﻿ 特斯拉涡轮技术研究进展综述
 舰船科学技术  2020, Vol. 42 Issue (2): 12-19 PDF

1. 武汉理工大学能源与动力工程学院，湖北 武汉 430063;
2. 武汉理工大学 船舶动力工程技术交通行业重点实验室，湖北 武汉 430063;
3. 武汉理工大学 国家水运安全工程技术研究中心可靠性工程研究所，湖北 武汉 430063

Review on research progress of tesla turbine basic theories and technology
PENG Di1, YUAN Cheng-qing1,2,3, SUN Yu-wei1,2,3
1. School of Energy and Power Engineering, Wuhan University of Technology, Wuhan 430063, China;
2. Key Laboratory of Marine Power Engineering and Technology (Ministry of Transport), Wuhan University of Technology, Wuhan 430063, China;
3. Reliability Engineering Institute, National Engineering Research Center for Water Transport Safety (WTS Center), Wuhan University of Technology, Wuhan 430063, China
Abstract: As a kind of dynamic mechanical structure which utilizes fluid to impact impeller rotation, turbine has been widely used in power generation, aviation, navigation and other fields. The traditional turbine has the problems of complex structure, leakage between power devices and so on, which makes Tesla turbine simple in structure, relatively low manufacturing tolerance requirements and sealing performance. These features can be highlighted and returned to the view of researchers, but the Tesla turbine is still unable to be put into production due to its relatively low energy conversion efficiency.
Key words: tesla turbines     boundary layer effect     engine     efficiency ratio
0 引　言

1 特斯拉涡轮机的应用领域

2 特斯拉涡轮机的研究方法 2.1 特斯拉涡轮机数学建模方法

1）数学模型

Deam等[13]开发了一种简单的特斯拉涡轮机的分析模型，用来考虑不可压缩性和一维流动问题。

 $\begin{array}{*{20}{c}} {{\rm{F}} = {\rm{A\chi }}{P_{res}}f\left( \theta \right)}\text{，}\\ {{\eta _{1D}} = \sqrt {\left( {1 - \chi f\left( \theta \right)} \right)} {\rm{\chi }}f\left( \theta \right)\theta }\text{。} \end{array}$
 \begin{aligned} & {\text{求导后}},{\text{得}}\\ & \frac{\partial {{\eta }_{1D}}}{\partial \chi }={{f\left( 1-\chi f \right)}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}\theta -\frac{1}{2}{f^{2}}\chi {{\left( 1-\chi f\right)}^{{}^{-1}\!\!\diagup\!\!{}_{2}\;}}\theta \text{。} \end{aligned}

 图 1 低质量流率条件下的计算结果[14] Fig. 1 Results of calculation under the condition of low mass flow rate[14]

2）计算方法

Couto等[16]提出了一项简单的计算程序，用于估计特斯拉涡轮机内部所需的圆盘数量，以达到确认最佳圆盘数量的要求。该计算是基于旋转圆盘上旋转流体的边界层厚度进行的估算，计算结果为层流边界层厚度δ，但是该程序在计算过程中使用了绝对切向速度来确认相对旋转参考系的边界层厚度，会造成较大的偏差。此外，该计算也没有进行实验或数值验证。

 ${\rm{\delta }} \approx 5\sqrt {\frac{{v \cdot \left( {{r_1} - {r_2}} \right)}}{U}} \text{。}$

Guha等[17]提出了一种系统的计算流体动力学研究设计方法，以满足实际的约束条件，并提供了计算功率和效率最高值的方法。通过追踪动态相似数、入口切向速度和入口进气角三个无量纲参数，确认了与传统涡轮机中的流体摩擦只会产生负面作用不同，特斯拉涡轮机中的流体摩擦虽然增加了径向压降但是同时提高了发电效率。通过对这一双重作用进行全面的分析和量化，可以得到两者之间的平衡动态相似数的最优值和入口切向速度比，实现效率最大化。

2.2 特斯拉涡轮机几何建模仿真方法

 图 2 γ≥1时的相对流动路径[29] Fig. 2 Relative flow paths when γ≥1[29]

 图 3 γ>10时的相对流动路径[29] Fig. 3 Relative flow paths of γ>10[29]

 图 4 γ<1时的相对流动路径[29] Fig. 4 Relative flow paths of γ<1[29]

 图 5 输出功率随体积分数的变化结果[31] Fig. 5 Variation of output power with volume fraction[31]
2.3 特斯拉涡轮机运行效率分析方法

1）截断级数代换法[22]，即通过开发一种扰动流解和迭代方案的程序，提高雷诺数的解决方案。程序的运行结果取决于雷诺数和质量流率这2个参数,其得到的结果通常是渐近解。为得到进一步准确结果，需要补充圆盘外径、切向速度等其他参数。使用截断级数代换法的问题通常只需要少量参数就能解决，但同时也造成精确度不高的后果；

2）批量参数分析法[2324]，即针对转子内流动过程和多盘泵的极限性能和效率的一种“先近似”分析法。在无量纲参数的基础上，给出了大量的几何和流量参数，通过数值计算得到方程的解。但由于摩擦因素概念的缺失，批量参数分析法在绝大多数情况下用处不大[25]

3 特斯拉涡轮机的关键问题 3.1 特斯拉涡轮机的层流边界层稳定性问题

 $\Delta = \frac{{{v_r} \cdot {b^2}}}{{v \cdot r}}\text{。}$

3.2 特斯拉涡轮机的整机运行效率问题

Rice[23]对特斯拉涡轮机进行了进一步的实验和分析，通过用9个圆盘组成了一个转子，其外半径为88.9 mm，圆盘间隙间距为1.59 mm，圆盘之间的各个间隙通过单个喷嘴单独供应空气，空气进入温度约为37.8 ℃，该喷嘴指向与圆盘的切向方向成15°的角度，从该涡轮机的测试中得到了如表2所示的一组数据。

 图 6 优化参数后涡轮机的代表性性能数据[23] Fig. 6 Representative performance data of turbine after optimization parameters[23]

 图 7 优化参数前实验效率预测对比[49] Fig. 7 Prediction of experimental efficiency before optimization of parameters[49]

 图 8 优化参数后实验效率预测对比[49] Fig. 8 Prediction of experimental efficiency after optimization of parameters[49]

Guha[40]通过对特斯拉涡轮机效率损失主要来源的系统研究，发现喷嘴和进口的性能是特斯拉涡轮机整体效率的一个限制因素（损失约占13% ~ 34%），为了优化特斯拉涡轮机的进气性能，设计并测试了一种利用增压室完成进气的新型喷嘴（见图9），实验测定的喷嘴和入口压力损失小于1%。该设计仅需要对套管进行微小改变，就能实现将增压室和喷嘴集成到特斯拉涡轮机上，并可以通过将喷嘴设计成其他几何形状，以研究流体喷射到转子中的方式整体机器效率的影响，为研究转子效率提供了可行方案。

 图 9 利用气室完成进气的新型喷嘴[40] Fig. 9 A new type of nozzle that uses the air chamber to complete the air intake[40]
4 结　语

1）特斯拉涡轮的工质为纳米流体时，只有当流量参数的选择合适时，才能够保证在实现最高效率值的同时，提供足够高的输出功率，因此流量参数的优化设计有待开展。

2）特斯拉涡轮机的喷嘴实现增压并保障流体均匀平稳喷出，将进一步提升机体运行效率。

3）特斯拉涡轮机的圆盘之间的流体稳定性分析还没有彻底完成，计算的精度不高，需要完成进一步的定量分析。

4）特斯拉涡轮机的进口处产生的湍流会严重影响机体运行的平稳性，需要对涡轮机进口进行优化设计以降低湍流出现的频率。

 [1] KAUFUI V WONG, OMAR De Leon. Applications of nanofluids: current and future[J]. Advances in Mechanical Engineering, 2010, 2010(2): 519659-519670. [2] AGRAWAL S K, Gardner G, Pledgie S. Design and fabrication of an active gravity balanced planar mechanism using auxiliary parallelograms[J]. Journal of Mechanical Design, 2001, 123(4): 525-528. DOI:10.1115/1.1413771 [3] STEIDEL R, WEISS H. Performance test of a bladeless turbine for geothermal applications: UCID-17068[R]. Lawrence Livermore Laboratory, 1974. [4] ALOIS P, ROLF V, VOLKER M K. Performance analysis of a miniature turbine generator for intracorporeal energy harvesting[J]. ASME, 2014, 136(8): 81101-81110. [5] LAMPART P, KOSOWSKI K, PIWOWARSKI M, et al. Design analysis of tesla micro-turbine operating on a low-boiling medium[J]. Polish Maritime Research, 2009, 16(Special): 28-33. [6] CAREY V P. Assessment of Tesla turbine performance for small scale solar rankine combined heat and power systems[J]. Journal of Engineering for Gas turbines and Power, 2010, 132(12): 122301-122309. DOI:10.1115/1.4001356 [7] CHOON T W, RAHMAN A A, JER F S, et al. Optimization of Tesla turbine using computational fluid dynamics approach, 12442761[R]. Langkawi: Industrial Electronics and Applications (ISIEA), IEEE Symposium, 2011. [8] HASAN, ALI M. Investigating the possibility of using a tesla turbine as a drive unit for an automotive air-conditioning compressor using CFD modeling[J]. ASHRAE Transactions, 2016, 122(1): 146-158. [9] SONG Jian, GU Chun-wei, LI Xue-song. Performance estimation of Tesla turbine applied in small scale organic rankine cycle (ORC) system[J]. Applied Thermal Engineering, 2017, 110(1): 318-326. [10] DAMODHAR R, MRUTHYUNJAYA K N, NAVEEN, et al. Design and fabrication of portable water turbine[J]. International Research Journal of Engineering and Technology, 2017, 4(6): 56-72. [11] MURATA S, YUKATA M, YOSHIYUKI. A study on a disk friction pump[N], Bulletin of the Japanese Society of Mechanical Engineers, 1976-02-25(354). [12] HARWOOD P. Further investigation into Tesla turbomachinery[R]. Senior Project Report, Mechanical Engineering Department, University of Newcastle, United Kingdom, 2008. [13] DEAM R T, LEMMA E, MACE B, et al. On scaling down turbines to millimeter size[J]. Journal of Engineering for Gas Turbines & Power, 2008, 130(5): 819-825. [14] TALLURI L, FIASCHI D, NERI G, at el. Design and optimization of a Tesla turbine for ORC applications[J]. Applied Energy, 2018, 226: 300-319. DOI:10.1016/j.apenergy.2018.05.057 [15] HOYA G P, GUHA A. The design of a test rig and study of the performance and efficiency of a Tesla disc turbine[J]. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2009, 223(4): 451-465. DOI:10.1243/09576509JPE664 [16] COUTO H S, DUARTE J B F, BASTOS-NETTO D. The Tesla turbine revisited[R]. Sochi: 8thAsia-Pacific International Symposium on Combustion and Energy Utilization, 2006. [17] GUHA A, SENGUPTA S. A non-dimensional study of the flow through co-rotating discs and performance optimization of a Tesla disc turbine[J]. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2017, 231(8): 721-738. DOI:10.1177/0957650917715148 [18] ENGIN T, ÖZDEMIR M, ÇEMECI S. Design, testing and two-dimensional flow modeling of a multiple-disk fan[J]. Experimental Thermal & Fluid Science, 2009, 33(8): 1180-1187. [19] SENGUPTA S, GUHA A. Analytical and computational solutions for three-dimensional flow-field and relative pathlines for the rotating flow in a Tesla disc turbine[J]. Computers & Fluids, 2013, 88(11): 344-353. [20] NECKEL A L, GODINHO M. Influence of geometry on the efficiency of convergent-divergent nozzles applied to Tesla turbines[J]. Experimental Thermal & Fluid Science, 2015, 62(62): 131-140. [21] SENGUPTA S, GUHA A. Flow of a nanofluid in the microspacing within co-rotating discs of a Tesla turbine[J]. Applied Mathematical Modelling, 2016, 40(1): 285-499. [22] MATSCH L, RICE W. An asymptotic solution for laminar flow of an incompressible fluid between rotating disks[J]. Journal of Applied Mechanics, 1968, 35(2): 155-159. [23] RICE W. An analytical and experimental investigation of multiple-disk turbines[J]. Journal of Engineering for Gas Turbines & Powe, 2014, 87(1): 29-36. [24] SCHROEDER H B. An investigation of viscosity force in air by means of a viscosity turbine[R]. BAE Thesis, Rensselaer Polytechnic Institute, 1950. [25] RICE W. Tesla turbomachinery[M]. Handbook of Turbomachinery, 2003: 861-874 [26] GREGORY N, STUART J T, WALKER W S. On the stability of three dimensional boundary layers with application to the flow due to a rotating disk[J]. Philosophical Transactions of the Royal Society B Biological Sciences, 1955, 248(943): 155-199. DOI:10.1098/rsta.1955.0013 [27] FALLER A J, KAYLOR R E. Numerical study of the instability of the laminar ekman boundary layer[J]. Journal of the Atmospheric Sciences, 1966, 23(4): 466-480. [28] SAVAS Ö. On flow visualization using reflective flakes[J]. Journal of Fluid Mechanics, 1985, 152(152): 235-248. [29] SAVAS Ö. Stability of bödewadt flow[J]. Journal of Fluid Mechanics, 1987, 183(183): 77-94. [30] PIKHTOV S V, Smirnov E M. Boundary layer stability on a rotating disk with corotation of the surrounding fluid[J]. Fluid Dynamics, 1992, 27(5): 657-663. [31] SCHOUVEILER L, GAL P L, CHAUVE M P. Stability of a traveling roll system in a rotating disk flow[J]. Physics of Fluids, 1998, 10(11): 2695-2697. DOI:10.1063/1.869793 [32] SERRE E, CRESPO DAE, BONTOUX P. Annular and spiral patterns in flows between rotating and stationary discs[J]. Journal of Fluid Mechanics, 2001, 434(434): 65-100. [33] SANK′OV P I, SMIRNOV E M. Bifurcation and transition to turbulence in the gap between rotating and stationary parallel disks[J]. Fluid Dynamics, 1984, 19(5): 695-703. [34] GAUTHIER G. GONDRET P, MOISY F, et al. Instabilities in the flow between co- and counter-rotating disks[J]. Journal of Fluid Mechanics, 2002, 473(473): 1-21. [35] WU P S. Evaluation of analytical models for multiple-disk pump rotor calculations[D]. M.S. Thesis, Department of Mechanical and Aerospace Engineering, Arizona State University, 1986. [36] NENDL D. Dreidimensionale laminare instabilitäten bei ebenen wänden[J]. Z. Angew. Math. Mech, 1973, 56(56): 211-213. [37] NENDL D. Reibungsturbine[J]. VDI-Berichte, 1973, 193(193): 287-293. [38] KRISHNAN V G, IQBAL Z, MAHARBIZ M M. A micro Tesla turbine for power generation from low pressure heads and evaporation driven flows[C]. China: The 16th International Conference on Solid-State Sensors, Actuators and Microsystems, 2011: 1851-1854. [39] SONG Jian, REN Xiao-dong, LI Xuesong, et al. One-Dimensional model analysis and performance assessment of Tesla turbine[J]. Applied Thermal Engineering, 2018, 134: 546-554. DOI:10.1016/j.applthermaleng.2018.02.019 [40] GUHA A, SMILEY B. Experiment and analysis for an improved design of the inlet and nozzle in Tesla disc turbines[J]. Proceedings of the Institution of Mechanical Engineers Part A Journal of Power & Energy, 2010, 224(2): 261-277.