Radial turbine

Last updated April 16, 2024

A radial turbine is a turbine in which the flow of the working fluid is radial to the shaft. The difference between axial and radial turbines consists in the way the fluid flows through the components (compressor and turbine). Whereas for an axial turbine the rotor is 'impacted' by the fluid flow, for a radial turbine, the flow is smoothly orientated perpendicular to the rotation axis, and it drives the turbine in the same way water drives a watermill. The result is less mechanical stress (and less thermal stress, in case of hot working fluids) which enables a radial turbine to be simpler, more robust, and more efficient (in a similar power range) when compared to axial turbines. When it comes to high power ranges (above 5 MW) the radial turbine is no longer competitive (due to its heavy and expensive rotor) and the efficiency becomes similar to that of the axial turbines.

Advantages and challenges

Compared to an axial flow turbine, a radial turbine can employ a relatively higher pressure ratio (≈4) per stage with lower flow rates. Thus these machines fall in the lower specific speed and power ranges. For high temperature applications rotor blade cooling in radial stages is not as easy as in axial turbine stages. Variable angle nozzle blades can give higher stage efficiencies in a radial turbine stage even at off-design point operation. In the family of water turbines, the Francis turbine is a very well-known IFR turbine which generates much greater power with a relatively large impeller.

Components of radial turbines

Ninety degree inward-flow radial turbine stage
Velocity triangles for an inward-flow radial (IFR) turbine stage with cantilever blades

The radial and tangential components of the absolute velocity c₂ are c_r2 and c_q2, respectively. The relative velocity of the flow and the peripheral speed of the rotor are w₂ and u₂ respectively. The air angle at the rotor blade entry is given by

\,\tan {\beta _{2}}={\frac {c_{r2}}{c_{\theta 2}-u_{2}}}

Enthalpy and entropy diagram

The stagnation state of the gas at the nozzle entry is represented by point 01. The gas expands adiabatically in the nozzles from a pressure p₁ to p₂ with an increase in its velocity from c₁ to c₂. Since this is an energy transformation process, the stagnation enthalpy remains constant but the stagnation pressure decreases (p₀₁ > p₀₂) due to losses. The energy transfer accompanied by an energy transformation process occurs in the rotor.

Spouting velocity

A reference velocity (c₀) known as the isentropic velocity, spouting velocity or stage terminal velocity is defined as that velocity which will be obtained during an isentropic expansion of the gas between the entry and exit pressures of the stage.

\,C_{0}={\sqrt {2C_{p}\,T_{01}\,\left(1-\left({\frac {p_{3}}{p_{01}}}\right)^{\frac {\gamma -1}{\gamma }}\right)}}

Stage efficiency

The total-to-static efficiency is based on this value of work.

{\begin{aligned}\eta _{\text{ts}}&={\frac {h_{01}-h_{03}}{h_{01}-h_{3ss}}}={\frac {\psi \,u_{2}^{2}}{C_{p}\,T_{01}\left(1-\left({\frac {p_{3}}{p_{01}}}\right)^{\frac {\gamma -1}{\gamma }}\right)}}\end{aligned}}

Degree of reaction

The relative pressure or enthalpy drop in the nozzle and rotor blades are determined by the degree of reaction of the stage. This is defined by

R={\frac {\text{static enthalpy drop in rotor}}{\text{stagnation enthalpy drop in stage}}}

The two quantities within the parentheses in the numerator may have the same or opposite signs. This, besides other factors, would also govern the value of reaction. The stage reaction decreases as C_θ2 increases because this results in a large proportion of the stage enthalpy drop to occur in the nozzle ring.

Stage losses

The stage work is less than the isentropic stage enthalpy drop on account of aerodynamic losses in the stage. The actual output at the turbine shaft is equal to the stage work minus the losses due to rotor disc and bearing friction.

Skin friction and separation losses in the scroll and nozzle ring
They depend on the geometry and the coefficient of skin friction of these components.
Skin friction and separation losses in the rotor blade channels
These losses are also governed by the channel geometry, coefficient of skin friction and the ratio of the relative velocities w₃/w₂. In the ninety degree IFR turbine stage, the losses occurring in the radial and axial sections of the rotor are sometimes separately considered.
Skin friction and separation losses in the diffuser
These are mainly governed by the geometry of the diffuser and the rate of diffusion.
Secondary losses
These are due to circulatory flows developing into the various flow passages and are principally governed by the aerodynamic loading of the blades. The main parameters governing these losses are b₂/d₂, d₃/d₂ and hub-tip ratio at the rotor exit.
Shock or incidence losses
At off-design operation, there are additional losses in the nozzle and rotor blade rings on account of incidence at the leading edges of the blades. This loss is conventionally referred to as shock loss though it has nothing to do with the shock waves.
Tip clearance loss
This is due to the flow over the rotor blade tips which does not contribute to the energy transfer.

Blade to gas speed ratio

The blade-to-gas speed ratio can be expressed in terms of the isentropic stage terminal velocity c₀.

\,\sigma _{s}={\frac {u_{2}}{c_{0}}}=[2(1+\phi _{2}\cot {\beta _{2}})]^{-{\frac {1}{2}}}

for

β₂ = 90^o

σ_s ≈ 0.707

Outward-flow radial stages

In outward flow radial turbine stages, the flow of the gas or steam occurs from smaller to larger diameters. The stage consists of a pair of fixed and moving blades. The increasing area of cross-section at larger diameters accommodates the expanding gas.

This configuration did not become popular with the steam and gas turbines. The only one which is employed more commonly is the Ljungstrom double rotation type turbine. It consists of rings of cantilever blades projecting from two discs rotating in opposite directions. The relative peripheral velocity of blades in two adjacent rows, with respect to each other, is high. This gives a higher value of enthalpy drop per stage.

Nikola Tesla's bladeless radial turbine

In the early 1900s, Nikola Tesla developed and patented his bladeless Tesla turbine. One of the difficulties with bladed turbines is the complex and highly precise requirements for balancing and manufacturing the bladed rotor which has to be very well balanced. The blades are subject to corrosion and cavitation. Tesla attacked this problem by substituting a series of closely spaced disks for the blades of the rotor. The working fluid flows between the disks and transfers its energy to the rotor by means of the boundary layer effect or adhesion and viscosity rather than by impulse or reaction. Tesla stated his turbine could realize incredibly high efficiencies by steam. There has been no documented evidence of Tesla turbines achieving the efficiencies Tesla claimed. They have been found to have low overall efficiencies in the role of a turbine or pump.^[1] In recent decades there has been further research into bladeless turbine and development of patented designs that work with corrosive/abrasive and hard to pump material such as ethylene glycol, fly ash, blood, rocks, and even live fish.^[1]

Notes

1 2 "Author, Harikishan Gupta E., & Author, Shyam P. Kodali (2013). Design and Operation of Tesla Turbo machine - A state of the art review. International Journal of Advanced Transport Phenomena, 2(1), 2-3" (PDF).

Related Research Articles

A steam turbine is a machine that extracts thermal energy from pressurized steam and uses it to do mechanical work on a rotating output shaft. Its modern manifestation was invented by Charles Parsons in 1884. Fabrication of a modern steam turbine involves advanced metalwork to form high-grade steel alloys into precision parts using technologies that first became available in the 20th century; continued advances in durability and efficiency of steam turbines remains central to the energy economics of the 21st century.

A turbine is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced can be used for generating electrical power when combined with a generator. A turbine is a turbomachine with at least one moving part called a rotor assembly, which is a shaft or drum with blades attached. Moving fluid acts on the blades so that they move and impart rotational energy to the rotor. Early turbine examples are windmills and waterwheels.

The Tesla turbine is a bladeless centripetal flow turbine invented by Nikola Tesla in 1913. Nozzles apply a moving fluid to the edges of a set of discs. The engine uses smooth discs rotating in a chamber to generate rotational movement due to the momentum exchange between the fluid and the discs. The discs are arranged in an orientation similar to a stack of CDs on a pole.

Centrifugal compressors, sometimes called impeller compressors or radial compressors, are a sub-class of dynamic axisymmetric work-absorbing turbomachinery.

An isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no net transfer of heat or matter. Such an idealized process is useful in engineering as a model of and basis of comparison for real processes. This process is idealized because reversible processes do not occur in reality; thinking of a process as both adiabatic and reversible would show that the initial and final entropies are the same, thus, the reason it is called isentropic. Thermodynamic processes are named based on the effect they would have on the system. Even though in reality it is not necessarily possible to carry out an isentropic process, some may be approximated as such.

A de Laval nozzle is a tube which is pinched in the middle, making a carefully balanced, asymmetric hourglass shape. It is used to accelerate a compressible fluid to supersonic speeds in the axial (thrust) direction, by converting the thermal energy of the flow into kinetic energy. De Laval nozzles are widely used in some types of steam turbines and rocket engine nozzles. It also sees use in supersonic jet engines.

A compressor is a mechanical device that increases the pressure of a gas by reducing its volume. An air compressor is a specific type of gas compressor.

The Francis turbine is a type of water turbine. It is an inward-flow reaction turbine that combines radial and axial flow concepts. Francis turbines are the most common water turbine in use today, and can achieve over 95% efficiency.

An axial compressor is a gas compressor that can continuously pressurize gases. It is a rotating, airfoil-based compressor in which the gas or working fluid principally flows parallel to the axis of rotation, or axially. This differs from other rotating compressors such as centrifugal compressor, axi-centrifugal compressors and mixed-flow compressors where the fluid flow will include a "radial component" through the compressor.

Turbomachinery, in mechanical engineering, describes machines that transfer energy between a rotor and a fluid, including both turbines and compressors. While a turbine transfers energy from a fluid to a rotor, a compressor transfers energy from a rotor to a fluid. It is an important application of fluid mechanics.

Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic axisymmetric work-absorbing turbomachinery. The fluid enters the pump impeller along or near to the rotating axis and is accelerated by the impeller, flowing radially outward into a diffuser or volute chamber (casing), from which it exits.

A compressor map is a chart which shows the performance of a turbomachinery compressor. This type of compressor is used in gas turbine engines, for supercharging reciprocating engines and for industrial processes, where it is known as a dynamic compressor. A map is created from compressor rig test results or predicted by a special computer program. Alternatively the map of a similar compressor can be suitably scaled. This article is an overview of compressor maps and their different applications and also has detailed explanations of maps for a fan and intermediate and high-pressure compressors from a three-shaft aero-engine as specific examples.

A jet engine performs by converting fuel into thrust. How well it performs is an indication of what proportion of its fuel goes to waste. It transfers heat from burning fuel to air passing through the engine. In doing so it produces thrust work when propelling a vehicle but a lot of the fuel is wasted and only appears as heat. Propulsion engineers aim to minimize the degradation of fuel energy into unusable thermal energy. Increased emphasis on performance improvements for commercial airliners came in the 1970s from the rising cost of fuel.

<span class="mw-page-title-main">Betz's law</span> Aerodynamic power limitation for wind turbines

In aerodynamics, Betz's law indicates the maximum power that can be extracted from the wind, independent of the design of a wind turbine in open flow. It was published in 1919 by the German physicist Albert Betz. The law is derived from the principles of conservation of mass and momentum of the air stream flowing through an idealized "actuator disk" that extracts energy from the wind stream. According to Betz's law, no wind turbine of any mechanism can capture more than 16/27 (59.3%) of the kinetic energy in wind. The factor 16/27 (0.593) is known as Betz's coefficient. Practical utility-scale wind turbines achieve at peak 75–80% of the Betz limit.

In turbomachinery, degree of reaction or reaction ratio (R) is defined as the ratio of the static pressure rise in the rotating blades of a compressor (or drop in turbine blades) to the static pressure rise in the compressor stage (or drop in a turbine stage). Alternatively it is the ratio of static enthalpy change in the rotor to the static enthalpy change in the stage.

Compressor characteristic is a mathematical curve that shows the behaviour of a fluid going through a dynamic compressor. It shows changes in fluid pressure, temperature, entropy, flow rate etc.) with the compressor operating at different speeds.

Compounding of steam turbines is a method of extracting steam energy in multiple stages rather than in a single stage in a steam turbine. A compounded steam turbine has multiple stages with more than one set of nozzles and rotors. These are arranged in series, either keyed to the common shaft or fixed to the casing. The result of this arrangement allows either the steam pressure or the jet velocity to be absorbed by the turbine in a number of stages.

An axial turbine is a turbine in which the flow of the working fluid is parallel to the shaft, as opposed to radial turbines, where the fluid runs around a shaft, as in a watermill. An axial turbine has a similar construction as an axial compressor, but it operates in the reverse, converting flow of the fluid into rotating mechanical energy.

Three-dimension losses and correlation in turbomachinery refers to the measurement of flow-fields in three dimensions, where measuring the loss of smoothness of flow, and resulting inefficiencies, becomes difficult, unlike two-dimensional losses where mathematical complexity is substantially less.

Isentropic nozzle flow describes the movement of a gas or fluid through a narrowing opening without an increase or decrease in entropy.

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