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Comparison of Inviscid and Viscous Transonic Flow Field in VKI Gas Alexandria Engineering Journal (2014) xxx, xxx–xxx Alexandria University Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com ORIGINAL ARTICLE Comparison of inviscid and viscous transonic flow field in VKI gas turbine blade cascade S.A. Moshizi *, A. Madadi, M.J. Kermani Department of Mechanical Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran Received 8 August 2013; revised 3 March 2014; accepted 12 March 2014 KEYWORDS Abstract In this paper, the viscous and inviscid flow fields of a gas turbine blade cascade are inves- Gas turbine cascade; tigated. A two-dimensional CFD solver is developed to simulate the flow field through VKI blade Viscous flow; cascade. A high resolution flux difference splitting scheme of Roe is applied to discretize the con- Inviscid flow; vective part of Navier–Stokes equations. Baldwin Lomax (BL) model is used to account for turbu- Turbulent flow; lent effects on the viscous flow field of the blade cascade. For validation of the code, the flow field Roe scheme; was solved by Ansys Fluent commercial software. The flow solution was done by third order flux Shock creation difference splitting scheme of Roe and k–x turbulence model. The findings show that the high tur- bulent and the shock creation in the flow field, lead to the same results in viscous and inviscid flows. Also, the results show that the grid and solver’s focus must be on the precise prediction of the shock effects, when the shock is occurred in the domain. ª 2014 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. 1. Introduction refine their accuracy in predicting flow phenomenon in turb- omachines. Although the results from such tests are not as pre- Gas and steam turbines are widely used to generate power in cise as the data obtained from the tests conducted on the the power generation industries, because they are capable of operating turbomachine, cascade test provides a blade designer producing power in hundred of megawatts. The aerodynamic a more economical alternative to determine the aerodynamic performance is a major factor for the turbine efficiency. efficiency of the blades under various operating conditions. Cascade tests have been implemented during the years to find In addition, these programs are able to predict losses reason- out aerodynamic losses in turbomachines. The cascade results ably well for subsonic flows. However, in transonic flow, are used to validate flow computation programs and to further shock-boundary layer interaction is evident and the structure of this interaction is complex and difficult to predict. Until significant progress is achieved in refining the available flow * Corresponding author. Tel.: +98 9363761760. E-mail address: [email protected] (S.A. Moshizi). computation programs in the industries, cascade test is still Peer review under responsibility of Faculty of Engineering, Alexandria an effective method to determine aerodynamic losses of turb- University. omachines [1]. Based on the importance of cascade investigation, many researchers have been studied turbomachine cascades experi- mentally and numerically. Arts et al. [2] experimentally Production and hosting by Elsevier investigated the aerodynamic and thermal performance of 1110-0168 ª 2014 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. http://dx.doi.org/10.1016/j.aej.2014.03.007 Please cite this article in press as: S.A. Moshizi et al., Comparison of inviscid and viscous transonic flow field in VKI gas turbine blade cascade, Alexandria Eng. J. (2014), http://dx.doi.org/10.1016/j.aej.2014.03.007 2 S.A. Moshizi et al. Nomenclature Cp pressure coefficient n stream wise generalized direction c blade chord l viscosity P static pressure Re Reynolds number Subscripts S blade pitch 0 stagnation condition us friction velocity 1 parameter at blade inlet u+ non-dimensional velocity 2 parameter at blade outlet y+ non-dimensional normal distance ti internal layer # kinematic viscosity to external layer j von Karman constant x derivative relative to x a angle of attack y derivative relative to y b outlet flow angle tur turbulent g normal generalized direction 1 free stream VKI (von Karman Institute) gas turbine blade cascade. They on the shock-boundary layer interaction in a high turning tran- studied the various flow conditions, and discussed the effects sonic cascade with the help of schlieren flow visualization. of Mach number, Reynolds number and flow turbulence inten- McBean et al. [16] used a parallel multiblock Navier–Stokes sity on the aerodynamic and thermodynamic performance of with k–x turbulence model to solve the unsteady flow through the blade. Dennis et al. [3] investigated the optimal design of an annular turbine cascade, the transonic Standards Test Case a two-dimensional blade cascade. They studied the VKI blade 4, Test 628. After determining the unsteady surface pressure cascade compressible flow field using Navier–Stokes solver and the aerodynamic damping, they compared them with the with unstructured grid and k–e turbulent model. Also, per- two- and three-dimensional inviscid, viscous simulations and forming a supersonic through-flow fan (STF) blade cascade, experimental data. The results showed that the three-dimen- Chesnakas and Ng [4] showed that the leading edge radius is sionality of the cascade model and the presence of a boundary a major source of losses in STF blades. Their results reported layer separation cause differences between stability predictions that losses from the leading-edge bluntness are convected by the two- and three-dimensional computations. downstream into the blade wake and are difficult to distinguish Although a number of studies have been investigated flow from viscous losses. Shock losses account for 70–80% of the field in the different blade cascades in inviscid and viscous losses in the STF cascade. flows, none of these has dealt with numerical losses due to In 1905, Ludwig Prandtl [5] assumed that for the fluids with boundary layer and shock formation. In the present work, small viscosities except near the solid surface, where the flow the inviscid and viscous flow field through gas turbine blade must satisfy the no-slip conditions, in all other areas of the cascade is analyzed with accurate computational fluid dynam- flow field, the viscous forces can be ignored. Hence, in fluid ics (CFD) calculations by means of Ansys Fluent software [17] flows near the body surfaces, a thin layer, called ‘‘Boundary and an in-house developed code. The outlet parameters of Layer’’ would appear in which the viscosity effects are signifi- blade cascade are computed and studied for losses existence cant [6]. There is an extensive literature on the boundary layer due to shock waves and boundary layer. flow, but we only refer to few recent studies [7–11]. Boundary layers in turbines are usually thin and an increase in Reynolds 2. Governing equations number of the flow leads to the layer get thinner. Since, at the inlet stage of a turbine the boundary layer is laminar; the fric- Full conservative Navier–Stokes equations for the viscous fluid tion loss from viscous interaction with the blade surface is low. and two-dimensional unsteady compressible flow considering The creation of boundary layer in turbomachines decreases its no body force are used to simulate the flow filed between efficiency. Singhal and Spalding [12] presented a finite different blades [18] as follows scheme for calculating the steady two-dimensional flows in tur- @Q @F @G @F @G þ þ ¼ v þ v ð1Þ bine blade cascade issues. @t @x @y @x @y Recent investigations in the inviscid–viscous interaction as where Q is the conservative vector, also F and G are the invis- well as more complex Navier–Stokes codes are very encourag- cid flux vectors. F and G are viscous flux vectors. ing, but still the transonic flow fields with strong imbedded 2 3 2v v3 2 3 q qu qv shock waves and boundary layer separations create tremen- 6 7 6 7 6 7 6 qu 7 6 qu2 þ P 7 6 quv 7 dous difficulties. Giles [13] showed that the strong shocks in Q ¼ 6 7; F ¼ 6 7; G ¼ 6 7; 4 5 4 5 4 2 5 a single-stage turbine produced 40% variation in the rotor qv quv qv þ P qet quht qvht blade lift. Paniagua et al. [14] investigated a detailed physical 2 3 2 3 ð2Þ analysis of the stator–rotor interaction in a transonic turbine 0 0 6 7 6 7 6 s 7 6 s 7 stage at three pressure ratios. They studied the behavior of 6 xx 7 6 xy 7 Fv ¼ 4 5; Gv ¼ 4 5 shock-boundary layer interaction in the stator–rotor system. sxy syy Graham and Kost [15] performed steady flow investigations usxx þ vsxy À qx usxy þ vsyy À qy Please cite this article in press as: S.A. Moshizi et al., Comparison of inviscid and viscous transonic flow field in VKI gas turbine blade cascade, Alexandria Eng. J. (2014), http://dx.doi.org/10.1016/j.aej.2014.03.007 Comparison of inviscid and viscous transonic flow field in VKI gas turbine blade cascadearison of inviscid and viscous transonic () 2 where sxx, sxy, and syy are stress tensor components and qx and CWKymaxudif Fwake ¼ min y F ; ð12Þ qy are conductive heat transfer in x- and y-directions, respec- max max Fmax tively. By using the chain derivative rule, Eq. (1) is transported from the physical space (x, y) to the computational space (n, g) and, as follows: udiff ¼ðVtotÞmax ðVtotÞmin ð13Þ @Qà @Fà @Gà @Fà @Gà pffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ þ ¼ v þ v ð3Þ where V ¼ u2 þ v2 is the velocity magnitude.
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