a set of parameters, which depend on the flow characteristics, is finite. Among this set of isolated set of independent parameters defining characteristics investigated. Their values are independent of the method by which the system (part of the flow system and gas nozzle) was transferred into a given state. By the nature of relations with the environment adopted type adiabatically isolated system. The physical interpretation of the gas-dynamic phenomena in the flow of the nozzle apparatus and the output of it is based on the provisions of the theory of formation and propagation of shock waves in supersonic flow of bodies taking into account the concept of average velocity of turbulent flow and the possibility of an approximate consideration of the flow in the one-dimensional formulation based on averaging it parameters in cross section. Accounting random velocity fluctuations that characterize the turbulent flow, manifested in the values of the error of measurement results. A solution of tasks based on the experimental data obtained with the use of staging methods of physical and numerical experiments, as well as regulations and laws of gas dynamics, and statistical techniques. Working hypotheses have been put forward before you start: Low-efficiency microturbines due to lack efficacy nozzle units due to the formation of the secondary vortex near the end faces of the nozzles of the nozzle channel relatively low due to the presence of a pressure gradient acting in the transverse direction in the flow core; optimization of nozzle units carried out without regard to their interaction with the impeller does not guarantee the achievement of the maximum speed ratio. The required set of measurements obtained as a result of the model experiment designed to stand [23]. During experimental studies developed formal mathematical models (the definition of the regression coefficient values produced by the method of least squares) ratio nozzle device speed and the angle of the real output of gas from it (1). 5
5
5
b0 bi xi b ji xi x j φ, α1 i 1
(1)
i 1 j i
where:
x 1
x5
f
f 1,91 x2 ; f f exit f min ; 0,91
М с1t
1к
M c1t 2, 261 ; u u a1min u 1,168
1к 7 2
x3 ;
1к
334,83 T0* ; M c1t
1к 11 3
2 Р0* Р1
; x4
k-1
k
u
1
u 0, 22 0, 22
;
k-1 ;
f exit – normal cross-sectional area of the nozzle outlet; f min – the minimum area of the nozzle; 1к – nozzle exit angle (degrees); 1к – angle of the front edge of the impeller (degrees); u – circumferential speed of the impeller at
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the middle diameter flow (m/s); a1min – speed of sound in the minimum section of the nozzle (m/sec); T0* – hindered temperature gas stream upstream nozzle (K); Р0* – pressure hindered the flow of gas to the nozzles; Р1 – the static the pressure of the nozzles; k – isentrope factor (for air k 1,4 ); f – the expansion nozzle; u – dimensionless peripheral speed. When using the formula (1) be aware that the values should be in the field of – 1 x1 ; x2 ; x3 ; x4 ; x5 1 . The values of the coefficients bi, bji – to calculate φ and α1 shown in Table 1. Table 1. The coefficients of the polynomial to compute φ and α1.
j
0 1 2
φ
α1
i
i
0
1
2
3
4
5
0
1
2
3
4
5
+0,811
-0,058
-0,036
+0,044
-0,032
+0,114
+12,390
-4,819
+4,922
-1,415
+0,843
+12,588
-0,028
+0,042
+0,015
-0,023
+0,149
+0,793
-0,615
-0,175
+0,514
-6,603
+0,041
+0,004
+0,001
-0,057
-0,480
-0,671
+0,152
+3,862
-0,010
-0,007
+0,003
-0,229
+0,085
-0,855
+0,007
+0,062
+0,182
-0,980
3 4 5
-0,169
+9,236
Confirmation of the adequacy of the results obtained using the regression models, the results of the experiment were tested using Fisher's exact test. Besides adequacy was confirmed by comparing the results obtained by the formula (1) with the results of the control samples of the experiment (the experimental points which are not participating in the development of a regression model). To increase rotor speed is suggested to use the results of [25] to translate the microturbine to operate on gaslubricated bearings; Further research is planned to be based on the use of acoustic methods used in other fields of science, especially in medicine. [26]. 5. Practical significance
established an engineering method of designing high-performance nozzle units, operated as part of microturbines; developed regression models to determine the speed ratio of the nozzle devices and the angle of exit gas from them, to be used in gas-dynamic calculations microturbines; developed a method of determining the scale of similarity coefficient for modeling gas-dynamic characteristics of the nozzles to transfer the results of model tests on full-scale nozzle apparatus [24]. This will improve the accuracy of the use of results by taking into account criteria such as the Reynolds number and Euler's criteria, as well as the criterion of the complex obtained on the basis of the conservation of energy equation (without heat
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exchange with the environment) and the account number of the impeller blades and nozzles including Strouhal affecting on unsteady flow. 6. Conclusions
Analysis of the results revealed a pattern nozzle device speed ratio changes depending on the factors. 1. The most strongly on the efficiency of the nozzle apparatus having a Mach number calculated from the theoretical parameters, due to the fact that its value depends on the intensity of the shock waves, the formation of which is wasted energy flow. Increasing the Mach number decreases the degree of influence of the impeller blade tips microturbines to gas dynamic characteristics of the gas flow exiting from the nozzles of the nozzle apparatus, caused by an increase of the axial component of flow velocity. This reduces the relative movement speed jump in the flow direction, which prevents separation at the back of the nozzle profile. In addition, the reduced duration of the impact of shocks to the oblique cut of the nozzle unit as a result of increasing the relative velocity jump. It should be noted that an increase in output flow rate from the nozzle device involves increasing its kinetic energy, which reduces the impact on the flow perturbation from the impeller edge. 2. In second place on the effect on the rate coefficient of the nozzle apparatus is such a factor as the expansion nozzles (nozzle area ratio in the output section normal to the minimum area), thanks to which the acceleration of the flow. In the case of the insufficient magnitude of the expansion nozzle the working fluid does not accelerate to the desired speed, with an excessively large magnitude of the expansion nozzle occurs overexpansion flow, accompanied by a decrease in its speed. 3. In the third place on the influence on the speed ratio value of the nozzle apparatus is the installation angle of the leading edge of the impeller blades, despite the fact that it is itself slightly, but the magnitude of the installation angle of the leading edge of the impeller vane determines the direction reflected by the edges of rotor blades percussion waves or simply disturbances, thereby improving or gas flow conditions, or separation. 4. Such factors as the dimensionless peripheral speed are the twofold impact on the ratio of the nozzle unit rate. When it decreases, on the one hand, the movement speed of the shock wave decreases and increases the duration of its effect on the nozzles, which increases the loss, on the other hand, this prevents the occurrence of separation at the back of an oblique cut, which positively in terms of efficiency of the nozzle apparatus. 5. Reducing the nozzle outlet angle increases the sensitivity of the flow coming from the nozzles to the presence of the impeller, especially when the latter rotates. This phenomenon is explained by the fact that the axial component of the flow velocity becomes less than unity and decreases with small nozzle exit corners. Reflected on the impeller blades edge shock wave through the axial velocity component affects the flow, which negatively affects the efficiency of the bevel. References [1] V.A. Yufereva, A.A. Odintsov, Use of a low-power turbine for emergency cooling of the reactor, Scientific session MIFI-2007. 8, 151 p. (in Russ.) [2] Ju.P. Kuznetsov, A.B. Tchouvakov, A Testing device for research of small-size turbine stages, Proceedings of the higher educational institutions, Machine building. 4 (2013) 58–64 (in Russ.) [3] Ju.P. Kuznetsov, Creation of non-autonomous turbo-drives based on the synthesis of high-performance microturbines of various kinematic schemes, dissertation thesis of the doctor of Sience in Engineering, Saint-Peterburg, 1995. (in Russ.) [4] V.L. Himich, Ju.P. Kuznetsov, A.G. Voevodin, A.B. Chuvakov, S.N. Hrunkov, A.A. Kraynov, Experimental stand for the study of microturbines and grinding machines with turbine drive, In the collection: modern technologies in shipbuilding and aviation education, science and production, A collection of reports of the all-Russian scientific-practical conference dedicated to the centenary of the birth of R.E. Alekseeva. (2016) 426–437. (in Russ.) [5] Ju.P. Kuznetsov, V.L. Himich, A.B. Chuvakov, S.N. Hrunkov, A.A. Kraynov, Calculated characteristics of a two-stage radial microturbine, In the collection: modern technologies in shipbuilding and aviation education, science and production. A collection of reports of the all-Russian scientific-practical conference dedicated to the centenary of the birth of R.E. Alekseeva. (2016) 347–359. (in Russ.) [6] V.L. Himich, Ju.P. Kuznetsov, A.G. Voevodin, A.B. Chuvakov, S.N. Hrunkov, A.A. Kraynov, High-speed pneumatic spindles with gasdynamic rotor bearings, In the collection: modern technologies in shipbuilding and aviation education, science and production, A collection of reports of the all-Russian scientific-practical conference dedicated to the centenary of the birth of R.E. Alekseeva. (2016) 417–425. (in Russ.)
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