the shape of turbomachines and the ongoing role of...

The Shape of Turbomachines and the Ongoing Role of Specific Speed

Paul Gostelow1*, Aldo Rona2, Ali Mahallati3

ISROMAC 2016

International

Symposium on

Transport

Phenomena and

Dynamics of

Rotating Machinery

Hawaii, Honolulu

April 10-15, 2016

Abstract A wide-ranging taxonomy of turbomachinery types is given. The requirements of steam turbines and aircraft engines established a traditional approach to aerodynamic design analyzing orthogonal planes. Computers facilitated this and led to a greater reliance on Computational Fluid Dynamics, offering exciting developments in three dimensional modeling. A balance should be sought between analytical, computational and experimental work. In work on an axial flow pump rig photographic investigations of cavitation over the rotor tip have given insights including the very abrupt collapse of cavitation bubbles. Although essential for supersonic regions blade sweep can also be used effectively at lower speeds and can provide significant performance improvements. Further integration of the design and research communities should lead to an improved understanding and predictability. One such area is the unexpected appearance of streamwise vortices on blade suction surfaces. This provides a good base for understanding blade sweep and its effects.

Keywords

Shape — Taxonomy — Cavitation — Sweep

1,2 Department of Engineering, University of Leicester, Leicester, United Kingdom 3 Concepts NREC, White River Junction, Vermont, U.S.A.

* Corresponding author: [email protected]

INTRODUCTION

turbo – turbinis (L) __ I spin Turbomachinery design is a broad field with distant

historical credentials. Figure 1 shows a 2000 year old impulse turbine from Hero of Alexandria. Today’s young engineer, when confronted with an unusual turbomachine like this, should be able to classify it and understand how it operates. The student should be able to repair it and maybe re-design it to work better. An essential requirement is for a rotating component to

spin. This allows the transfer of energy between a component and a fluid. This paper is a reminder that there are many obstacles to, and diverse ways of achieving, the objective of spinning.

Figure 1. 2000 Year Old Turbine: Hero of Alexandria.

A taxonomy of turbomachines is presented in Fig. 2. This permits turbomachines of widely varying geometry to be identified, classified and designed. Does it look cluttered? It is, because we are dealing with a very wide range of machines. A question will be “are the techniques for enclosed flow machines applicable to open flow machines?” The opportunities and context for open flow ones will be addressed first. A question for turbines will be “are all the differences in configuration justified, or does it mean that we have not converged on the optimal solution yet?” The process will be illustrated with reference to different configurations of compressors, turbines, fans and pumps.

A traditional approach to turbomachinery design was to use two different intersecting planes and to address such features as the specific speed for guidance on the overall shape. Computational fluid dynamics (CFD) approaches based on the Navier-Stokes equations and a suitable closure model, are routinely used in the design and analysis of many modern turbomachines.

Although the shapes of turbomachines for aircraft gas turbines may seem to have converged, exciting advances are being made in design tools and techniques. There are still enormous challenges, with progress to be made for the economy and the environment, in addressing these.

mailto:[email protected]

The Shape of Turbomachines and the Ongoing Role of Specific Speed — 2

Figure 2. Taxonomy of Turbomachines.

1. APPROACHES AND REQUIREMENTS FOR THE DESIGN OF TURBOMACHINES

The classification of turbomachines is approached first; this is illustrated by some modern examples of open and closed turbomachines. The framework employed for the analysis and design of enclosed axial flow turbomachines will be considered. Some research advances in understanding the roles of vorticity and of blade sweep in axial turbomachines will be described.

1.1 Design Methodologies

With the advent of digital computers came the traditional approach to the design of enclosed turbines using intersecting two-dimensional planes. Within this tradition the radial equilibrium equation was solved [1] and the S1 and S2 planes were identified [2]. The use of advanced RANS and LES computational procedures is now routine [3] but some flow features are not always well-predicted, even for enclosed and axial flow turbomachines. The difficulties presented by secondary flows and three-dimensional flows are discussed. Relevant research advances in understanding the roles of vorticity and of blade sweep in axial turbomachines will be described.

A recent discovery is that of organized fine-scale streamwise vortical structures on the suction surfaces of turbine blading. This has aerodynamic and heat transfer implications and raises questions of leading edge bluntness, surface curvature and blade sweep. The sweep question seems particularly relevant for most contemporary approaches to the design of free flow turbines.

These issues are addressed but largely remain as questions to be resolved. For progress to be maintained it is essential for analytical, computational and experimental work to proceed in a balanced, collaborative and interactive manner. This would best be achieved by the relaxation of traditional disciplinary barriers in universities and industry.

1.2 Current Challenges

There are still significant challenges, with progress needed for the economy and the environment. For example the recent growth in intermittent solar and wind power generation increases the run duration for conventional power turbomachines under off-design conditions at high loads. A wider look at some opportunities in newer kinds of turbomachine, for which designs have not yet converged, is resulting in improvements. Universities and industry have collaborated in the last two decades to produce highly-loaded low pressure turbines.

These have been deployed in commercial aircraft and major savings in engine weight and cost have been achieved, but with a penalty in turbine efficiency. Research is now aimed at regaining lost efficiency whilst retaining weight and cost advantages.

With this great variety of shapes and sizes how does the designer set about selecting the most appropriate for the application? From dimensional analysis, the concept of specific speed (Ns) is useful. This works for pumps and turbines, in air or water, and is very effective for cavitation avoidance.

Low Ns – Pelton Wheel High Ns – Axial Turbine

Figure 3. What Specific Speeds Do the Power and Head Indicate?


2. DIMENSIONAL ANALYSIS

The established procedures of dimensional analysis are particularly effective in optimizing the shape of a particular turbomachine. The outcome of applying dimensional analysis to turbomachines is the specific speed concept. Because of their differing flow and head characteristics the work-absorbing and work-producing machines result in differing relationships for pumps and turbines.

The specific speed of a pump is given by

Ns=N (Q1/2

H-3/4

) . (1)

For a work producing turbomachine, for instance a turbine, the relationship is

Ns = N (P1/2

H-5/4

) . (2)

The specific speed and the related flow and load coefficients provide a common analytical framework for characterizing networks of differently shaped fluid machines. Specific speed is seen in the developing presence of a wide range of new turbomachinery designs; the approach has been developing over many years in aircraft engines and steam turbines. It is also a driving force in pumps and water turbines. It should be a governing factor in how wind and water turbines are to develop. It is no longer necessary to guess their shape. A methodology exists for deducing the shape, from the earliest Savonius rotor to the modern axial flow wind or water fluid machines. This extreme variety enables differing configurations of fluid machines to be handled under a common conceptual framework. The Pelton Wheel of Fig. 3 is a reminder of the traditional distinction between impulse turbines and reaction turbines [3]. Figure 3 also illustrates the enormous difference in configuration between hydraulic turbines with low and high specific speeds.

2.1. Cavitation

Dimensional analysis also gives a cavitation number

σ = (pa – pv + H)/ (½ ρ v2). (3)

This, the Thoma coefficient, is a reliable indicator for cavitation avoidance and can be monitored by real-time signal processing in the operation of water pumps and turbines to prevent un-intended cavitation. Acosta [4] has identified three modes of cavitation in turbomachines. These are blade surface cavitation, bubble cavitation and tip clearance cavitation. Axial flow pumps are particularly susceptible to cavitation.

Investigations on the axial flow pump rig at the University of Technology Sydney have been performed by Wong [5]. He observed the different modes, clarifying their impact on pump performance. The rig has a transparent casing and the photographic observations of cavitation were made in the rotor tip region and on the blade surfaces.

Figure 4(a) Cavitation Bubbles at Impeller Tip Section

Figure 4(b) Abrupt Collapse of Cavitation Bubbles

Figure 4(a) shows visualization by fully developed cavitation bubbles in the rotor tip vortex and Fig. 4(b) shows the abrupt bubble collapse of that cavitation mode. The rig was also equipped with miniature pressure transducers over the rotor tip aσnd analysis of the ensuing pressure distributions is ongoing.

Earlier investigations had been made by Rains [6] and others. There remains considerable scope for further investigation and improvement of flows in axial, mixed flow and centrifugal pumps as well as various types of turbine. Developments in cavitation observation on pumps and turbines offer considerable scope for performance improvement.

2.2. Blade Sweep

Figure 5 illustrates how the freedom from the traditional radial stacking is made possible by the introduction of canted blades. Fan and turbine designers are now taking advantage of these exciting aerodynamic design freedoms. These blades encounter a wide range of subsonic, transonic and supersonic relative velocities or specific speeds.

The distinction between sweep and dihedral was given by Smith and Yeh [7] and is illustrated in Fig.6, from Lewis and Hill [8]. This shows the definition for an aircraft wing and practical applications for Francis and axial turbines. The wide variation in shape shows the


Figure 5. Swept and Canted Blading.

profound impact of sweep encountered by different types of turbine.

It is usual to associate sweep with high speed flows such as those on modern aircraft wings. That is only one use of aerodynamic sweep and the turbomachinery aerodynamicist will be familiar with a broader and richer family of applications.

The General Electric CF6-6 engine was one of the very first of the high by-pass civil engines that are now universal. The CF6 had a supersonic fan in the outer regions, thus providing an aerodynamic challenge. However there was an additional need to impart body forces on the subsonic air flowing inward to the core of the engine. The layout is shown in Fig. 7. This problem was solved by imparting inward body forces, using both sweep and lean.

Early steam turbine blading, reported by Deych and Troyanovsky [9] (Fig. 8), gave a remarkable reduction

Figure 6. Sweep and Dihedral of Lifting Surfaces [8].

Figure 7. Sweep and Lean Used to Impart Inward Body Forces.

in loss by applying 13 dihedral. Similar improvements were reported by Filippov and Wang [10] from curvilinear nozzle blading tested in cascade.

Despite these excellent results relatively little is understood about the basic fluid mechanics of swept and leaned flows. The latest engines do seem to be heading in the right direction in thermal efficiency gain with some quite spectacular fan designs (Fig. 9) and some improvements in turbine performance.

Improvements so far have been based largely on the power of CFD, and in particular of RANS computations. However the performance of turbine components is still falling short and this seems to be the result of a failure to accurately predict the 3-D flows. These result from tip leakage and the inevitable vortices, of which there are many different types, some of which are strong.

To resolve these dilemmas, and have better accuracy in flow calculation, more research is needed on the physics of the flows. The authors’ research has focused on the state of the blade surface boundary layers and in particular the presence of streamwise vorticity on the convex suction surface of blades (Fig. 10).

Figure 8. Improvement in Steam Turbine Blading Losses by Application of Dihedral [9].


Figure 9. Advanced Low Pressure System Design (Courtesy Rolls-Royce).

Observation of the streamwise vortices was

unexpected; the phenomenon seems to be very resilient. These are the very fine striations with a small lateral spacing of the order of a millimeter or two, as first predicted by Kestin and Wood [11]. Since these suction surface vortices were first observed other researchers have made similar observations on both cascades and circular cylinders.

The streamwise vortices distort the laminar boundary layer; it is now clear that the laminar layer on a convex surface is far from two-dimensional. The vortices are also very resilient, surviving separation regions, boundary layer transition and persevering in the subsequent turbulent layer. The streamwise vortices observed by the authors on turbine blades tend to survive all the way from the leading edge to the trailing edge. Experimental work was performed on the high speed cascade tunnel at the Canadian National Research Council (NRC) in Ottawa. Subsequent tests were performed on circular cylinders in the 1.5 m tri-sonic tunnel at the NRC.

Figure 10. Visualization of Suction Surface at Me=1.16

Figure 11. Normalized Spacings of Striations.

It has now been possible to undertake wider ranging tests on a circular cylinder. The results from the circular cylinder have confirmed those on the turbine cascade. The cylinder was readily suited to variation of the sweep angle. In addition to the zero sweep results [11] testing had been conducted by Poll [12] with sweep angles

between 55 and 70. The present results agreed well with those of Poll and were compatible with the cosine rule.

Figure 11 shows the measured transverse spacing of these striations normalized by the cosine rule. They

demonstrate a peak around 30o, indicating that values

of sweep above 30 should be approached with caution.

CONCLUSIONS

A principal requirement of all turbomachines is to spin. This was understood throughout history. A taxonomy of turbomachinery types is given. This covers a very wide range which is potentially confusing for the new or specialist engineer.

The requirements of steam turbines and aircraft engines established a traditional approach analyzing orthogonal planes. Digital computers facilitated this with developments such as the Wu S1 and S2 stream surfaces and the solution of the radial equilibrium equation. It is now more common to use three-dimensional CFD in the later stages of design. This offers exciting developments but also stern challenges. It should always be recognized that the flow through all turbomachines is three-dimensional and unsteady.

A balance should be sought between analytical, computational and experimental work. As a result of Dimensional Analysis the concept of Specific Speed is important, especially for pumps and hydraulic turbines that vary widely in shape. In work on an axial flow pump rig photographic investigations of cavitation over the rotor tip have given insights including the very abrupt


collapse of cavitation bubbles. This suggests scope for improvement in the behavior of pumps by careful hydrodynamic design.

The use of blade sweep and lean in fans and low pressure turbines is discussed. Although essential for supersonic regions sweep can also be used effectively at lower speeds and is capable of providing significant performance improvements. This is pioneering work for CFD and further integration of the design and research communities should lead to better understanding and predictability. One such area is the unexpected appearance of streamwise vortices on blade suction surfaces. Although the understanding of this is still incomplete the phenomenon is surprisingly widespread, as are its implications. Streamwise vorticity provides a good base for understanding blade sweep and its effects, offering the prospect of design guidance for swept blading.

NOMENCLATURE

H Total head per stage m

Me Discharge Mach Number

N Rotational speed deg/s

Ns Specific Speed m/s

P Power N.m

Q Flow coefficient

Re Reynolds Number

S1,S2 Planes defined by Wu [2] m

v Flow velocity m/s

Λ, λ Sweep angle deg

λ Lateral spacing between streaks mm

λo Normalized lateral spacing

ζ Loss coefficient

σ Cavitation coefficient (Thoma number)

Subscripts:

a Ambient pressure kPa

v Vapor pressure kPa

μ Dihedral deg

ACKNOWLEDGMENTS

The authors wish to acknowledge the support of the National Research Council of Canada and the University of Leicester.

REFERENCES

[1] L. H. Smith Jr., The Radial Equilibrium Equation of

Turbomachinery, Trans ASME J. Eng. Power,

88,1, 1966.

[2] Chung Hua Wu., A General Theory of Three-

Dimensional Flow in Subsonic and Supersonic

Turbomachines of Axial, Radial and Mixed Flow

Types, NACA TN 2604, 1952.

[3] S. L. Dixon and C. A. Hall., Fluid Mechanics and

Thermodynamics of Turbomachinery, Elsevier,

2010.

[4] A. Acosta., Cavitation and Fluid Machinery, Conf.

Arr.by IMechE, Herriot-Watt University, Edinburgh,

1974.

[5] K. K. Wong., Observations of Cavitation on an

Axial Flow Pump Impeller, Master of Engineering

Thesis, University of Technology, Sydney,

Australia, 1994.

[6] D. A. Rains., Tip Clearance Flows in Axial Flow Compressors and Pumps, California Institute of Technology, Hydrodynamics and Mechanical. Engineering Laboratories, Report No. 5, 1954.

[7] L. H. Smith Jr. and H. Yeh., Sweep and Dihedral Effects in Axial Flow Turbomachinery, Trans ASME J. Basic Eng., Pg. 401, 1963.

[8] R. I. Lewis and J. M. Hill., The Influence of Sweep and Dihedral in Turbomachinery Blade Rows, J. Mech. Eng. Sci., 13, 4, 1971.

[9] M. E. Deych and B. M. Troyanovskiy., Investigation and Calculation of Axial Turbine Stages, USAF Trans. FTD-MT-65-409, 1965

[10] G. A. Filippov and Zhong-Chi Wang., The Effect of Flow Twisting on the Characteristics of Guide Rows, Teploenergetija, 5, 1964.

[11] J. Kestin and R. T. Wood., On the Stability of Two-Dimensional Stagnation Flow, Journal of Fluid Mechanics, 44, 461-479, 1970.

[12] D. I. A. Poll., Some Observations of the Transition Process on the Windward Face of a Long Yawed Cylinder, Journal of Fluid Mechanics, 150, 329-356, 1985.

the shape of turbomachines and the ongoing role of...

Documents