Numerical Simulatin f the Flw Field in a Frictin-Type Turbine (Tesla Turbine) Institute f Thermal Pwerplants Vienna niversity f Technlgy Getreidemarkt 9/313, A-6 Wien Andrés Felipe Rey Ladin Schl f Engineering, Natinal niversity f Clmbia, Calle 7c N. 4-1 Ap. 419, Bgtá, Clmbia, Tel.: ++7/1/317, Email: e32642@student.tuwien.ac.at INTRODCTION In the cntext f research prject at Institute fr Pwerplants at the Vienna niversity f Technlgy in jint study with the Natinal niversity f Clmbia, the flw inside the Tesla turbmachine is investigated. The Tesla turbine, an uncnventinal turbmachinery that uses smth disks instead f blades, is described principally by the lading cefficient curve, the efficiency and degree f reactin vs. the flw rate parameter. In rder t describe its behaviur, the rtatinal speed is maintained cnstant and the flw rate is changed with the purpse f simulate a virtual brake. Since the flw is characterized in a transitinal regime, bth laminar and turbulent cases are simulated. The wrk presented represents an initial significant step twards the analysis f this type f flw using CFD tl. Starting frm a simple axi-symmetric mdel f the flw between tw c-rtating disks in tw dimensins, the mdel is imprved including the utlet f the turbine with the casing, and at the end a 3D simulatin f a single disk is perfrmed including the effects f the nzzles. A cmplete mdel f a Tesla turbine is restricted by cmputer resurces. The simulatins were carried ut in winter and summer semester 23-24. The cmmercial cmputatinal fluid dynamics (CFD) cde FLENT as well as the grid generatin sftware GAMBIT were used fr the investigatin. Bth cdes are available n the CFD-server COMPAQ SC4 (Fluid Dynamics and Finite Element Server) f the Cmputer Center f Vienna niversity f Technlgy. PREVIOS WORK Starting frm the patent f Nikla Tesla [1], (Figure 1), extensive analytical wrk were made in the 6 s, and 7 s. Mst f literature cnsider the flw laminar and incmpressible, but als sme turbulent apprach were made. The flw is characterized by the Reynlds number and the Mach number. It is fund varius regimes f flw and prcess as laminar, turbulent, frward transitin and relaminarizatin frm turbulent t laminar. Figure 1.: American Patent N. 1,61,26 f Tesla turbine [1]. Figure 2.: Schematic diagram f Tesla turbine [2].
GEOMETRY AND MESHING Fllwing the experimental wrk and gemetry used by Rice [2], three mdels with similar gemetry are prpsed and slved. The gemetry is characterized by the rati f radii: r 1 /r 2 =6,6 and the rati f the gap t the uter radius: r 1 /b=2 (these gemetrical parameters are the same in the three mdels); the angle f the nzzle is =2. The flw is simulated fr 2 Reb b 2.9. Figure 3.: Gemetry fr ne gap 2D mdel. Figure 4.: 2D Mdel f the turbine with full peripheral admissin. DESCRIPTION OF THE NMERICAL METHOD Figure.: Mesh fr the 3D slide mdel. Gverning equatins. The Navier Stkes equatins are slved fr steady flw, incmpressible, laminar and turbulent case, and 2D (Axisymmetric Swirl) and 3D apprach. Fluent uses the Finite Vlume Methd and in additin the duble precisin characteristic was used. The fllwing ptins were selected: Segregated and implicit slver, and fr the discretizatin: PRESTO! (Pressure Staggering Optin), SIMPLE (Semi-Implicit Methd fr Pressure-Linked Equatins) fr Pressure-Velcity cupling, Secnd Order pwind was selected fr Mmentum. Fr turbulent slutin the standard k- mdel with near wall treatment is used. The y + < relatin near the wall must be accmplished. Bundary Cnditins. Inlet was specified with a fixed velcity-inlet bundary. Fr the turbulence simulatins was selected a value f % f turbulence intensity. The nndimensinal turbulent kinetic energy is set t k*=.37, and the turbulent dissipatin rate is *=2,693x -4. Outlet cnditin was specified with a pressure-utlet bundary, with a gauge pressure value f. Disks and husing emply n slip cnditin rtating at.. The walls are adiabatic. Cnvergence and cmputed time. The slutin f the first mdel (Figure 3) take 4 minutes t cnverge with 6.8 quadrilateral cells, the secnd mdel (Figure 4) with 237,62 cells tk 3h t reach a suitable slutin and finally the 3D mdel (Figure ) with 2,412, cells cnsume 14 days after, iteratins. RESLTS First Mdel: Flw between disks. Figure 6 shws the velcity prfile at three radial statins, inlet, middle and utlet. The strng acceleratin between t frntier statins is nticed. Figure 7 presents ne characteristic f the radial flw that appears nly in the laminar case: the inflectin
f the prfile in the middle f the radius. Figure 8 depicts the change f pressure (ttal, dynamic and static). As it can be seen, in the radial directin, the ttal pressure in the middle f the gap des nt shw variatin, meaning that the flw in this plane d nt perfrm wrk, but in ther plane, at % f the gap frm the wall, the variatin is mre appreciable. Laminar slutin Figure 6.: Velcity magnitude, laminar slutin. Figure 7.:Inflectin f radial velcity fr different radial statins. Figure 8.: Pressure distributin alng radius, laminar slutin. Characteristic curves f the Tesla turbine are presented in Figure 9 and Figure. 2 Lading Cefficient T m 2 r.4.4.3.3.2 Pshaf t m pttal 1.2.1 Flw Parameter r Flw Parameter r Figure 9.: Characteristic curve, lading cefficient, frm laminar case. Figure.: f an islated disk, laminar, nn-dimensinal slutin. Turbulent slutin Frm turbulent case, the acceleratin f the flw between inlet and utlet is lwer (Figure 11) with a higher trque (Figure 14) and als higher efficiency; Mre energy is extracted with higher turbulence, the drag is higher. The ttal pressure at inlet is higher in cmparisn t the laminar case. Figure 11.: Ttal velcity, turbulent case. Figure 12.:Inflectin f radial velcity fr different radial statins. Figure 13.: Pressure distributin alng radius, turbulent slutin.
Lading Cefficient T m 2 r.9.8.7.6..4 Pshaf t m pttal 2 1.3 Flw Parameter r Flw Parameter r Figure 14.: Lading cefficient fr turbulent slutin, islated disk. Figure 1.: fr turbulent slutin, islated disk. Rtr: This mdel includes the utlet f the turbine, Figure 17 presents the difference f cmputed efficiency f nly the rtr and the rtr with the utlet, with a pipe length f 7 frm the rtr utlet. The lsses due t the utlet are cnsiderable due t change f area and directin. The lw efficiency value is als cmparable t the recently experimental wrk f Schmidt [3]. Lading Cefficient.9.8 2 1 T m 2 r.7.6..4 Rtr Turbina Tesla.3 Flw Parameter r flw parameter vs _rtr flw parameter vs efficiency_7 Flw Parameter r Figure 16.: Lading cefficient fr turbulent slutin, turbine. 3D rtr slide mdel: Figure 17.: fr turbulent slutin, turbine. Figure 18.: Pathlines clred by velcity magnitude. Figure 19.: Cnturs f ttal pressure at the middle f the gap.
Lading Cefficient 3. 2.8 2.6 2 2 2.4 1 2.2 2. 1.8 1.6 Figure 2.: Lading cefficient fr turbulent slutin, turbine. Figure 21.: fr turbulent slutin, turbine. The 3D mdel includes the effects due t the nzzle and the lsses present in this zne are nt very high when lading cefficient and efficiency are cmpared (Figure 2 and Figure 21). Figure 22.: Vectrs f velcity magnitude and ttal pressure cnturs at the middle f the gap. SMMARY The flw in the Tesla turbine was simulated with different gemetrical mdels and laminar and turbulent apprach. Since the flw itself is fund in a transitin regime with multiple prcesses - as transitin, relaminarizatin, recirculatin, between ther phenmena- an exact simulatin that full fills all the physical requirements is quite difficult t achieve with CFD tl. Nevertheless, bth apprximatins are valid and they wuld shw different features, characteristics and behaviur typical fr each case and fr the Tesla turbine. One f these differences is that the inflectin pint fr laminar flw disappears in the turbulent case, fr which the turbulent effects act as a mechanism f balanced in the axial directin. In cntrast, experimental research cannt measured velcities prfiles, nly static pressure as it was reprted by Adams [], due t the fact that the gap between disks is very thin; CFD prvide slutin t this prblem and furthermre t micr turbines. The flw hat als high swirling velcity cmpnents with significant gradients f acceleratin, which makes the slutin mre difficulty and need extra iteratins in rder t
achieve a gd cnvergence slutin. Cnvergence is an imprtant issue in CFD because f the iterative nature f the slutin, and it can give evidence f a well psed mdel indicating sme physical facts. Extended details and results can be fund in the diplma thesis f Rey A.F. [6]. The results shw that multiple disk turbines are wrkable and feasible, in the engineering sense, but they present a lw efficiency in bth laminar and turbulent cases; lwer fr laminar case; the difference between these cases is significant. Mrever, the simulatin f the gap and the results f 3D slide mdel shw that the efficiency was nt as high as it was suggest by experimental reprts in literature that implying the lw efficiency due t the presence f the nzzle. The efficiencies are similar in the three mdels. The machine is feasible fr a lw range f pwer where the efficiency f cnventinal turbmachinery is nt very high and it can handle wrking fluid with particles, cntaminants and high viscsity. Sme cnclusins f each mdel are: 2D tw disks mdel: Fr the laminar slutin, the prfile f the radial velcity cmpnent shws an inflectin at abut the middle radius; The flw presents strng acceleratin especially at the utlet; The gap can be reduced. 2D turbine mdel:the effects f the walls n the verall perfrmance are nt much significant when the efficiency is cmpared with 2D tw disks mdel; The lsses due t the utlet are high, where the flw presents high swirls and change f area and directin; The leading edge and trailing edge f each disk can be imprved. 3D turbine mdel: The high velcity f the flw increases the trque even thugh with the presence f znes f ventilatin; The lsses wed t the nzzles are nt very high; The tangential cmpnent f velcity remains nearly cnstant frm the uter t the inner regin f the rtr, because f the high velcity after the nzzle. Future Wrk Sme f the fllwing tpics wuld be interesting fr further investigatin: 1. Cmpressible analysis f the Tesla turbine; 2. Effects f the number f nzzles n perfrmance f the turbine; 3.Optimizatin f the gemetry, fllwing analytical and the experimental wrk f Rice [2], and recently by Schmidt [3], the analytical wrk f Lawn and Rice [4] is useful fr ptimizatin;.imprvement f the numerical methd in rder t handle transitinal flws as well as evaluatin f ther turbulence mdels t use in the simulatins. LITERATRE 1. Tesla, N.: Turbine nited States Patent N. 6126, May 6, 1913. 2. Rice, W.: An Analytical and Experimental Investigatin f Multiple-Disk Turbines, Jurnal f Engineering fr Pwer, Trans. ASME, series A, Vl. 87, N. 1 Jan. 196, pp. 29-36. 3. Schmidt, D. D.: Bimass Bundary Layer Turbine Pwer System, Califrnia Energy Cmmissin (CEC), EISG PROGRAM [nline] Available frm Internet: <RL: http://eisg.sdsu.edu/fullsums/-6.htm > <RL: http://eisg.sdsu.edu/shrtsums/shrtsum6.htm>, 1991, Califrnia, SA. 4. Lawn, Jr. J., Rice, W.: Calculated Design Data fr the Multiple Disk Turbine using Incmpressible fluid, Jurnal f Fluids Engineering, Trans. ASME, Vl. 96 N. 3, September 1974, pp. 22-28.. Adams, R., Rice, W.: Experimental Investigatin f the Flw Between Crtating Disks, Jurnal f Applied Mechanics, Vl. 37, Trans. ASME, Vl. 92 series E, N. 3, September 197, pp. 844-849. 6. Rey A. F.: Numerical Simulatin f the Flw Field in a Frictin-Type Turbine (Tesla Turbine) Diplma thesis at the Institute f Thermal Pwerplants, TWien, Viena, Austria, July 24.