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Prof. Dr. Rishi Raj Design of an Impulse Turbine Blades Hasan-1

The main purpose of this project, design of an impulse turbine is to understand the concept of turbine blades by defining and designing the parameters that requires to obtain inlet and outlet velocity for the known mass flow rate of the steam. Also another objective is to design the length, size and shape of the blades as well that allows achieving the maximum efficiency of the designed steam turbine. Therefore in the following report of the impulse stage of turbine blades for a power plant the concepts have been used from mathematics, thermodynamics and physics simultaneously to derive the relation between mass flow rate and the velocity triangles, to design the parameters such as velocity triangles, length, size and shape of the blades and also achieving the better efficiency of the steam turbine power plant cycle in its first two impulse stages.


Abbreviation Property Unit h Enthalpy Btu

lbm

∆h Change in Enthalpy Btulbm

v Specific Volume 3ftlbm

V Absolute fluid flow velocity fts

U Velocity of blade fts

α2 Angle at which absolute fluid flow hits the blade β Angle at which real fluid γ Angle at which real fluid leaves the blade gc Constant A Area of blade cm ri Inside diameter cm ro Outside diameter cm P Power KW

m•

Mass flow rate of steam lbm

thη Efficiency % Table-1 (shows the abbreviation, property and units)


Basic Rankine cycle is practical but relatively inefficient in producing power, therefore in a modern steam plant a number of modifications are made to this basic cycle to improve the efficiency. A steam turbine operates when the thermal energy of steam is converted into kinetic energy and then into mechanical energy. The history of steam turbine development is a long one, it has first in 150 B.C. when Hero of Alexandria built his first crude device that contains a rotating-reaction, nozzled-equipped sphere. The following device was a pure reaction type and generated no useful work.

Figure-1 (Alexandria Crude Device)

In 1831 Foster and Avery obtained a United States patent for a reaction wheel similar to Hero’s. In 1882 Gustaf De Laval applied the turbine principal to a prime mover for his cream separator and few years later produced a series of small impulse turbines. At the very same time Sir Charles S. Parsons has developed a reaction turbine and used it in a marine application. During the period of 1896, C. G. Curtis, an American has developed another kind of impulse turbine. Steam turbine has made it the principal prime mover of generating stations from the last several years. At the present the average maximum unit size is approximately 600,000 kW for a single shaft fossil unit. In 1920’s the progress was made from 5000 to 30,000 kW turbines frequently and the most units used 200 psi and 550 F with some significant changes in steam conditions also. But, at the present moment the most units are designed steam of 2400 psi and 1000 F. Generally steam turbines are classified into two main groups, an impulse turbine and reaction turbine. In Impulse Turbines steam expands in stationary nozzle to attain the high velocity and then flows over the moving blades, converting some of its kinetic


energy into mechanical energy. Similarly in Reaction Turbine steam expands both in stationary nozzle and moving blades. The relative amount of expansion between impulse and reaction turbine varies from design to design. However, for the practice purposes in generating the power both impulse and reaction sections are required to be used.


Most of the steam turbine plants use impulse steam turbines, whereas gas turbine plants do not use impulse very often. However, the working principles are the same whether the gas or steam is used as a working fluid. In impulse steam turbine the following facts are very important to remember;

• Blades are usually symmetrical • Entrance and exit angles are around 20o • Enthalpy drop and pressure drop occur in the nozzle • Used in the entrance high-pressure stages

WORKING PRINCIPLE The steam is supplied to a single-wheel impulse turbine expands completely in the nozzle and leaves with absolute velocity (V) at an angle α and substracting the blade velocity vector (U) the relative velocity vector at entry to the rotor can be determined. The relative velocity makes an angle of β with respect to blade velocity vector. The increase in a value of an angle α decreases the value of the absolute velocity component, V cosα and increases the axial or flow component. In the following working principle the two important and particular points are the inlet and exit of the blades. Furthermore, vectorially substracting the blade speed results in absolute velocity. The steam leaves tangentially at an angle β with relative velocity. The important fact is that the impulse steam turbine can not have 180o in an actual application, similarly blade entrance angle and blade exit angle cannot be zero.

Figure-2 (blade entrance and exit angle)


THEORY Motion (Newton’s second law) The law relates the net force on an object to the acceleration of that object. It is given by;

𝐹𝐹 = 𝑚𝑚𝑚𝑚 Continuity The continuity equation in Cartesian coordinates is given as follows;

𝛿𝛿(𝜌𝜌𝜌𝜌)𝛿𝛿𝛿𝛿

+𝛿𝛿(𝜌𝜌𝜌𝜌)𝛿𝛿𝛿𝛿

+𝛿𝛿(𝜌𝜌𝜌𝜌)𝛿𝛿𝛿𝛿

= −𝛿𝛿𝜌𝜌𝛿𝛿𝛿𝛿

1-D steady flow: 𝛿𝛿(𝜌𝜌𝜌𝜌)𝛿𝛿𝛿𝛿

= 0

Intergral form :

�𝜌𝜌𝑖𝑖𝐴𝐴𝑖𝑖𝑉𝑉𝑖𝑖 = 0 𝑓𝑓𝑓𝑓𝑓𝑓 1 ≤ 𝑖𝑖 ≤ 𝑛𝑛

Momentum Momentum of the fluid as it expands in the turbine is integral to work output. Momentum equation.

�𝐹𝐹𝛿𝛿 =∆𝑚𝑚𝑉𝑉𝛿𝛿𝑑𝑑𝛿𝛿

=𝑚𝑚𝑉𝑉2

𝑑𝑑𝛿𝛿−𝑚𝑚𝑉𝑉1

𝑑𝑑𝛿𝛿

Where V2 and V1 are given by: (𝑚𝑚𝑉𝑉𝛿𝛿)1 = (𝑚𝑚𝑉𝑉𝛿𝛿)𝛿𝛿 + 𝑉𝑉𝑖𝑖𝑑𝑑𝑚𝑚𝑖𝑖 (𝑚𝑚𝑉𝑉𝛿𝛿)2 = (𝑚𝑚𝑉𝑉𝛿𝛿)𝛿𝛿 + 𝑉𝑉𝑒𝑒𝑑𝑑𝑚𝑚𝑒𝑒 Substituting,

(𝑚𝑚𝑉𝑉𝛿𝛿)1 − (𝑚𝑚𝑉𝑉𝛿𝛿)2 = [(𝑚𝑚𝑉𝑉𝛿𝛿)𝛿𝛿+𝑑𝑑𝛿𝛿 − (𝑚𝑚𝑉𝑉𝛿𝛿)𝛿𝛿𝑖𝑖 ] + [(𝑉𝑉𝛿𝛿𝑑𝑑𝑚𝑚)𝑒𝑒 + 𝑉𝑉𝑖𝑖𝑑𝑑𝑚𝑚𝑖𝑖]

Taking the time derivative for 1-D flow, �𝐹𝐹𝛿𝛿 = 𝑚𝑚[(𝑉𝑉𝑒𝑒) − (𝑉𝑉𝑖𝑖)]𝛿𝛿

Power :

𝑃𝑃 =𝛿𝛿𝜌𝜌𝛿𝛿𝛿𝛿

= 𝑚𝑚𝑉𝑉𝑚𝑚(𝑉𝑉1𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐 + 𝑉𝑉2𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐)


Analyzing and mechanically designing the first two stages of steam turbine will be done by obtaining the length of blades, shape of blades, efficiency and the other parameters and evaluate each by assuming the first two stages are impulse stages further more the velocity triangles need to be drawn. Analysis of this impulse stage is also based on the information that has been obtained from the optimizing and designing the steam turbine. Such information as a design specifications are given as, Power Plant Power output = 150000 kW Inlet Pressure = 1500 psi Inlet Temperature = 1000 oF Maximum Moisture Level = 13% Mass Flow Rate = 740045 lbm/hr = 12334 lbm/min = 206 lbm/sec FIRST STAGE ANALYSIS The very first stage of the impulse turbine is a velocity analysis, which is the very important analysis in the cycle. It is known that the before entering into the impulse stage steam has normally a velocity (v1) of range between 100 ft/s to 200 ft/s (normally assumed to be at 100 ft/s). When steam enters the stator its velocity changes from v1 to v2 and when it goes out the velocity once again changes from v2 to v3. This change is required to be determined and it can be analyzed through the velocity triangle that is created in between stationary and moving blades. This following stage is based on few steps that can be shown in the analysis and calculations. VELOCITY ANALYSIS AT THE STATOR The entering velocity of the steam to the rotors is v2 that can be determined and is given as,

𝜌𝜌𝑓𝑓 = 𝜌𝜌2 = 222√∆ℎ Where ∆h is the amount of heat required to be converted, which can be selected from the range of 30 Btu/lbm to 70 Btu/lbm. Hence for the calculation purposes it is selected to be 30 Btu/lbm. Therefore the velocity to be found as,

𝜌𝜌𝑓𝑓 = 𝜌𝜌2 = 222√30 = 1216𝑓𝑓𝛿𝛿𝑐𝑐

In determining the exit velocity v3 the relative velocity is other important parameters that is required to find before the exit. The stator velocity that has been found to be v2 = 1216 ft/s is the absolute steam velocity and through this velocity determining the exit velocity is not an appropriate analysis. Therefore using simple geometric transformations the relative velocity can be determined that can further required in analyzing the exit


velocity. Thus the relative velocity u can be calculated from the velocity ratio that is given as;

𝜇𝜇 =𝜌𝜌𝜌𝜌2

= 0.38

The above velocity ratio is always equal to 0.38 but, 0.37 or 0.36 can also be used for the designing purposes. However, it is known for the fact that the velocity ratio is equal to 0.5 only when the design is ideal. Thus due to the irreversibility that can be more likely a friction the velocity ratio is suggested to be 0.38 for the following designing the turbine blades, Thus,

𝜌𝜌 = 0.38𝜌𝜌2 = 0.38 x 1216 = 462.08fts

Since the blade velocity is determined to be u, therefore the relative velocity can be determined and is given as,

𝜌𝜌1 = 𝜌𝜌2 − 𝜌𝜌 The relative velocity is an important parameter that is required to be analyzed through the velocity diagram that is shown below,

Figure-3 (Velocity Triangle At The Entrance of A Stator) Let α2 be the angle at which the absolute fluid flow hits the blade and β is the angle of the real fluid. For the designing purposes α2 is the angle that can be chosen from 8o to 180o however the 16o is the best to be chosen but, in this design the angle is chosen to be 20o. Therefore the axial and tangential component can be determined with respect to the relative velocity and the angle of the real fluid, hence it is given as,

𝜌𝜌2𝑐𝑐𝑖𝑖𝑛𝑛𝑠𝑠 = 𝜌𝜌2𝑐𝑐𝑖𝑖𝑛𝑛𝑐𝑐2 (𝐴𝐴𝛿𝛿𝑖𝑖𝑚𝑚𝐴𝐴 𝑐𝑐𝑓𝑓𝑚𝑚𝑐𝑐𝑓𝑓𝑛𝑛𝑒𝑒𝑛𝑛𝛿𝛿) Similarly,

u

u

V2 w2


𝜌𝜌2𝑐𝑐𝑓𝑓𝑐𝑐𝑠𝑠 = 𝜌𝜌2𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐2 − 𝜌𝜌 (𝑇𝑇𝑚𝑚𝑛𝑛𝑇𝑇𝑒𝑒𝑛𝑛𝛿𝛿𝑖𝑖𝑚𝑚𝐴𝐴 𝑐𝑐𝑓𝑓𝑚𝑚𝑐𝑐𝑓𝑓𝑛𝑛𝑒𝑒𝑛𝑛𝛿𝛿) Thus by substituting the known parameters the above equation becomes,

𝜌𝜌2𝑐𝑐𝑖𝑖𝑛𝑛𝑠𝑠 = 𝜌𝜌2𝑐𝑐𝑖𝑖𝑛𝑛𝑐𝑐2 = 1216𝑐𝑐𝑖𝑖𝑛𝑛(20𝑓𝑓) = 415.90 𝑓𝑓𝛿𝛿 𝑐𝑐�

Also, 𝜌𝜌2𝑐𝑐𝑓𝑓𝑐𝑐𝑠𝑠 = 𝜌𝜌2𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐2 − 𝜌𝜌 = 1216𝑐𝑐𝑓𝑓𝑐𝑐(20𝑓𝑓) − 462.08 = 680.59𝑓𝑓𝛿𝛿 𝑐𝑐�

Thus knowing the trigonometric identities the angle of the real fluid can be found which either can be substituted in an axial or tangential component to determine the relative velocity. Thus the angle and the velocity is given as,

𝑠𝑠 = 31.43𝑓𝑓 𝐴𝐴𝑛𝑛𝑑𝑑 𝜌𝜌2 = 797.57𝑓𝑓𝛿𝛿 𝑐𝑐�

Therefore at the end of the first part of the analysis that is the velocity determination at the stator end, the steam velocity, the blade speed, the relative velocity and the real fluid angle was calculated and are found to be as,

𝜌𝜌2 = 1216𝑓𝑓𝛿𝛿 𝑐𝑐� ; 𝜌𝜌 = 462.08𝑓𝑓𝛿𝛿 𝑐𝑐� ; 𝜌𝜌2 = 797.57𝑓𝑓𝛿𝛿 𝑐𝑐 � 𝐴𝐴𝑛𝑛𝑑𝑑 𝑠𝑠 = 31.43𝑓𝑓

VELOCITY ANALYSIS AT THE ROTOR Once the fluid leaves the stator it exits the blade with the velocity v3 through the rotor at an angle γ, an angle at which real fluid leaves the blade. At this point it is important to keep in mind that the parameters such as blade speed (u), relative velocity (w2) and the angle (β) remains constant through out the whole process.

Figure-4 (Velocity Triangle At The Exit of A Rotor) Since it is known that leaving velocity of the steam is absolute velocity and it can be determined in a similar way as the relative velocity and the real angle of the fluid has

u

u

w2 v2


determined through the axial and tangential component. Thus the tangential and axial components are given as,

𝜌𝜌3𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐 = 𝜌𝜌3𝑐𝑐𝑓𝑓𝑐𝑐𝑠𝑠 − 𝜌𝜌 (𝑇𝑇𝑚𝑚𝑛𝑛𝑇𝑇𝑒𝑒𝑛𝑛𝛿𝛿𝑖𝑖𝑚𝑚𝐴𝐴 𝑐𝑐𝑓𝑓𝑚𝑚𝑐𝑐𝑓𝑓𝑛𝑛𝑒𝑒𝑛𝑛𝛿𝛿) Similarly,

𝜌𝜌3𝑐𝑐𝑖𝑖𝑛𝑛𝑐𝑐 = 𝜌𝜌3𝑐𝑐𝑖𝑖𝑛𝑛𝑠𝑠 (𝐴𝐴𝛿𝛿𝑖𝑖𝑚𝑚𝐴𝐴 𝑐𝑐𝑓𝑓𝑚𝑚𝑐𝑐𝑓𝑓𝑛𝑛𝑒𝑒𝑛𝑛𝛿𝛿) Since the relative velocity is constant i.e. w2 = w3 = 797.57 ft/s, therefore by substituting the known parameters the equation becomes as,

𝜌𝜌3𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐 = 𝜌𝜌3𝑐𝑐𝑓𝑓𝑐𝑐𝑠𝑠 − 𝜌𝜌 = 797.57𝑐𝑐𝑓𝑓𝑐𝑐(31.43𝑓𝑓) − 462.08 = 218.47 𝑓𝑓𝛿𝛿 𝑐𝑐�

Also, 𝜌𝜌3𝑐𝑐𝑖𝑖𝑛𝑛𝑐𝑐 = 𝜌𝜌3𝑐𝑐𝑖𝑖𝑛𝑛𝑠𝑠 = 797.57𝑐𝑐𝑖𝑖𝑛𝑛(31.43𝑓𝑓) = 415.90𝑓𝑓𝛿𝛿 𝑐𝑐�

Thus knowing the trigonometric identities the angle of the real fluid can be found which either can be substituted in an axial or tangential component to determine the relative velocity. Thus the angle and the velocity is given as,

𝑐𝑐 = 62.26𝑓𝑓 𝐴𝐴𝑛𝑛𝑑𝑑 𝜌𝜌2 = 469.91𝑓𝑓𝛿𝛿 𝑐𝑐�

Therefore at the end of the second part of the analysis that is the velocity determination at the rotor end, the steam velocity, the blade speed, the relative velocity and the real fluid angle was calculated and are found to be as,

𝜌𝜌3 = 469.91𝑓𝑓𝛿𝛿 𝑐𝑐� ; 𝜌𝜌 = 462.08𝑓𝑓𝛿𝛿 𝑐𝑐� ; 𝜌𝜌2 = 𝜌𝜌3 = 797.57𝑓𝑓𝛿𝛿 𝑐𝑐 � 𝐴𝐴𝑛𝑛𝑑𝑑 𝑐𝑐 = 62.26𝑓𝑓

Through the velocity analysis of the stator and rotor the results suggest that the absolute velocity of the steam has increased when it passes through the stator and decreases drastically when exits the blade through the rotor. This following change in the velocity is due to the change in pressure that creates the kinetic energy which further transform to mechanical work. This mechanical work is mainly responsible to generate the energy as an output by rotating the shaft through the high velocity moving through the blades. Once the blade speed, entrance and exit velocity with real fluid angle and leaving fluid angle with the relative velocity for the whole system is determined then the other important parameters are required to be calculated. The other parameters are length, shape, efficiency of the blade for the impulse stages.


SHAPE OF THE BLADE

Figure-5 (One Rotor Blade) The shape of the blade is another important feature in analyzing the stage of the impulse turbine. It is important to have a shape of turbine blade in such a way that the flow of the fluid remains to be continuous. Therefore the symmetric blades with the curvature allows the steam to transfer most of the energy and saved enough amount of the energy to reach the next rotor; thus the cycle is kept moving in a similar fashion from one stator to another and so on. The suggested shape of the blade is shown in the figure-5. Once the shape of the blade is decided the next parameter is to analyze its dimensions that includes the axial velocity, mass flow rate (based on project-1, cycle-5), and area. The area of the blade is a very critical dimension that is required to be evaluated very carefully, thus the mass flow rate will help in obtaining the required area of the blade. Therefore the mass flow rate can be calculated and is given as,

�̇�𝑚 = 𝜌𝜌𝑉𝑉𝛿𝛿𝐴𝐴 Thus the area becomes,

𝐴𝐴 =�̇�𝑚𝜌𝜌𝑉𝑉𝛿𝛿

Let �̇�𝑚 be the mass flow rate and can be found in connection to the project-1 from the cycle-5, and it has found to be as,

𝑚𝑚 = 740045 𝐴𝐴𝑙𝑙𝑚𝑚 ℎ𝑓𝑓� = 12334 𝐴𝐴𝑙𝑙𝑚𝑚 𝑚𝑚𝑖𝑖𝑛𝑛� = 206 𝐴𝐴𝑙𝑙𝑚𝑚 𝑐𝑐𝑒𝑒𝑐𝑐�̇ Let ρ be the density of the steam and can be found from the given inlet pressure and inlet temperature that has given as 1500 psi and 1000 oF respectively. Therefore the 1 lbm of steam and the specific volume at the given inlet pressure and temperature can be obtained from the superheated tables require in determining the density of the steam and is given as,


𝜌𝜌 =𝑚𝑚

𝜌𝜌@1500𝑐𝑐𝑐𝑐𝑖𝑖 ,1000℉=

10.54031

= 1.851 𝐴𝐴𝑙𝑙𝑚𝑚 𝑓𝑓𝛿𝛿3�

The axial velocity that is perpendicular to the inner rotor blades can be determined and is given as,

𝑉𝑉𝛿𝛿 = 𝑉𝑉2𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐2 = 1216𝑐𝑐𝑓𝑓𝑐𝑐(20)𝑓𝑓 = 1143𝑓𝑓𝛿𝛿 𝑐𝑐�

Therefore the area of the blade can be determined from the above equation that has derived from the mass flow rate equation and is given as,

𝐴𝐴 =206

1.851 x 1143= 0.09737𝑓𝑓𝛿𝛿2

In above determination of the area the mass flow rate has been obtained from the project-1 of cycle-5. However, it is important to know that the mass flow rate in general can be determined from the power equation and is given as,

�̇�𝑚 =𝑃𝑃 x 3412∆ℎ𝑛𝑛𝑒𝑒𝛿𝛿

From the above calculated area of the blade the other parameters such as length, mean radius, inner and outer radius of the blade will be required to determine and these parameters can be calculated as; As the area of the blades known to be 0.09737 ft2; however, the area can be mathematically is given as,

𝐴𝐴 = 𝜋𝜋(𝑓𝑓𝑓𝑓2 − 𝑓𝑓𝑖𝑖2) = 0.09737𝑓𝑓𝛿𝛿2 Algebraically the equation can be further reduced and solved to determine the inner and outer radius of the blade and is given as,

(𝑓𝑓𝑓𝑓 − 𝑓𝑓𝑖𝑖)(𝑓𝑓𝑓𝑓 + 𝑓𝑓𝑖𝑖) =0.09737

𝜋𝜋

As we know that the overall length (L) and the mean radius (rm) of the blade is determine as,

𝐿𝐿 = 𝑓𝑓𝑓𝑓 − 𝑓𝑓𝑖𝑖 And,

𝑓𝑓𝑚𝑚 = 𝑓𝑓𝑓𝑓 + 𝑓𝑓𝑖𝑖 The mean radius can be determined from the calculated blade speed running at the certain designed rpm, n in rpm is required to assume either 1800 rpm or 3600 rpm. Thus for the following calculation purposes rpm has to be assumed as 1800 rpm. Therefore mean radius is to be determined as,

𝜌𝜌 =2𝜋𝜋𝑛𝑛60

𝑓𝑓𝑚𝑚


Solving above equation for rm the equation becomes,

𝑓𝑓𝑚𝑚 =60𝜌𝜌2𝜋𝜋𝑛𝑛

=60 x 462.082 x π x 1800

= 2.45𝑓𝑓𝛿𝛿 = 29.4𝑖𝑖𝑛𝑛 Substituting the length and the mean radius of the blade in the area equation that has been obtained in terms of inner and outer radius of the equation becomes,

𝐿𝐿𝑓𝑓𝑚𝑚 =0.09737

𝜋𝜋

Solving the equation in terms of L to obtain the desired length of the blade and is given as,

𝐿𝐿 =0.09737𝜋𝜋𝑓𝑓𝑚𝑚

=0.09737𝜋𝜋 x 2.45

= 0.01265𝑓𝑓𝛿𝛿 = 0.1518𝑖𝑖𝑛𝑛

Substituting the length and mean radius in equation the outer radius and inner radius of the blade can be determined and is given as,

𝑓𝑓𝑓𝑓 − 𝑓𝑓𝑖𝑖 = 0.1518𝑖𝑖𝑛𝑛 Also,

𝑓𝑓𝑓𝑓 + 𝑓𝑓𝑖𝑖 = 29.4𝑖𝑖𝑛𝑛 Solving the equation simultaneously allow to obtain the inner and outer radius of the blade as,

𝑓𝑓𝑓𝑓 = 14.8𝑖𝑖𝑛𝑛 𝐴𝐴𝑛𝑛𝑑𝑑 𝑓𝑓𝑖𝑖 = 14.6𝑖𝑖𝑛𝑛 Now once the length, inner, outer and mean radius for the blade is calculated, the number of blades is the other required parameter and it can be determined using the following formula that is given as,

𝑁𝑁 =2𝜋𝜋𝑓𝑓𝑚𝑚𝑐𝑐

The Zweifel factor (Ψ) is required to be assumed in determining the s-axial chord, in general for the designing requirements it is suggested to assume and is given to be 0.85. But, mathematically the Zweifel factor is given as,

Ψ =2𝑐𝑐𝑙𝑙

(𝛿𝛿𝑚𝑚𝑛𝑛𝑐𝑐2 + 𝛿𝛿𝑚𝑚𝑛𝑛𝑐𝑐)𝑐𝑐𝑓𝑓𝑐𝑐2𝑐𝑐 Solving the above equation in terms of s the equation becomes,

𝑐𝑐 =𝜓𝜓𝑙𝑙

2(𝛿𝛿𝑚𝑚𝑛𝑛𝑐𝑐2 + 𝛿𝛿𝑚𝑚𝑛𝑛𝑐𝑐)𝑐𝑐𝑓𝑓𝑐𝑐2𝑐𝑐


Substituting Ψ = 0.85 and b ≈ c (chord Length) = 2.0 in = 0.166 ft the equation determines the axial chord and is given as,

𝑐𝑐 =𝜓𝜓𝑙𝑙

2(𝛿𝛿𝑚𝑚𝑛𝑛𝑐𝑐2 + 𝛿𝛿𝑚𝑚𝑛𝑛𝑐𝑐)𝑐𝑐𝑓𝑓𝑐𝑐2𝑐𝑐=

0.85 x 0.1662 x (𝛿𝛿𝑚𝑚𝑛𝑛(20)𝑓𝑓 + 𝛿𝛿𝑚𝑚𝑛𝑛(62.26)𝑓𝑓) x 𝑐𝑐𝑓𝑓𝑐𝑐2(62.26)𝑓𝑓

= 0.14374𝑓𝑓𝛿𝛿 Therefore the axial chord value can be substituted in number of blades determining equation to calculate the number of blades are required for the following design and is given as,

𝑁𝑁 =2𝜋𝜋 x 2.450.14374

= 107 The above analysis shows that there 107 blades are required to design the impulse turbine blade for the power plant. Finally the efficiency is required to determine for the single impulse stage and is given as,

𝜂𝜂 = 4𝜌𝜌𝜌𝜌2�𝑐𝑐𝑓𝑓𝑐𝑐𝑐𝑐2 −

𝜌𝜌𝜌𝜌2�

𝜂𝜂 = 4 x 462.081216

x �cos(20)o −462.081216

� = 0.85 Therefore the efficiency for the following designed impulse stage turbine is found to be 85%


Over a last decade the importance of the efficiency of the stem turbine has been much improved and increased. In this modern era the manufacturers are very much interested in using the combination of the impulse and a reaction turbine due to the fact that there is hardly pure impulse turbine is seen in the market these days. In determining the equation in analysis part the law of conservation of energy has been used to derive those equations. Since the energy is always conserved therefore the main purpose of the steam turbine is to transform the heat to the mechanical work by means of the rotational motion. Another important aspect of designing the stages of turbine is to understand the relationship between the velocity and the mass flow rate that are directly proportional to each other. Therefore both the mass flow rate and the velocity will affect the momentum and the force at the blades, which finally provides the work out put as a result. Finally the designing the first two stages are the important in such a way that allows the designer to choose the parameters such as the velocity of the steam that is coming in and leaving the blades, length of the blade, shape and size of the blade as well. All these parameters are designed during these two first stages of an impulse turbine helps in understanding the whole steam turbine cycle regardless the process consists of many cycles.


Acknowledgement

1. Cengel A. Yunus, Boles A. Michael, Thermodynamics An Engineering Approach, Vapor and combined Power Cycle, pg#551-576, 5th edition.

2. http://en.wikipedia.org/wiki/Hero_of_alexandria

prof. dr. rishi raj design of an impulse turbine blades ...ssh-cv-engineering.webs.com/impulse...

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