The Influence of Aerodynamic Characteristics of the Elements of the Flow Range of the Radial Two-row Microturbine on its Dynamic Characteristics

Transcription

1 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp The Inflence of Aerodynamic Characteristics of the Elements of the Flow Range of the Radial Two-row Microtrbine on its Dynamic Characteristics Vladimir Leonidovich Khimich, Alexander Borisovich Chvakov, Sergey Nikolaevich Khrnkov, Artem Alexandrovich Kraynov R.Y. Alekseev Nizhny Novgorod State Technical niversity,, l. Minina, Nizhni Novgorod 60950, Rssian Federation. Abstract Within the one-dimensional strip theory of trbomachines, the athors performed the comptational stdies of the effect of flow range parameters of the two-row radial microtrbine with a jet-reactive centrifgal stage and a centripetal speed stage developed at the NST. The main characteristics of the proposed two-row microtrbine were obtained, inclding the dependencies of the inlet and otlet speeds of the microtrbine stages, dependencies of the energy performance of the individal stages and the microtrbine as a whole on the /C 0 characteristic ratio. The qantitative assessment of the inflence of aerodynamic perfection of the individal elements of the microtrbine flow range on its efficiency was obtained. It was revealed that at the speed rate of microtrbine operation, at the vale of the characteristic ratio of circmferential speed to the theoretical gas flow rate C 0, determined by the available heat drop, /C 0 = 0.15 while redcing the speed ratio from 0.9 to 0.8 for all the elements of a flow range, the redction in the efficiency of the microtrbine as a whole will be cased by the inflence of aerodynamic perfection of jet-reactive centrifgal stage by approximately 60%, by the inflence of aerodynamic perfection of intermediate adjstable vane by approximately 0%, and by the inflence of aerodynamic perfection of centripetal speed stage by approximately 10%. Keywords: microtrbine, gas dynamics, nozzle apparats, impeller, actator, pnematic tool INTRODCTION As is well known [1- ], there are serios scientific and technological isses that make it difficlt to se a trbine drive in a manal pnematic tool. The main problem lies in the difficlty of creating the microtrbine, effectively working at a small velocity ratio /C , where is the blade velocity, C 0 is the relative velocity of the flow from the trbine nozzles, calclated by the available heat drop. The se of mlti-stage trbines is the traditional approach to solving this problem for a fll-size trbine drives. For microtrbines, sch a soltion is difficlt becase of the extremely small sizes of their flow range. In the Nizhny Novgorod State Technical niversity n.a. R.E. Alekseev, the grop of researchers fond a soltion to this problem throgh the se of radial stages with doble centripetal and centrifgal impeller in the microtrbine drive of the manal pnematic tool [5-7]. In the microtrbine created (Figre 1), the radial centrifgal jet-reaction trbine with a 100% degree of reactivity is sed as the first stage (JRT pressre stage), and the qasiactive centripetal trbine (I impeller centripetal speed stage), JRT CS microtrbine as a whole, is sed as a second stage. Changing the flow direction from the centrifgal to centripetal one is performed in an intermediate centrifgal centripetal gide vane (IGV). As the microtrbine drive developed in the NNT is based on a patented new type of radial trbine, the theoretical dependence of the effect of the parameters on its flow part on the external characteristics are not described in the scientific literatre. The objectives of this stdy are to obtain basic characteristics of the proposed two-row microtrbine within the onedimensional strip theory of trbomachines [8], namely: - dependencies of the inlet and otlet speeds of the microtrbine stages on the /C 0 characteristic ratio; - dependencies of the specific work of the individal stages and the microtrbine as a whole on the /C 0 characteristic ratio; - dependencies of the energy performance of the individal stages and the microtrbine as a whole on the /C 0 characteristic ratio; - the inflence of the aerodynamic perfection of the individal elements of the microtrbine flow range on its efficiency

2 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp R the gas constant of the working flid, for air R=97 J/(kg K); T 1 the working flid temperatre at the inlet to the stage, in the calclation we take T 1 = 9 K; p 1 the static pressre at the inlet to the stage, in the calclation we take p 1 = 10 kpa; p the fll pressre at the otlet from the stage, in the calclation we take p = 60 kpa. The actal velocity of the working flid flow relative to the gas passage, on the one hand, will be increased by the effect of centrifgal forces, and on the other hand, redced throgh speed loss in the working channels. nder the assmption that the working flid entry speed in the stage working channels is zero, the relative velocity of the working flid flow at the otlet from the stage W may be defined as follows: W SА h0. The projection of the absolte speed of the working flid flow from the channel C, to the direction of the circmferential velocity (Figre ) is defined as the difference between the projection of the relative flow speed W and the circmferential stage speed at the otlet of the channel: С W cos h cos SА 0. Figre 1: Trbine drive. 1 trbine wheel; intermediate centrifgal centripetal gide vane; jet-reactive centrifgal stage; centripetal stage; 5, 6 covering wheels of centrifgal and centripetal stages, respectively; 7 highpressre chamber; 8 atmospheric pressre chamber; 9 air feed; 10 sealing plg; 11 trbine wheel shaft. ANALYSIS OF THE JET-REACTIVE CENTRIFGAL PRESSRE STAGE Consider the otlet velocity diagram of the jet-reactive centrifgal stage, Figre. The relative working flid flow rate C 0, calclated from the available heat drop h 0, will be: C 0 h. 0 The available heat drop h 0, defined as the difference between the enthalpies of the working flid at the inlet in the jetreactive microtrbine stage i 1 and at the otlet from the stage i, may be defined sing the working flid parameters: k p1 h 0 i1 i R T1 1 k 1 p where k1 k k the working flid adiabatic index, for air k = 1.;, From the examination of the otlet velocity diagram of the jetreactive centrifgal stage of microtrbine, the absolte velocity of the working flid will be: С W W cos. The reslts of the calclations of the otlet velocity diagram of the jet-reactive centrifgal stage of two-row microtrbine for the speed factor φ SA= 0.87, and the nozzle-stream angle δ = 1 are presented in Figre. Figre : Otlet velocities of the jet-reactive centrifgal stage 1150

3 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp φ SA= 0.87; δ = 1 Figre : Otlet velocities of the jet-reactive centrifgal stage, m/s The circmferential performance factor of the jet-reactive centrifgal stage of a microtrbine is defined by the losses of kinetic energy with the efflent and the energy losses in the working channels cased by irreversible components of the occrring processes (friction, sdden expansion, vortex activity, and other types of losses). The circmferential performance factor can be calclated by the ratio of the specific work on the circmference and the available work: l l0. According to Eler's eqation of the one-dimensional strip theory of centrifgal machines, the specific circmferential work is defined as the prodct of the impeller circmferential speed and the projection on its direction of the absolte otlet speed of the working flid C : l C. Given that the relative velocity of the working flid at the otlet of the impeller W can be defined based on the velocity ratio φ SA throgh the available heat drop h 0 and the nominal speed C 0: l C W cos SА h0 cos SА C0 cos. Then, considering that the available work can be defined throgh the enthalpy drop by conventional speed C 0, the circmferential performance factor may be calclated as follows: l SА C0 cos 1 cos SА l0 C0 C0 C0 The reslts of the calclations of the circmferential performance factor of the jet-reactive pressre stage of the centrifgal centripetal microtrbine with the nozzle-stream angle δ = 0 are presented in Figre. C 0 Figre : The efficiency factor of the jet-reactive centrifgal stage 1150

4 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp ANALYSIS OF THE CENTRIPETAL VELOCITY STAGE Based on the calclation of the jet-reactive centrifgal stage, we know the vale of the absolte velocity C at the inlet to the intermediate gide apparats that acts as a nozzle nit for centripetal stage. The velocity at the inlet to the centripetal velocity stage impeller (Figre 5) may be defined by the velocity of the working flid flow from the first stage: С. IGV С The direction of the absolte working flid velocity C is defined by the geometry of the intermediate gide vane. The angle of the flow entry to the impeller θ is shown in Figre 5. With regard to the relative flow velocity of the working flid at the inlet to the impeller channel W, its direction and vale depend on the impeller rotational speed, and ths the ratio of the circmferential speed and the absolte flow velocity, Figre 6 a, b, c. It is clear that with the increase of the impeller rotating velocity, and, as a reslt, with the increase of circmferential velocity, the relative velocity W will decrease in magnitde and its direction will be closer to the radial one. At a certain impeller rotating velocity, the direction of the relative velocity W will take radial position, and with a frther increase of the impeller velocity it will deflect in the direction opposite to the circmferential velocity. Figre 5: Inlet and otlet velocities at the centripetal stage To determine the relative speed W, let s consider the inlet velocity diagram, Figre 5. The following relationship will be valid for it: W cos W С. sin This ratio allows creating a qadratic eqation for the desired speed W : W sin W C 0. By rejecting the qadratic eqation "srpls" radical, we get the eqation for determining the relative velocity W : W sin C 1 sin. The direction of the relative velocity of inlet to the centripetal stage can be fond by considering the velocity diagrams, Figre 7: C sin a tan. C cos The relative movement of the working flid in the channels of the impeller centripetal stage is de to srpls kinetic energy obtained in the jet-reactive stage. Local losses and losses de to friction may be considered by the velocity ratio φ IMP. However, when calclating the velocity W, it shold be borne in mind that the movement is performed against the centrifgal forces. Then, based on the well-known theorem of mechanics on the maintenance of the nchanged vale of the sm of potential energy, the work of srface forces, and the difference between the kinetic energy in the relative and figrative motion for the projections of velocities W and W to the radial direction (Figre 8), taking into accont the absence of the enthalpy change, it can be written as follows: W r IMP W r. sing the last formla, the velocity vale W may be expressed. W W cos IMP. cos To calclate the relative otlet flow velocity it is necessary to specify its direction. In order to ensre a minimm degree of reactivity the otlet direction can be taken as coinciding with the largest inlet direction:. It is obvios that the more is the impeller rotational velocity the more will be the proportion of the flow kinetic energy to 1150

5 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp be expended to overcome the centrifgal forces of inertia, and the otlet velocity W will decrease ntil it reaches zero. The condition for the onset of this phenomenon is the following formla: W cos. Ths, the circmferential speed corresponding to the described operating mode of centripetal stage depends on the following variables: f SА, IGV, h0, circ. Figre 8: Otlet velocity diagrams of centripetal stage in different modes of operation Figre 7: The inlet velocity diagrams of centripetal stage in different modes of operation As for the absolte otlet flow rate, from the consideration of the otlet velocity diagram (Figre 8) it can be written as follows: W cos W С. sin The latter formla allows creating an expression to determine the absolte velocity at the otlet of the centripetal stage: C sin. W W The otlet circmferential velocity can be determined sing the following expression: r r R, where ω the anglar rotational velocity of the stage impeller, 1/s; 11505

6 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp R the radis of the impeller at the flow inlet; in calclations we take R = 0.0 m; r the radis of the impeller at the flow otlet; in calclations we take r = 0.05m. The direction of the working flid otlet from the impeller of centripetal stage will be also defined from the inlet velocity diagram: W a cos cos. C The analysis of the expressions shows that at low speeds and hence at small vales of peripheral velocities, the projection of the working flid absolte velocity at the otlet of the centripetal stage to tangent line has the direction opposite to circmferential velocity. As the impeller rotational velocity increases, the direction of the absolte otlet velocity is getting closer to the radial one. The condition of the change of the projection direction of the working flid absolte velocity at the otlet of the impeller to the tangent line can be determined by considering the otlet velocity diagram (Figre 8): C cos. W The specific circmferential work obtained at the impeller centripetal stage can be determined from the known Eler eqation: l C C C cos C sin. The circmferential efficiency factor of the velocity centripetal stage may be determined by the following formla:. С l 0 The reslts of the calclation of centripetal velocity stage, based on the reslts of the calclations of centrifgal jetreactive stage of a microtrbine, are set forth in Figres 9, 10, 11. Φ SA= 0.87; δ =1; φ IGV = 0.8; θ = 6. Figre 9: Inlet velocities of centripetal stage, m/s φ SA= 0.87; δ = 1; φ IGV = 0.8; θ = 6; φ IMP = 0.9. Figre 10: Otlet velocities of centripetal stage, m/s 11506

7 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp φ SA= 0.87; δ = 1; φ IGV = 0.8; θ = 6; φ IMP = 0.9. Figre 11: The efficiency factor of centripetal velocity stage Design Characteristics of Two-row Microtrbine Integral characteristics of two-row microtrbine with jetreactive pressre stage and centripetal velocity stage is obtained by smming the individal stage performance based on accepted vales R = 0.0 m; r = 0.05 m; φ SA= 0.87; δ = 1; φ IGV = 0.8; θ = 6; φ IMP = 0.9. The reslts are presented in Figre 1. Figre 1: Efficiency factor of two-row microtrbine with jet-reactive centrifgal pressre stage and centripetal velocity stage 11507

8 International Jornal of Applied Engineering Research ISSN Volme 11, Nmber (016) pp DISCSSION OF THE RESLTS To qantify the inflence of aerodynamic perfection of the individal elements of a flowing passage of two-row microtrbine on its efficiency we se the proportionality factor A [8-1]. This factor shows the change in the percentage of the efficiency factor of the whole microtrbine per variation of 1% of the velocity factor of one of the elements of a flowing passage: Аi i i, where Ai and i the proportionality factor and velocity factor of the jet-reactive centrifgal stage A SA and SA, of the intermediate gide vane A IGV and IGV and the centripetal velocity stage A IMP and IMP, respectively. Let s make sch a comparison with the se of sch factor of one-stage radial centrifgal trbine with the 100% reactivity degree of the Segner wheel A SW, Figre 1. Figre 1: Inflence of elements of a flowing passage on the efficiency of two-row microtrbine compared to the Segner wheel The analysis of the graphs presented in Figre 1 shows that the effect of aerodynamic perfection of the jet-reactive centrifgal pressre stage of the two-row microtrbine on its effectiveness is significantly greater than for the Segner wheel. Within the adopted one-dimensional strip theory of trbomachines, the inflence of the individal elements of a flowing passage of two-row microtrbine on its efficiency was revealed. The aerodynamic perfection of jet-reactive centrifgal stage has the greatest inflence on the efficiency of the two-row microtrbine. The aerodynamic perfection of intermediate gide vane has half the effect on performance than the perfection of the first stage. The inflence of aerodynamic perfection of the second stage on the microtrbine efficiency is the smallest one. The qantitative assessment of the inflence of aerodynamic perfection of the individal elements of the microtrbine flow range on its efficiency was obtained. Ths, a decline of 1% of the velocity factor characterizing the aerodynamic efficiency of the elements of a flowing passage, in the microtrbine operation mode at a vale of the characteristic ration /C 0 = 0.15, leads to a decrease in efficiency as a whole by.%, inclding throgh the first stage by 1.8%, de to the intermediate gide vanes by 0.69%, de to the second stage by 0.%. ACKNOWLEDGEMENTS The research, the interim reslts of which are otlined in this article, is being held in Nizhny Novgorod State Technical niversity n.a. R.E. Alekseev, with the financial spport of the Ministry of Edcation and Science of the Rssian Federation within the framework of the Agreement No with the Federal State Bdgetary Edcational Instittion of Higher Edcation "Nizhny Novgorod State Technical niversity n.a. R.E. Alekseev" (niqe project identifier RFMEFI5771X010). Sbject of the Applied research: "Development of high-performance range of grinding machines with an innovative type of microtrbines for the shipbilding, aviation and other branches of engineering"; the indstrial partner of the project: LLC "Mobile GazService". REFERENCES [1] Cho, C.-H., Cho, T.-H., & Cho, S.-Y. Performance Characteristics of a Small-Scale Axial-Type Trbine Operated in a Low Partial Admission Rate, International Jornal of Trbo and Jet Engines, (), pp. 11-1,

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