Most designers associate drilled nozzles in turbomachinery with something exotic, uncharted, and specific only to a minuscule amount of high-loaded turbines operating with a high-pressure drop. Meanwhile, many engineers are not aware that this nozzle design has been applied since the very first turbomachines.
Karl Gustaf Patrik de Laval patented a turbine with asymmetric convergent-divergent nozzles in 1888. At that time the shape of the nozzle allowed him to reach more effective kinetic energy transformation and have an entirely new level of turbine performance.
Over a hundred years later, drilled nozzles (or asymmetric nozzles, Laval’s nozzles) have been extensively used in rocket engines, flying vehicles, driving turbines, ORC turbines, and other units for which low cost and weight-dimension constraints play an important role.
Despite the wide application range of turbines with these nozzles, each has its own specific features.
Drilled Nozzles
The main characteristics of drilled nozzles in a turbine (Fig. 2) are the partial admission input, high heat drop per first stage, low reaction, and a low number of stages.
For these turbines, the most critical point during the design process is the first nozzle design. The first supersonic nozzle provides the throughput of the turbine. The main kinetic energy transformation and the main portion of the available isentropic heat drop relates to the first nozzles. As a result, the Mach number at the outlet section of nozzles can reach 3.0 and even be higher. To operate in such regimes, the convergent-divergent vane channels are preferable.
Convergent-Divergent Vane Channels
Convergent-divergent vane channels in turbines can be implemented by drilled nozzles as well as milled nozzles (rectangle channels). For both nozzle types, the divergent acceleration (supersonic) part design is based on the method of characteristics for which the main influence has working fluid parameters and an outlet Mach number. As a result of calculations, the expansion ratio, the length of the divergent part (expansion angle), and the shape of its contours can be determined.
Nozzle Outlet Angle
One important parameter selected during the first step of turbine design is the nozzle outlet angle Aout (Fig. 3). A typical range for this angle (angle of drilling) is between 12 and 30 degrees (tan. direction). Lower values cause a problem related to small wall thickness between adjacent channels.
The expansion angle Aexp of the divergent part usually doesn’t exceed 14 or 15 degrees. Higher angles allow for the decrease in the axial dimension of the nozzle but increase the possibility of flow separation.
Contours of divergent parts can be designed conically as well as profiled similar to the Laval nozzle. The second variant allows for reaching the highest efficiency with the lowest performance at off-design modes of the turbomachine.
Disadvantages of Drilled Nozzles
The obvious disadvantages of drilled nozzles are the inability to provide the full admission input, higher outer diameter at the inlet (Fig. 4), and higher weight-dimension parameters of nozzles in comparison with milled nozzles.
The form of nozzle outlet area is elliptic. Due to this fact, the “trailing edge” thickness is variable along the radius and increases substantially from the mean radius to hub and tip, which also increases the unevenness of parameter distribution along the radius. To reduce this negative influence, nozzles can be located with overlapping (Fig. 5).
Despite trailing edge losses decreasing in the case of overlapping, the losses caused by shock waves due to supersonic jets mixing in the region between ellipses are increased at the same time. The relation between these losses determines the optimal overlapping and depends on the geometrical parameters of the nozzle.
Advantages of Drilled Nozzles
The benefits of drilled nozzles are a simple design, shorter manufacturing time, higher flow pattern uniformity in the divergent part of the nozzle, and exclusion of secondary losses.
Also, the design process of drilled nozzles takes less time in comparison with milled nozzles. The main challenges found in milled nozzle profiling include consideration of parameter distribution along the blade height, uncertainty with conformal transformation between the plane and cylindrical surface used while designing the nozzle section, and influence of fillets.
The reasonable range of drilled nozzle application is limited by the Mach number range of 1.8 through 2.0. In the lower Mach number region, the intensity of supersonic flow effects is reduced which decreases the divergent part and makes a more aerodynamically effective convergent.
In some cases, the application of drilled nozzles in regions with a lower Mach number can be justified by the cost reduction, labor reduction, and need for a more compact machine with a low number of stages.
References:
1 Abramov V., Filipov G and V.Frolov “Teplovoy raschet turbin” [Turbine design], Moscov, Machinostroenie, 1974 (in Rus)
2 Barber R. and M. Schultheiss “Effect of nozzle geometry on off-design performance of partial admission impulse turbine”, Sundstrand. Report AER No. 486 April 1967 NONR Contract No N00014-66-C0204.
3 Yemin O. and C. Zaritsky “Vozdushnie I gazovie turbinyi s odinochnyimi soplamy” [Air and gas turbines with single nozzle], Moskov, Machinostroenie, 1975 (in Rus).
4 Johnston, I. H. and Dransfield, D. C. The Test Performance of Highly Loaded Turbine Stages Designed for High Pressure Ratio. ARC R & M 3242, 1959.
5 Matveev V and A. Sulinov “Proektirovanie odnostupenchatih i dvuhstupenchatih avtonomnyih turbin turbonasosnyix agregatov gidkostnyix rakentyih dvigateley” [Design of single-stage and 2-stages turbopump turbine for liquid rocket engines], Samara, 2011 (in Rus)
6 Nichols K., “How to select turbomachinery for your application”, Barber-Nichols engineering company, Arvada, Colorado, USA, 2012.
7 Patent US 522066 Steam turbine, C.G.P. de Laval, 1894.
8 Sebelev A. “Sovershenstvovanie malorazmernyih turbin s osesimmetrichnyimi soplami” [Improvement of low-scale turbines with asymmetric nozzles], Ph.D thesis, Peter the Great St. Petersburg Polytechnic University, 2017 (in Rus).
9 Seume J, Peters M. and H. Kunte “Design and test of a 10kW ORC supersonic turbine generator”, Journal of Physics: Conference Series 821 (2017), Nr. 1, 12023.
10 Stratford B. and G. Sansome “ The performance of supersonic turbine nozzles”, ARC R & M 3273, 1959.
Source: https://blog.softinway.com/drilled-nozzle-application-in-supersonic-turbines/
