Project Report - Complete 2

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More than 70% of total power generation in India is contributed by steam

and gas turbines and improving the efficiency of these turbines is of prime

importance. Average life of a thermal power plant is about 30 years. Cost of

installing new capacity is much more than the capacity obtained by improving

the performance of existing units. New blades have very smooth surface finish

and fine profile, but as the turbine operates under severe conditions of

temperature and pressure, with usage the blade surface deteriorates under the

combined effect of corrosion, erosion and deposits. In the turbines, the steam

flows between the blade passages of fixed and moving blades and due to the

movement of the fluid, there is constant wear of the blade surfaces. Some solid

particles come along with the steam and hit the blade surfaces. Also, there are

salts dissolved in steam that get precipitated and deposited over the blades. In

some cases erosion is more dominated while in other cases corrosion or

deposits are more significant, depending on the conditions prevailing in the

turbine. These factors adversely affect the blade surface, leading to increase in

roughness. All these badly affect the blade profile of the turbine which gets

distorted.

The deterioration of the surface finish has direct effect on the efficiency

of the turbine, leading to increase in losses. Turbine blade roughness is one of

the major contributors to losses, this has been confirmed from steam path

audits conducted at Vindhyachal, Ramagundam and many others power

stations of National Thermal Power Corporation Limited.

The primary objective of this project is to numerically study the effect of

change in blade profile due to roughness on the turbine efficiency. On the

model of rectilinear cascade of turbine blades, discretization will be done with

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the help of Gambit, with various grades of roughness at different positions.

Then Fluent is used on the flow through the blades. From the data, effect of

roughness on mass average loss coefficient, total and static pressure

coefficient, turbulence kinetic energy, turbulence intensity, Mach number willbe studied.

Samsher [1] had conducted experiments in wind tunnel to study the

behavior of fluid with three levels of roughness for three different blade

profiles. He applied nine different patterns of roughness on each of the three

different blade profiles after studying the roughness pattern observed in

various running turbines. Then Behera [2] had numerically studied the effect of

roughness of one profile used by Samsher [1] up to roughness level of 178 m.

First the same model of a rectilinear cascade of smooth blades was

made; similar to one used by Samsher [1] and Behera [2] and meshing was

done with the help of Gambit. The mesh was checked for the equi-skewness

angle and aspect ratio. Then model was tested on fluent after setting proper

operating and boundary conditions. The static pressure, total pressure, velocity

angle was then measured at the measuring plane at 15% downstream of the

cascade and static pressure was also measured at the blade suction and

pressure surface compared with the experimental results of Samsher [1].

Profile losses were calculated from the model and this was compared with the

experimental results.

After the validation of model with the experimental results of the smooth

profiles, the model of rectilinear cascade was made with a layer of roughness

over the smooth blades, which was equivalent to the roughness generated by

the deposits on the actual turbine. After proper meshing and testing, this model

was used in Fluent and the parameters as discussed above were measured at

the measuring plane. Again these results were compared with the experimental

results of Samsher [1]. After the validation of cascade of rough blades, this

model was used to determine static pressure, total pressure, velocity angles for

the different levels of roughness encountered in actual turbine and profilelosses were calculated at different levels of roughness. Data related to the

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roughness pattern in actual running turbines was collected from various

running units. And this model was subjected to different levels of roughness at

higher Mach numbers prevailing in the modern turbines and profile losses were

calculated.

By determining the effect of roughness on the efficiency of the steam

and gas turbines, various decisions regarding the replacement of the blades

can be taken with improved certainty. Based on this information a cleaning

schedule can be made and updated regularly and methods can be developed

for improving surface finish. Losses occurring due to change in blade profile

and due to increase in roughness can also be ascertained.

After the validation of model the profile losses were calculated at the

Mach number encountered in running turbines and the effect of roughness was

studied from 0 to 500 m of roughness on the entire surface of blades. The

velocity angle, turbulent kinetic energy and turbulent dissipation rate was also

studied at the higher Mach number prevalent in modern turbines.

The report has been organized in the following sequence. An overview

of the related literature has been given in Chapter 2. Description of modeling

domain, governing equations used, selection of turbulence model, boundary

and operating conditions applied on the cascade have been described in

Chapter 3. Results followed by discussions are presented in Chapter 4.

Conclusions and scope for future work is presented in Chapter 5. References

are presented after Chapter 5, followed by appendixes.

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The review of published literature on the related aspects has been

presented in this chapter. Samsher [1] and Behera [2] has already done

literature review on the same aspect, the literature which appeared later or not

covered by them has been presented in this chapter. The studies have been

organized in the following broad categories, viz., roughness mechanism,

roughness measurements, and effect of roughness on blade performance

(experimental and computational works), products and software status,

conclusions from literature survey and scope of present study. A glossary of

terms has been presented in Appendix 1.

The irregularities on turbine blade profiles are called surface roughness.

The roughness on turbine blade profiles is caused by corrosion, erosion,

deposition or combined effect of all these. The three different mechanismswhich cause roughness have been explained briefly.

2.1.1 Corrosion

Dissolved oxygen present in steam water cycle contributes to corrosion

induced roughness in turbine blades. The pitting and crevice corrosion primarily

affects LP blades and rotors. However, these localized corrosion processes can

also affect HP and IP turbines, particularly in creviced areas. McCloskey [3]

found that pitting and crevice corrosion have two deleterious effects. The

damage is produced, acts as a local stress concentration of steady state and

cyclic stresses, and it allows the formation of stagnant corrosion cells where

corrodent concentration can proceed.

2.1.2 Deposits

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Chemical compounds are soluble in superheated steam, and their

solubility sharply decreases as the steam expands through the turbine. As this

occurs, deposition proceeds. There is a direct relationship between the high

levels of steam impurities, concentration of those impurities in steam pathdeposits, and subsequent damage or failures of turbine components. Even if

failures do not occur, deposits can result in considerable loss of capacity and

efficiency. Deposits results in lower unit capacity and efficiencies. Efficiency loss

occurs when deposition (or corrosion) results in increased surface roughness,

disrupting the flow. The deposits on turbine blade are shown in Figure 2.1.

Figure 2.1 Roughness caused by deposits on turbine blades M/s Encotech.

2.1.3 Erosion

Solid particle erosion is caused by oxide scale that exfoliated from high

temperature boiler surfaces including superheater, reheater tubing, outlet

headers, main and hot reheater piping. It becomes entrained in the steam flow

to the turbine causing erosion of the steam path and turbine components

especially turbine blades. Erosion causes not only wear and alteration of blade

and nozzle profiles but also increases surface roughness as shown in Figure

2.2.

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Figure 2.2 Roughness caused by solid particle erosion of turbine diaphragm

(NTPC Vindhyachal).

Schofield [4] explained that damage from solid particle erosion is

widespread in the turbine, but it was most severe in the first stage

nozzles/stators of HP and/or IP turbine. Following initial damage to the first

stages of HP and IP turbine wear progressed through the other stages of HP

and IP turbine, although it is not uncommon for it to miss a row. In the initial

stage of the HP turbine, damage usually initiated at the trailing edge, andconcave side of the stationary elements. Damage also occurred to the leading

edges of initial stage nozzles from direct impact of particles. In rotating

elements of the first HP stage, damage occurred to either leading or trailing

edges. In case of heavy erosion damage, the leading edge which was typically

slightly rounded got converted to knife edge. There was also significant erosion

at the root and tip passages and in the steam balance holes. In the first stage

of the IP turbine, damage is usually most severe on the convex side, trailing

edge, of the stationary vanes (nozzles foils). Damage also occurred to the

leading edge, to the pressure surface, to blade covers, tenons, and to trailing

edges.

As previously noted, the surface roughness of real turbine blades can

vary significantly. Because of this variation, it is both necessary and helpful to

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develop an analogous relationship between differing surfaces. In order to do

so, several statistical parameters can be applied to characterize each surface.

Some of the more common parameters used to describe surface roughness are

average centerline roughness, Ra, root-mean-square roughness, Rq, andmaximum peak-to-height roughness, Rt. Additional parameters may include

surface skewness, Sk, and kurtosis, Ku.

Figure: 2.3 Roughness Trace from Erosion Panel Bennett [5]

Average centerline roughness is typically used to describe machined

surfaces Bennett [5]. It is measured along a line of length L, as shown in

Figure 2.3, and is defined as the mean surface level such that equal areas of

surface lie above and below it. The mean surface level can mathematically be

written as:

oyN

i

i ==1

(2.1)

Where N is the number of elements measured along the trace length L.

Ra is the measure of the variability in a given set of data and provides

one with the average of the absolute deviations of the surface heights from

their mean. Ra is mathematically given by:

=

=N

i

iyN

R1

a1

(2.2)

The root-mean-square roughness is the most important statistical

parameter and is typically used to describe the finish of optical surfaces. It is

defined as the square root of the average of the squares of the surface heights

from their mean surface level and can be written as:

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=

=N

i

iq yN

R1

21(2.3)

Rms roughness, like Ra, is also measured along the trace length L, but is

additionally dependent upon the surface area of the measurement and the

distance between the elements. Consequently, there is no specific rms value for

a given surface.

For surfaces composed of small, consistent roughness elements, Raand

Rq will be very similar. Conversely, if the surface has a significant number of

large peaks or valleys, the second order terms in Rqdictate the calculation and

Rqbecomes larger than Ra

The maximum peak-to-height roughness, Rt, is simply that, a measure of thetotal size of the elements. It is mathematically written as:

Rt =ymax ymin (2.4)

where ymaxis the largest positive deviation from the mean centerline and yminis

the largest negative deviation from the mean centerline.

Skewness, Sk, is a characterization of the degree of asymmetry of a

surface about its mean centerline and is written as:

=

=

N

i

i

q

k yNR

S1

3

311

(2.5)

The sign of skewness relates whether the deviations generally lie above or

below the mean centerline. Thus, bumps on a surface will result in a positive

skewness and pits or holes in the surface will, conversely, result in a negative

skewness. It is also noteworthy that skewness, like rms, is greatly governed by

its higher order term. As a result, Sk is more sensitive to deviations that lie

farther from the mean centerline

Kurtosis is defined as the relative peakedness or flatness of a

distribution compared with its normal distribution. A large kurtosis is

representative of peaked distributions while a small kurtosis indicates a

relatively flat distribution. Kurtosis is defined as:

=

=

N

i

i

q

u yNR

K1

4

3

11(2.6)

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2.3

2.3.1 Experimental works

Hamed et al. [6] investigated the turbine vane and blade materialsurface deterioration caused by solid particle impacts. The tests were

conducted in wind tunnel for coated and uncoated blade materials at various

impacts conditions. Surface roughness measurements obtained prior and

subsequent to the erosion tests were used to characterize the change in

roughness caused by erosion. With the help of experiment based particle

restitution models, numerical simulations for the three dimensional flow field

and particle trajectories through a low pressure gas turbine were employed to

determine the particle impact conditions with stator vanes and rotor blades.

The measurements indicated that both erosion and surface roughness increase

with impact angle and particle size. Turbine vane and blade surface

deterioration was strongly dependent on the turbine geometry, blade surface

material, and particle characteristics. Experimental results indicated that

erosion rate and surface roughness increase with the eroding particle impact

velocities and impingement angles and that large particle produce higher

surface roughness. Prediction based on the computed particle trajectories and

the experimental characterization of coated vane material indicated a narrow

band of high erosion at the vane leading edge and pressure surface erosion

increasing towards the trailing edge.

Hummel et al. [7] evaluated the aerodynamic performance of a turbine

blade via total pressure loss measurements on a linear cascade. The Reynolds

number was varied from 600,000 to 1,200,000 to capture the operating regime

for heavy-duty gas turbines. Four different types of surface roughnesses on the

same profile were tested in the High Speed Cascade Wind Tunnel of the

University of the German Armed Forces Munich and evaluated against a

hydraulically smooth reference blade. The ratios of surface roughness to chord

length for the test blade surfaces were in the range of 7.6x1006 to 7.9x1005.

The total pressure losses were evaluated from wake traverse measurements.

The Reynolds number dependency was measured.

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It was found that maximum loss increases due to surface roughness that

occurred at the highest Reynolds number tested. Maximum loss increases due

to the highest surface roughness analyzed was 40% at nominal flow conditions

compared to a hydraulically smooth reference blade. In addition to the tests acomparison to a loss model according to literature showed good agreement to

both the results from this test series and further data from literature.

Zhang et al. [8] investigated the effects of surface roughness on the

aerodynamic performance of a turbine vane for three Mach number

distributions (where M = 0.35 to 0.71), one of which resulted in transonic flow

and matched an arrangement employed in an industrial application. Four

turbine vanes, each with the same shape and exterior dimensions, were

employed with different rough surfaces. The non-uniform, irregular, three-

dimensional roughness on the tested vanes was employed to match the

roughness which existed on operating turbine vanes subjected to extended

operating times with significant particulate deposition on the surfaces. Wake

profiles were measured for two different positions downstream the vane trailing

edge.

The wakes become broader with increased roughness size or with

increased exit Mach number Mex due to higher advection velocities,

augmentations of mixing and turbulent transport, thicker boundary layers,

earlier laminar-turbulent transition and increased turbulent diffusion. Peak

values of total pressure loss coefficients also increased dramatically as Mex

increases. In general, these profiles were asymmetric because the effects of

surface roughness were much less apparent for positive y/cx values,

downstream of the pressure sides of the vanes. This was due to different

loading, different boundary layer growth, and different susceptibility to flow

separation on the different vane surfaces, which also caused the suction side

wakes (at negative y/cx) to be thicker than the pressure side wakes (at positive

y/cx). Overall, the wakes were pushed toward smaller y/cxvalues as they were

advected downstream (i.e. towards the vane suction side), regardless of the

level, uniformity, or variability of the roughness along the surfaces of the

vanes. Aside from this, the data from a vane with variable surface roughness

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showed different quantitative and qualitative trends compared to profiles

measured downstream of vanes with roughness spread uniformly over the

surfaces. This was partially due to different rates of boundary layer

development as different levels of roughness were encountered along the vanepressure surface.

Magnitudes of area-averaged loss coefficients YAgenerally increased as

either exit Mach number or equivalent sand grain roughness size increased.

The increases in YA magnitudes were especially substantial as the exit Mach

number increases from 0.5 to 0.7 for the smooth vane and the uniformly-

roughened vane with ks/cx= 0.0108. Mass-averagedloss coefficients Ypshowed

similar trends, since they also increasedas normalized mean roughness height

became larger for aparticular value of vane exit Mach number.

Yun et al. [9] measured mean line analysis of turbine efficiency

reduction due to blade surface roughness and conducted performance tests on

a low speed, single stage, axial flow turbine with roughened blades. They

reported that blade surface roughness severely degrades turbine efficiency.

The normalized total to static efficiency decreases by 8 % when both the stator

and rotor blade rows are roughed with sandpaper of ks = 106 m and by 19 %

with sandpaper of ks = 400. The efficiency penalty increased with increasing

roughness. A rotating turbines roughness was more sensitive to roughness on

the suction side of stator vanes than that on the pressure side. Roughness on

stator vanes increased loss through the rotor even when the rotor blades were

not roughened; however a roughened rotor does not affected loss across the

stator. Thus the roughened rotor induced a higher performance penalty than

roughened rotor. With increasing roughness, the flow coefficient corresponding

to maximum efficiency decreased, and this trend was captured with simple

mean line analysis.

Myers [10] conducted experimental and numerical studies to quantify

the aerodynamic degradation resulting from the presence of failed anti-icing

fluid on the upper surface of aircraft wings. Wind tunnel tests were conducted

on an un-swept wing of an NACA 4415 section with selected roughness profiles

applied to the leading edge, ahead of the aileron, with the same span-wise

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length as the aileron. Calculations were conducted for a two-dimensional NACA

4415 airfoil with aileron, a Fokker F-28 aircraft, an NASA LS(1)-0417 airfoil with

a flap, and the NACA 4415 wing-aileron studied in the wind tunnel, all with

varying amounts of simulated roughness.In the cases studied, decreasing the chord-wise extent of the roughness

had little influence on the magnitude of lift loss; presence of roughness at the

leading edge reduced the stall angle of attack by as much as 40; lift loss was

more pronounced for a downward aileron deflection than for an upward aileron

deflection; and increasing aileron deflection produced an increasing reduction

in maximum lift beyond stall. The roughness distributions studied, if applied to

only one wing combined with an attempt to rotate the aircraft to its maximum

allowable angle of attack at takeoff, could result in a significant loss of lift on

the wing together with loss of aileron effectiveness.

Zhang et al. [11] have determined the skin friction coefficients from

wake profile measurements. The method was applied to symmetric turbine

airfoils with rough surfaces, which operate in a compressible, high-speed flow

environment with Mach numbers in the free-stream flow just adjacent to the

airfoil ranging from 0.35 to 0.70. The roughness employed simulates that which

develops on operating turbine airfoils, over long operating times, due to

particulate deposition and due to spallation of thermal barrier coatings. Surface

roughness was characterized using equivalent sand grain roughness size.

Magnitudes of normalized equivalent sand grain roughness for the smooth

airfoil and two rough airfoils were 0, 0.00069, and 0.00164.

For the present airfoil, it was found that because of larger surface

roughness elements give thicker boundary layers at the airfoil trailing edge as a

result of higher turbulence transport levels and higher rates of free-stream fluid

entrainment. According to FLUENT 6.0 simulations, the differences in flow

separation extent and initiation near the airfoil trailing edge due to changing

surface roughness were very small for the present symmetric airfoil. Numerical

predictions also indicated that the flow around each of the airfoils tested was

fully turbulent or nearly fully turbulent along the length of each airfoil.

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With the same inlet experimental condition for each case, skin friction

coefficients for the rough airfoils, determined from the wake profiles of stream-

wise momentum, increased considerably as the magnitude of normalized

equivalent sand grain roughness size increased. For an inlet turbulenceintensity level of 0.9%, the skin friction coefficients for the smooth and two

roughened airfoils were 0.00192, 0.00637, and 0.00986, respectively. The

numerical prediction of the overall skin friction coefficient for smooth airfoil was

determined by using FLUENT 6.0 software.

The present skin friction determination technique was useful for any sort

of body in which different levels of surface roughness were considered. Here,

the values obtained were mostly due to surface shear stress forces along the

airfoils, however, the technique can be extended to also include the influences

of flow separation and form drag.

Budwig [12] measured the influence of realistic surface roughness on

the turbine blade flow and heat transfer. He measured the influence of realistic

surface roughness on the nearwall behavior of the boundary layer. He

achieved a turbulence intensity of over 5 % at the leading edge of the plate, to

model the elevated turbulence intensity that is found at the entrance to a high

pressure turbine. The results also reveal that the turbulence intensity decays in

the downward direction. This result was due to free stream acceleration and to

viscous dissipation. The experimental values of skin friction coefficient Cf rise

above the theoretical curve for the transitional range and after this range it was

just below the theoretical curve, which indicated that the boundary layer had

relaminarized. This relaminarization was due to strong favorable pressure

gradient.

Ellering [13] examined both the individual and combined effects of free

stream turbulence, pressure gradients, and surface roughness on skin friction

drag. The surfaces were not the usual approximated roughness, but instead a

scaled facsimile of actual turbine blade surfaces.

The statistical descriptors associated with a given surface could provide

great insight toward the surfaces physical appearance. The average centerline

roughness, Ra, commonly associated with equivalent sand grain roughness,

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was often used to predict Cf, but appeared inadequate in the specification of

skin friction effects. While the majority of the statistical descriptors yielded

insignificant relationships when compared to ks, skewness, kurtosis, and rms,

however, appeared to have a prevailing role in predicting skin frictioncoefficients, as panels having larger kurtosis generally resulted in greater

increases in shear drag. It was also found that increasing Reynolds number

exacerbates the effects of roughness.

As expected, increases in free stream turbulence resulted in increased

shear drag. When combined with roughness, the effect was worsened. This

was, again, further aggravated with increased Reynolds number. When the

combined effect of free stream turbulence and surface roughness was

compared to the sum of individual effects, it was found that the combined

measurements yielded consistently higher skin friction values than the

corresponding sum of the parts.

Though the pressure gradient tests were suspected due to the measured

pressure effects, the following qualitative comments were offered. When a

favorable pressure gradient was introduced, roughness effects were amplified.

Conversely, introduction of an adverse pressure gradient resulted in decreasing

roughness effects. Both pressure gradients, however, gave way to the

exacerbation seen at higher Reynolds numbers. In performing the pressure

gradient tests, it was also found that smoother surfaces were typically

dominated by the pressure forces seen at the leading and trailing edges,

whereas rougher surfaces were generally subjected to the shear forces.

Samsher [1] has conducted experiments in wind tunnel to study the

behaviors of fluid with three levels of roughness for three different blade

profiles. He applied nine different patterns of roughness on the each of the

three different blade profiles. He selected the three profiles one nearly, impulse

and two of different degree of reaction for testing. Six blades were assembled

in a rectilinear cascade at the designed stagger angle, pitch-chord ratio and

inlet flow angle, shown in Figure 2.4. The blower supplied air to the cascade

and the same was exhausted to ambient. Reynolds number based on exit

velocity and chord were 3.6 5.0x105. Static and total pressure at cascade

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inlet, static pressures on blade surfaces, and total and static pressure at 15 %

of chord downstream of the cascade outlet were measured and with the help of

these data profile loss coefficient and static pressure coefficient were

calculated.The profile loss coefficient increased with increase in roughness; the

rate of performance deterioration was high at smaller roughness and it reduced

at higher roughness. The entire pressure or suction surfaces with small

roughness have comparable detrimental effect; however for higher roughness

of 50 grade the detrimental impact was more with the roughness on the

suction surface. The shifting of wake towards the suction surface was

maximum when roughness was applied over the entire suction surface and also

at mid-chord region of suction surface, whereas shifting of wake towards the

pressure surface was less and limited when roughness was applied over the

entire pressure surface and localized roughness over the pressure surface.

Figure 2.4 Experimental set up of rectilinear cascade of blade Samsher [1]

The roughness over the entire suction surface was more detrimental

than that over the pressure surfaces for all the profiles (impulse as well as

reaction). The comparison of loss coefficients with identical roughness over the

suction surface leading edge, the mid-chord and trailing edge reveals that for

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higher roughness (50 grade) on impulse and reaction blades (entire blade of a

real turbine), mid-chord was most sensitive followed by trailing edge and then

leading edge. But for lower roughness values, leading edge region of impulse

and high reaction blade was more sensitive than that of trailing edge, whereasfor moderate reaction blade, the trailing edge was more sensitive. For similar

roughness at identical localized places over the suction surface, the most

detrimental location was the root profile followed by mid height section

(moderate reaction) and tip. Similarly, for the pressure surface for higher

roughness over the impulse and reaction blade profiles, mid-chord region was

least sensitive whereas leading and trailing edge regions were almost equally

detrimental. For lower roughness on impulse blades, leading and mid-chord

regions were almost equally detrimental and trailing edge region was least

sensitive. Similarly, for identical roughness (50 grade) over identical localized

places over pressure surface, for root section was most sensitive followed by

higher reaction and then moderate reaction.

The non uniformity of flow in pitch wise direction at the exit of a row of

blades has undergone a considerable increase with increase in level of

roughness over the blades for each profile compared to the corresponding

smooth blades. This was the result of the combined effect of increased

roughness and thicker trailing edges.

As the discharge pressure was low, the experiment could not be carried

out at higher Reynolds numbers and higher Mach numbers. Also data on skin

friction, turbulence kinetic energy, turbulence intensity, Mach number at all

locations is not available.

2.3.2 Computational works

Shan et al. [14] studied a direct numerical simulation with high-accuracy

and high resolution numerical methods to investigate the details of the flow

separation and transition over a NACA 0012 airfoil with an attack angle of 40

and a Reynolds number of 105 based on the free-stream velocity and the airfoil

chord length. The simulation included a two-dimensional case and a three-

dimensional case. The two-dimensional case was designed to study the flow

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separation and unsteady flow structures within the separated shear layer, while

the three-dimensional case was used to simulate both flow separation and

transition to turbulence.

In the two-dimensional simulation starting initially from the uniform flowfield, the first sign of the instability appeared in the near wake region as the

free shear layer responded to the background perturbation. The disturbances in

the near wake might have propagated upstream in the form of acoustic waves

and introduced a disturbance to the separated shear layer over the upper

surface of the airfoil. Since the free shear layer was inviscidly unstable via the

KelvinHelmholtz mechanism, the streamwise growth of the disturbance

resulted in oscillations of the separated layer and eventually leads to vortex

shedding.

The initial flow of the three-dimensional simulation was obtained from

the two-dimensional simulation results. No three-dimensional disturbance was

enforced in the simulation. The origin of three-dimensional instability that

emerges in the simulation came from the near wake region, where intensive

interactions between the large-scale vortical structure and the wake occurred.

The three-dimensional instability seemed to be self-sustained and lead to

transition to turbulence. The three-dimensional simulation results, showed the

correlation between the re-attachment and the transition, might shed light on

the separation control for an airfoil. For example, the disturbance introduced by

unsteady blowing would excite the inherent local instability wave and lead to

early transition to turbulence, which would reduce the size of separation zone

by an early reattachment.

Thakker and Hourigan [15] compared a three dimensional computational

fluid dynamics (CFD) analysis with empirical performance data of a 0.6 m

impulse turbine with fixed guide vanes used for wave energy power conversion.

Pro-Engineer, Gambit and Fluent 6 were used to create a 3-D model of turbine.

A hybrid meshing scheme was used with hexahedral cells in the near blade

region and tetrahedral and pyramid cells in the rest of the domain. The turbine

hub to tip ratio of 0.6 and results were obtained over a wide range of flow

coefficients.

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The torque produced by the turbine was predicted well. Certain

simplifications were make in the model, which were expected to lead to lower

prediction of loss and this was borne out in the comparison of the predicted

pressure drop across the turbine and the experimental results. The modelyielded a maximum efficiency of approximately 54 % as compared to a

maximum efficiency of around 49 % from experiment. The model also

predicted maximum efficiency at a higher flow coefficient than was obtained

from experiment.

Kang et al. [16] numerically investigated the blade roughness effects on

performances and flows of axial compressor and axial turbine stages. A wall

function option for roughened wall boundary condition was available in

TascFlow code. Flow calculations on the flat plate with various roughness

showed that normalized wall velocity drop due to roughness was coincidence

with that of Prandtl-Schlichtings empirical relation.

One-dimensional analyses were carried out to inspect the contributions

of absolute flow angles and loss coefficient. The boundary layer thickness

becomes thick with the roughness so that the boundary layer constricted flow

passage to change flow angles at the inlet and outlet and resulted in extra

pressure loss. They observed that even a small amount of roughness in

compressor critically affect the performance. Rather when roughness height

was sufficiently high enough to be in the fully rough regime, the performance

values became less sensitive to roughness. There were also similar reports of

sensitivity of the performance to small roughness height. For the turbine,

efficiencies decreased as the roughness height was increased, while work

coefficients show opposite trend. Efficiency drop due to roughness was also

completely affected by the loss generation.

Wissink [17] performed direct numerical simulations of flow through a

LPT passage to provide data for the development of turbulence models to be

applied in turbo-machinery applications and to further the understanding of the

underlying flow dynamics. The larger angle of attack of the inflow was kept in

the simulation, combined with a lower Reynolds number and a smaller angle

with which the wakes enter the computational domain. The larger angle of

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attack increased the adverse pressure gradient along the downstream half of

the suction side. As a result, during phases with no or a very low level of

incoming and/or impinging disturbances, the boundary layer flow was

separated. After some time the shear layer rolls up due to KelvinHelmholtzinstability, most likely triggered by incoming disturbances. Inside the rolls of re-

circulating flow, entrained disturbances were fostered resulting in the

production of large amounts of fluctuating kinetic energy. As the rolls move

downstream they gradually disappeared. Because of the smaller angle with

which wakes were introduced at the inflow plane, during some phases

elongated vertical structures were found along the upstream half of the suction

side. These structures were result of the stretching of wake vortices by the very

strong flow along the upstream half of the suction side boundary.

The elongated vortical structures found at the downstream half of the

pressure side during all phases, evidence of by-pass transition (in the present

simulation streaky structures were found) in the downstream half of the

boundary layer on the suction side and the accumulation of vorticity in the

bow-apex of the wake inside the LPT passage were among the most striking

ones.

Kalitzin et al. [18] studied the pattern of turbulent kinetic energy generated by

distortion and the effect of external disturbances on the boundary layer

transition. This was investigated with direct numerical simulation of grid

turbulence convected through a linear turbine blade cascade. Comparisons

were made with results from earlier computations of flow through the same

cascade with a turbulence free inflow and an inflow with migrating wakes.

The Direct Numerical Simulation (DNS) of blade passage flow with a grid

turbulence inflow confirmed an increase of turbulent kinetic energy inside the

passage towards the trailing edge of the pressure surface. Turbulence was

also amplified in the stagnation region near the leading edge of the blade. The

increase in turbulence kinetic energy was partly explained by the convection

process of the inflow turbulence. The consideration of different types of inlets

provided insight into the boundary layer transition on the blade surface. For a

turbulence free inlet, natural transition occurred near the trailing edge on the

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suction side of the blade. For the grid turbulence and wake inlets, bypass

transition occurred further upstream triggered by the convection of the inlet

disturbances to the boundary layer of the blade.

Behera [2] performed a computational study of rectilinear blade cascadeusing the same reaction blade profile used by Samsher in his experimental

setup with the help of commercially available software code Fluent. He had

applied a Reynolds number of 4.5 x 105 at the exit. Mass average loss

coefficient, static pressure coefficient over blade surface for different level of

roughness (applied over the entire blade surface) was computed and results

were compared with the Samshers experimental results and were found to

have a very good agreement. From experiment one cannot find skin friction,

turbulence kinetic energy, turbulence intensity, Mach number at all location for

analysis but with the help of computation methods these all can be studied.

For smooth blades the total pressure obtained from the computational

method in the wake zone was lower than experimental values by 6.5 %. The

width of wake obtained by simulation was more than the experimental results.

The exit angle was comparable at core flow region but slightly deviate at the

wake zone. The average exit angle at measurement plane obtained from

experiment was 63 as against 59 from computation.

For rough blades with 100 m roughness over the entire surface

predicted static pressure exhibited a good match with experimental results,

barring a few points in the semivaneless region. For the total pressure it was

observed that the wake from computation was different from that obtained

from the experiment. The experimental wake width was wider than the

computational wake and core flow region was more affected in the experiment

than the computation. For the profile loss peak values from the computation

were higher than experiment in the wake region.

The skin friction coefficient increased with increase in the level of

roughness. Width of the maximum skin friction coefficient also increased

towards the leading edge, with increase in level of roughness. This was due to

the boundary layer that got thickened from the leading edge for higher level of

roughness. So the thickening of boundary layer over the blade surface

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contributed a major loss component in the profile loss of the blade channel.

The effect of roughness on skin friction coefficient was more prominent in

suction surface than the pressure surface of the blade. The influence of

roughness on skin friction coefficient at leading edge was prominent, becauseof growth of boundary layer due to adverse pressure gradient experienced at

leading edge. In major portion of the pressure surface fluid flowed smoothly

with favorable pressure gradient, so skin friction coefficient was small. At the

trailing edge of pressure surface, the skin friction coefficient increased again

due to thickening of boundary layer. With the increase in roughness, the inlet

total pressure increased, where as the down stream total pressure decreased.

It was observed that the upstream pressure increased with increase in

roughness, the variation of total pressure increase with increase in distance

was not much. At the stagnation point the total pressure also increased with

increase in level of roughness. It was observed that the total pressure at wake

zone reduced with increase in level of roughness. For a smooth blade the total

pressure at minimum energy point was 96,000 Pa, it reduced to 90,000 Pa for

100 m blade roughness and it further reduced to around 87,000 Pa at 200 m

blade roughness. Also the low pressure area increased with increase in the

level of roughness.

The computation was not carried out for higher level of roughness as it

was limited only up to 178 m. Also the modeling was not done for higher

Reynolds numbers and Mach numbers under which are realistic for operating

turbines.

The turbine blades are produced by various manufacturers around the

world, with the advent of various CFD packages the blades are designed in

such a way that the total losses (primary and secondary) are minimized to gain

maximum efficiency. However, once these turbine blades are in service, there

is continuous deterioration of the blade surface due to erosion, corrosion or

deposits, which increase the surface roughness. Manufacturers do not

recommend any specific level of roughness for the replacement of turbine

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blades nor do they provide any roughness value up to which the turbine can be

economically operated.

There are various commercial CFD software packages which are used in

the design of new turbine blades, some of these are Gambit, Autocad, Fluent,

Star CD and CFX etc.; these can be used in evaluating the performance of the

turbines. The eSTPE computer program (by M/s Encotech) was used in steam

path audit of some units of NTPC. In this process dimensions of turbine internal

were taken and clearances of turbine seals were measured, along with the

roughness pattern on the blade and this data was fed to the computer, which

has vast data base related to clearances and roughness pattern. After

processing data, the software calculated various losses taken place in each

component of steam turbine.

It can be concluded here that roughness varies substantially from point

to point around the blade and roughness actually encountered over the steam

turbines is not so well characterized and documented. The related fluid

dynamics have been well-defined regarding roughness over the blades.Some

literature gives fundamentals of roughness formation and tries to quantify the

roughness. Few literatures were available for onsite measurement of roughness

of turbine during outage for example eSTPE computer program (by M/s

Encotech). Few published reports on computation methods for study of

roughness on turbo-machines were available.

The primary objective of this project is to numerically study the effect of

change in blade profile due to roughness on the turbine efficiency. Different levels

of roughness will be generated on three different profiles of the turbine blade and

static pressure, total pressure, velocity angles and profile losses will be calculated.

Then the model made will be validated with the available literature and

experimental results. If the results obtained from computation match with the

experimental work, then these models will be used to calculate the profile losses

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at different roughness levels and at higher Mach number which are actually

encountered in the steam turbines.

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The present work is to determine the profile losses on a rectilinear

cascade with various levels of roughness over blade surface computationally

using commercially available software FLUENT code. The FLUENT code is

based on finite volume technique and collocated grid method is used to

compute the flow domain. The wind tunnel consists of five flow channels using

six test blades placed in rectilinear cascade test section with appropriate

stagger angle, chord, pitch, and inlet fluid flow angle and inlet/outlet section for

fluid (air) to flow as shown in Figure 3.1, 3.2 and 3.3. The coordinates of all the

three profiles are given in Appendix 2.

Figure 3.1 Shape of turbine blade 6030 cascade model Samsher [1].

Profile 6030 and Profile 5530 are from last stage of LP turbine and are

reaction type, Profile 6030 is from the root of the blade and Profile 5530 is at

distance of 30% of blade height from the root. Profile 3525 is from the first

stage of HP turbine and is of reaction type.

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A 2 dimensional model of all the three profiles was created, with the

help of Gambit and the dimensions of the model were kept same as the

experiment performed by Samsher [1] from inlet measurement plane to exit of

the tunnel. The detail dimensions of the flow domain are given in Table 4.1.



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The model was divided into five parts and then each part was again

divided in to three parts. Then fine meshing (Quad-Map) was done on the

model keeping aspect ratio and equi-skewness angle under control. The

meshing of the curved portion of the cascade of the profile 3525 is shown infigure 3.4. After the completion of model, the quality of mesh was checked in

the Fluent. Then simulation was carried out by two dimensions double

precision method. The details of the options used on model in Fluent are

described in Appendix 3. The input data used in computation is given in

Appendix 4. Mass average loss coefficient, total and static pressure coefficient

over blade surface for different level of constant roughness were calculated

with the help of commercially available software fluent. With appropriate

boundary condition, the flow field was solved for different levels of roughness

and results were compared with corresponding experimental Samsher [1] data.

Figure 3.4 Meshing of the curved surface of Profile 3525 at location A.

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Cascade dimensions and flow parameter.

Parameters

Cascade of blade profile

Profile 6030 Profile 5530 Profile 3525

Cascade type Rectilinear Rectilinear Rectilinear

Inlet cross section 95 x 99.7 mm2 95 x 94.6 mm2 95 x 93.2 mm2

Type of test blade Reaction type Reaction type Impulse type

Chord (mm), c 50 50 50

Pitch (mm), S 22 24 29

Height (mm), l 95 95 95

Blade stagger angle 70 72 80

Inlet flow angle 65 52 40

Number of blades 6 6 6

Number of channels 5 5 5Working fluid Air Air Air

Inlet air temperature 30C 30C 30C

Reynolds number at

exit (Re2)

4.7 x 105 5.0 x 105 3.6 x 105

Roughness level 0 to 500 m 0 to 500 m 0 to 500 m

In the experiment the roughness on the model was provided by the pasting

emery papers of different grades on the smooth blade surface. The thickness of

emery papers of Grade 220, 100 and 50 was 0.35 mm, 0.44 mm and 0.76 mm

respectively. The nine different patterns of roughness were modeled These

were complete blade surface, complete suction and pressure surface and one

third each of pressure and suction surface at leading edge, mid chord and the

trailing edge. Separate model was developed for each pattern of roughness.

This thickness was added to the different positions in order to simulate samemodel for the computational work. The original profile and the extra layer of

thickness are shown in figure 3.5.

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Original

W ith extra laye

Figure 3.5 Profile 6030 original and with 0.35 mm of extra layer on surface.

Extra layer at TE

Original

Figure 3.6 Profile 6030 original and with 0.35 mm of extra layer on 1/3rd at

trailing edge of the pressure surface.

The fundamental governing equations solved for the fluid are as follows:-

1. The continuity equation.

2. The momentum equation.

3. The energy equation.

The general continuity equation in tensor notation is expressed as:-

mi

i

Suxt

=

+

)(

(3.1)

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The equation 3.1 is valid for both incompressible as well as compressible flow.

If the flow in which the density of the fluid remains constant, then the

continuity equation reduces to

mi

i

Sux

=

)( (3.2)

Where, is the density of the fluid,xi

is the divergent operator, ui is the

velocity vector of the fluid and Sm is the source term.

The conservation of momentum in an inertial reference frame in Cartesian

coordinate system is expressed as:-

ii

j

ij

j

ji

j

i Fgxx

puu

xu

t++

+

=

+

)()( (3.3)

Where p is the static pressure, ig is the gravitational body force, F i is the

external body force and ij is the stress tensor (which is expressed as below).

ij

j

i

i

j

j

iij

x

u

x

u

x

u

+

=3

2(3.4)

Where is the molecular viscosity and the second term on the right hand side

is the effect of volume dilation and ij is the Kroneckers delta.

The value of ij = 0 if, i j

= 1 if, i=j.

The conservation of energy equation is expressed as:-

)( Et

+ ))(( pEux

i

i

+

=ix

( '' ' jj ji

eff jhx

Tk

+ )effijju )( + Sh (3.5)

Where keff is the effective conductivity (k+kt, where kt is the turbulent thermal

conductivity) and jj is the diffusion flux of species j. The first three terms on

the right hand side of energy equation represent energy transfer due to

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conduction, species diffusion and viscous dissipation respectively. Sh source

term if any includes heat of chemical reaction.

The energy term E is further expanded as

2

2

iuphE +=

(3.6)

Where sensible enthalpy h is defined as

For ideal gases

= ' ''j jj hmh (3.7)And for incompressible flows

phmhjj j

+=

'' ' (3.8)

mjis the mass fraction of species j and enthalpy hj is expressed as

dTch

T

T

jpj

ref

= ',' (3.9)

In addition to the above three basic equations of flow, some other

equations are also solved depending on the nature of flow phenomenon

involved in the problem. For example, if swirling flow takes place in the flow

domain, then axial and radial momentum conservation equations are to be

solved, where the swirl velocity is included in the equation. Similarly, viscous

heating (dissipation) is important for compressible flows, PDF model in energy

equation for combustion process, energy source term for chemical reactions,

Boussinesq model for natural convection etc. The numerical solution of the

three basic equations of fluid flow gives a close approximation to the flow

problem for a steady and laminar flow. Most of the flow occurring in nature andengineering applications is turbulent. So treatment for turbulence is required to

have better solution to the problem.

Turbulent flows are highly irregular, unsteady, chaotic and always occur

at high Reynolds number. Turbulence is rotational and three dimensional and it

is characterized by high level of fluctuating vorticity. Turbulent flows arecharacterized by fluctuating velocity fields. These fluctuations mix transported

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quantities such as momentum, energy and species concentration and cause the

transported quantities to fluctuate. The instabilities are related to the

interaction of viscous terms and non linear inertia terms in the equations of

motion. This interaction is very complex: the mathematics of non linear partialdifferential equation has not been developed to a point where general solutions

can be given. The fluctuation of the transported quantities are of small scale

and high frequency, they are too computationally expensive to simulate directly

in practical engineering calculations. So the instantaneous governing equations

are time averaged, ensemble-averaged, or otherwise manipulated to remove

the small scales, which give a modified set of equations which are less

expensive to solve numerically. But the modified equations contain additional

unknown variables for which turbulence models are required to determine

these unknown quantities in terms of known quantities.

The most common used approach to address the turbulence effect on

flow is the Reynolds Averaged Navier-Stokes equation. The Reynolds Averaged

Navier-Stokes (RANS) equation represents transport equations for the mean

flow quantities only, with all the scales of the turbulence being modeled. The

approach of permitting a solution for the mean flow variable greatly reduces

the computational effort. A computational advantage is seen even in transient

situations, since the time step will be determined by the global unsteadiness in

the mean flow rather than by the turbulence. This approach is generally

adopted for engineering calculations. The most commonly used model -

and its variants, - and its variants, Spallart-Allmaras and the Reynolds

stress model (RSM) adopted the RANS approach for solving turbulent flow field.

In RANS approach, the solution variables in the instantaneous Navier-

Stokes equations are decomposed into the mean (ensemble-averaged or time

averaged) and fluctuating components. The velocity component in tensor

notation (3d) is expressed as

'

iii uuu += (3.10)

Where iu and iu' are the mean and instantaneous velocity components

Similarly for scalar quantities:

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' += (3.11)

Where denotes a scalar quantity such as pressure, energy, species

concentration.

Putting the values of flow variable into the instantaneous continuity and

momentum equation, the simplified equations are expressed as:

( ) 0=

+

i

i

uxt

(3.12)

( )''3

2ji

jl

lij

i

j

j

i

ji

i uuxx

u

x

u

x

u

xx

p

Dt

Du

+

+

+

= (3.13)

The above continuity and momentum equations have the same general

form as the instantaneous Navier-Stokes equations. Additional terms now

appear that represent the effects of turbulence, is called Reynolds stresses,

ji uu '' and must be modeled in order to close the modified momentum

equation.

The Realizable - turbulence model has been selected for the solution

of present problem (simulation of wind tunnel). The realizable - model is a

relatively recent development. This model is different from standard -

model in two aspects, this model contains a new formulation for the turbulent

viscosity and a new transport equation for the dissipation rate, , has been

derived from an exact equation for the transport of the mean square vorticity

fluctuation. From the name of the model it indicates that the model satisfies

certain mathematical constraints on the Reynolds stresses, consistent with the

physics of turbulent flow. Other two - models are not realizable. The

benefits of realizable - model is that it predicts more accurately the

spreading rate of both planar and round jets. This model provides superior

performance for flows involving rotation, boundary layers under strong

pressure gradient, separation and recirculation (as in case of flow past

aerofoil). Initial studies have shown that the realizable model provides the best

performance of all the - model versions for several validation of separated

flows and flows with complex secondary flow features.

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The modeled transport equations for and in the realizable -

model are:

)()(

j

j

ku

xt

k

+

=

+

jk

t

j x

k

x

+ kG + bG - - MY +Sk(3.14)

and

j

j

x

u

t

+

)()(

=

+

jk

t

j xx

+ SC1 -

+

2

2C +

SGCC b +31 (3.15)

Where C1 =

+ 5,43.0

, ijijSSS 2= and S= (3.16)

In the above equations kG is the turbulent kinetic energy due to mean

velocity gradients, bG is the generation of turbulent kinetic energy due to

buoyancy, MY is the contribution of fluctuating dilatation in compressible

turbulence to the overall dissipation rate, C2 and 1C are constants, and

are the turbulent Prandtl number for and respectively. These values are

computed as follows

kG = -i

j

jix

uuu

'' (3.17)

bG =it

ti

x

Tg

Pr

(3.18)

and is computed as = -pT

1(3.19)

For ideal gases the term is expressed as

bG =it

ti

xg

Pr(3.20)

MY =2

2 tM (3.21)

t = 2a

where is a is speed of sound (a = RT )

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When the roughness height is less than viscous sub-layer then the

surface is called hydro dynamically smooth surface. Modeling of wall roughness

was done using the law of the wall. Wall roughness has little influence upon

laminar flow. In turbulent flow, however, even a small roughness will break upthe thin viscous sub-layer and greatly increase the wall friction. Experiments in

roughened pipes and channels indicate that the mean velocity distribution near

rough walls, when plotted in semi logarithmic scale, has the same slope (1/k)

but a different intercept. Thus, the law of the wall for mean velocity modified

for roughness may be written as

w

puu *= )ln(

1 *

pyuE

k- B (3.22)

Where 21

4

1* Cu = and B is a roughness function that quantifies the shift

of intercept due to roughness effect. B depends, in general, on the type and

size of roughness. For a sand grain roughness B can be well correlated with

the non-dimensional roughness height

/*uKk ss =+

(3.23)

Where Ks is the physical roughness height and

2

1

4

1* Cu = (3.24)

The whole roughness regime is sub divided into three regimes viz. hydro

dynamically smooth, transitional and fully rough regime. And the value of B

is calculated by following formulae

For the hydro dynamically smooth regime (+

sk < 3~5)

B = 0

Transitional regime (2.25 90)

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B = )1ln(1 ++ sK KCk s

(3.26)

The modified law of the wall is then used to evaluate the shear stress at

the wall and other wall functions for the mean temperature and turbulent

quantities. For assigning the value of roughness constant Ks in FLUENT,

unfortunately a clear guide line is not available. But there is some experimental

evidence for non uniform sand grain, ribs and wire mesh roughness, the value

of the roughness constant Ks of 0.5 to 1 is more appropriate. When modeling of

roughness is to be included, the mesh size has to be taken care of. For best

result, the mesh height near to wall should be more than the roughness height

Ks.

Boundary conditions specify the flow and thermal variable on the

boundaries of the physical model. Therefore, boundary conditions are critical

components of the simulation and are important that the boundary conditions

be specified appropriately. The simulation shows that the Mach number

through the channel is more than 0.3, and does not become supersonic. So a

compressible flow solution is more appropriate. In compressible flow also

FLUENT solves the standard continuity and momentum equation, but the

computation of scalar quantity and density is to be computed using ideal gas

law. FLUENT recommends SIMPLE algorithm for compressible flow. For the

present simulation problem pressure inlet and pressure outlet boundary

conditions are used. A well posed set of inlet and exit boundary conditions for

this flow are:

For flow inlet plane - Inlet total pressure, inlet static pressure, inlet total

temperature, turbulent Kinetic energy and turbulent dissipation rate were to be

specified.

For flow exit plane - Exit static pressure, exit total temperature, turbulent

kinetic energy and turbulent dissipation rate were to be specified.

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The inlet total pressure and inlet static pressure are kept same as the

experimental work of Samsher [1]. The temperature at the inlet is calculated

from ideal gas equation, which is obtained by compressing pressure from

atmosphere to the total pressure at the inlet. The atmospheric temperature isassumed to be constant at 27 C, though in experiment it varied from 20 C to

35 C. As the variation in temperature is not very large the dynamic viscosity is

assumed constant at 27 C (Dynamic viscosity () = 1.846 510 N.s/m2). The

pressure outlet value at exit is assigned as zero gauge pressure, as the exit is

directly exposed to atmosphere.

FLUENT requires specification of transported turbulence quantities at

inlet and outlet, when flow enters a domain. The turbulent kinetic energy and

specific dissipation rate at the inlet and outlet are assumed uniform in the

present case. The turbulence quantities can be specified in terms of turbulence

intensity, turbulent viscosity ratio, hydraulic diameter, and turbulence length

scale. The turbulence intensity, I is the ratio of the root mean square of the

velocity fluctuations, u, to the mean flow velocity, uavg. The turbulence intensity

at the core of a fully developed duct flow can be estimated from the following

formula derived from an empirical correlation for pipe flows:

I =8/1)(Re16.0

' =HD

avgu

u(3.27)

The turbulence length scale l, is physical quantity related to the size of

the large eddies that contain the energy in turbulent flows. In fully developed

flows, l is restricted by the size of the duct, since the turbulent eddies cannot

be larger than the duct. An approximate relationship between l and the physical

size of the duct is as following:

I = 0.07L (3.28)

where L is the relevant dimension of the duct. The factor of 0.07 is based on

the maximum value of the mixing length in fully developed turbulent pipe flow,

where L is the diameter of the pipe. In a channel of non-circular cross-section,

L can be based on hydraulic diameter. In the present case, as the flow is

assumed fully developed, the hydraulic diameter is specified as L = DH. The

turbulent kinetic energy is derived from the turbulent intensity I as following:

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k =2)(

2

3Iuavg (3.29)

where uavg is the mean flow velocity.

The turbulent dissipation rate can be calculated from the turbulence length

scale l, by the following relationship:

=l

kC

2/34/3

(3.30)

where C is empirical constant specified in the turbulence model (approximately

0.09). From the above relations the values of turbulent kinetic energy and

turbulent dissipation rate are calculated for inlet and outlet and specified in

boundary conditions at inlet and outlet.

Behera [2] used mass flow boundary conditions at inlet, where velocity

is computed from the velocity head available at the inlet and this velocity is

used to compute the fluxes of all relevant solution variables into the solution

domain. After each iteration, the computed velocity is adjusted so that the

correct mass flow value is maintained. There are two ways to specify the mass

flow boundary conditions. The first is the mass flow rate and the second is to

specify the mass flux. If a total mass flow rate is specified, it converts internallyto a uniform mass flux by dividing the mass flow rate by the total inlet area

normal to the specified flow direction.

In the present problem, the total pressure and static pressure at the

inlet are available, so pressure inlet boundary conditions can be used. When

mass flow inlet boundary conditions are used, the velocity is calculated from

the pressure difference which is further used in calculating the mass, but in the

pressure inlet boundary conditions, there is no need of such calculations as

both total pressure and static pressure are directly available. For the blade

surfaces, wall boundaries are assigned and the roughness values are assigned

as per the solution requirement. And for the rest of bounded edges, wall

boundary conditions are prescribed.

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Operating pressure affects the solution in different ways for different

flow regimes. In a low Mach number compressible flow (like the present

simulation), the overall pressure drop is small as compared to the absolute

static pressure and can be significantly affected by numerical round off. Toavoid the problem of round-off error, the operating pressure (generally a large

pressure roughly equal to the average absolute pressure in the flow) is

subtracted from the absolute pressure. The relation between the operating

pressure, gauge pressure and absolute pressure is expressed as:

Pabs = pop + pgauge (3.31)

The location of the operating pressure is equally important when the

computational output is to be compared with experimental results. So the

location of the operating pressure is to be identified where the absolute static

pressure is known. In the present problem the pressure parameter at inlet is

known.

The operating pressure is considered 101325 Pa at the inlet measurement

point, at x = -0.165 m and y = 0 m

The measurement plane is at 7.5 % distance of chord distance as shown in

Figure 3.7.

Figure 3.7 Measurement plane at 15% of the chord.

The efficiency of cascade is expressed as Samsher [1]

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=shh

hh

21

21

= 22

2

2

sV

V=

2 (3.32)

= ( )( )spp

TTCTTC

20

20

=

0

2

0

2

1

1

T

TT

T

s

(3.33)

Where pC is the specific heat of air at constant temperature,T0 is the

temperature at inlet, T2 is the actual temperature at exit and T2s is the

temperature at exit when expansion in the cascade is isentropic.

In the cascade, the total and static pressures at outlet, P02 and P2

respectively and total pressure at inlet is P01, are measured with yaw probe and

total pressure probe. Therefore, in terms of the measured values, equation

3.33 can be written as:

=

1

01

2

1

02

2

1

1

P

P

P

P

s

(3.34)

Where

02

2

P

P=

0102

01

2

PP

PP

= ( )

01

020101

01

2

P

PPP

PP

=

01

0201

01

2

1P

PP

PP

=

201

201

01

0201

01

2

1PP

PP

P

PP

PP

(3.35)

or

02

2

P

P=

01

201

201

0201

01

2

1P

PP

PP

PP

PP

=

01

2

201

0201

01

2

11P

P

PP

PP

PP

(3.36)

Now substituting the value of P2/P02 from equation 3.36 in equation 3.34

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We have

=

1

1

01

2

01

2

201

0201

01

2

1

11

1

P

P

PP

PPPP

PP

s

Or

=

1

01

2

201

0201

1

01

2

1

01

2

1

01

2

201

0201

111

11

P

P

PP

PP

P

P

P

P

P

P

PP

PP

s

(3.37)

The profile loss coefficient y is calculated using the relation proposed by Dejc

and Trojanovskij [19], expressed as

y = 1- (3.38)

Substituting the value of in equation 3.37, we have

y = 1-

1

01

2

201

0201

1

01

2

1

01

2

1

01

2

201

0201

111

11

P

P

PP

PP

P

P

P

P

P

P

PP

PP

s

(3.39)

On simplification the above equation and putting value of P2 = P2s (as both

points are on same pressure line), equation 3.38 is expressed as follow

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y =

1

01

2

201

0201

1

01

2

1

01

2

201

02011

01

2

111

111

P

P

PP

PP

P

P

P

P

PP

PP

P

P

s

s

s

s

ss

(3.40)

The effect of change of pitch distance on the profile loss is shown in Figure 3.8.

Figure 3.8 Profile loss coefficient versus relative pitch Samsher [1]

Where, P2s is static pressure at outlet of cascade, P01 and P02 are the total

pressures at the inlet and outlet of cascade respectively, is the ratio of

specific heats for air.

To calculate a single value of energy loss coefficient, the mass average

value of loss coefficient were calculated using the relation from, Yahya [20]

=

s

a

s

ay

dyV

dyV

0

0

(3.41)

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Where is the mass average loss coefficient, Va is the axial velocity, is the

density of air, S is the pitch distance and dy is the elemental length in pitch

wise direction.

The non-dimensionalized parameter static pressure coefficient at a location onthe blade surface is given as follows:-

Cp = 21

1

2

1V

PP si

(3.42)

Where Cp is the static pressure coefficient, is the density of air, Pi is the

static pressure at the location on the blade, P1s is static pressure at the inlet of

cascade and V1 is the velocity of air at inlet of cascade.

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The models were made with different mesh size and three different

turbulence models the k- model, RNG k- model and Realizable k- model

were selected. The mesh size varied from 75,000 cells to 4.48105 cells and

results were compared with the experimental values. For grid independence

test, results were compared in Realizable k- model at 75,000, 2.28105,

3.36105 and 4.48105 mesh size, it was observed that there were some

variations while increasing mesh size from 75,000 to 2.28105, but did not

differ much when mesh size was increased from 2.28105 to 4.48105 as

shown in Figure 4.1, hence the results were well with in 5 % of variation and

independent of mesh size after reaching 2.28105 mesh size.

-10

0

10

20

30

40

50

60

-0.5 0 0.5 1 1.5Pitch distance

Profilelosses 4.28 Lacs

0.75 Lacs

Expt

2.28 Lacs

3.36 Lacs

Figure 4.1 Effect of variation in mesh size from 75000 to 4.48105 on profile

losses.

Similarly for the different turbulence models compared, it was observed

that the k- model was closer to the results in the wake region but it was

predicting more losses in the core flow region. Where as the Realizable k-

model was showing good results in the core region but it was predicting slightly

more losses in the wake region. RNG k- model was predicting more losses in

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the core flow region. Figure 4.2 shows the profile losses as predicted by various

models.

0

10

20

30

40

50

60

70

-0.5 0 0.5 1 1.5Pitch Distance

ProfileLoss% Experimental

RNG-4.48

RKE-4.48

KW-4.48

Figure 4.2 Effect of different models on profile losses at mesh size of 4.48105.

Thus, it was decided to use the mesh size of 2.28105 with the

Realizable k- model in the subsequent work.

-10

0

10

20

30

40

50

60

-0.5 0 0.5 1 1.5x/l values

Profileloss%

MP at 10%

MP at 15%

MP at 30%

Figure 4.3 Effect of variation of measuring plane on profile losses.

Effect of variation in measuring plane on the profile losses is shown in

Figure 4.3. The result varied from 47% to 53% by when the position of

measuring plane is varied from 10 % to 30 % to the chord length of the profile

at the downstream of the trailing edge.

Profile 6030 (Smooth blade)

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The total pressure distribution over the entire computation domain is

shown in figure 4.4. The total pressure remains constant before the

compressed fluid enters the cascade section. After entering the cascade section

the total pressure reduces due to expansion of fluid over the cascade sectionand at the exit of the cascade the wakes are formed, where the total pressure

drops significantly, however in the core flow region, the pressure drop is very

less. At significant distance from the trailing edge the intermixing of the core

flow and the wake takes place and the total pressure drops. Width of the wake

depends on the pressure drop in the cascade section, higher is the pressure

drop and larger is the width of the wake.

Figure 4.4 Total pressure distributions in wake region for smooth blade in Pa.

The velocity vectors over the computation domain are shown in Figure

4.5. The fluid moves with constant velocity up to the inlet section of the

cascade. The velocity reaches its highest value when the fluid passes through

the throat section of the cascade. The velocity reduces afterwards when the

core flow and the flow in the wake region mix. The flow further reduces in the

diverging portion of the model before finally escaping in to the atmosphere.

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Figure 4.5 Velocity vectors in wake region for smooth blade cascade (velocitymagnitude in m/s).

The experimental values and the computational results are compared for

the three different factors; these are profile loss in percentage, velocity angle

and the static pressure coefficient Cp. The profile loss and velocity angles are

measured at the measuring plane, which is at 15% of the chord length of the

blade profile. The static pressure coefficient Cp is calculated, which is a non

dimensional factor. The static pressure coefficient is plotted against the

percentage cord length from the leading edge, positive values of x/l

corresponds to the pressure surface and negative values of x/l corresponds to

the suction surface.

Computation was done for all the three profiles 6030, 5530 and 3525

each with three different layers of roughness and with nine different locations

of roughness on each profile and the results obtained from each computation is

compared with the experimental results shown in Appendix 6.

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Table 4.1 Comparison of profile loss coefficient at measuring plane with

experimental values of Samsher [1] and computational values of Behera [2]

x/s values Experimental values

in % Samsher [1]

Computed values ( y)

in % Behera [2]

Computed values ( y)

in %-0.36 0.3 0.235 0.544

-0.27 0.2 1.34 0.68

-0.18 0.3 7.73 3.16

-0.09 8.7 46.2 25.05

0 28.3 41.28 44.2

0.09 10.2 8.47 26.64

0.18 1.9 3.76 8.45

0.27 0.4 0.67 5.23

0.36 0.3 0.33 3.29

0.45 0.3 0.37 2.01

0.55 0.3 0.23 0.9

0.64 0.3 0.36 0.520.73 0.3 1.29 0.79

0.82 0.1 7.85 3.64

0.91 10.7 45.88 28.63

1 29 53.17 46.63

1.09 3.8 14.8 20.98

1.18 0.4 2.9 8.14

1.27 0.3 0.48 4.95

1.36 0.3 0.256 2.79

1.45 0.4 0.31 0.62

Table 4.2 Comparison of specific pressure coefficient Cp at blade surface with

experimental values of Samsher [1] and computational values of Behera [2].

x/l values Experimental valuesSamsher [1]

Computed values (Cp)Behera [2]

Computed values (Cp)

-0.083 -0.614 -0.37 -0.395

-0.159 -1.595 -0.81 -0.995

-0.258 -2.674 -1.51 -1.707

-0.485 -3.155 -2.62 -3.08

-0.598 -3.402 -2.87 -3.431

-0.727 -3.269 -3.19 -3.6530.064 -1.193 -1.15 -1.171

0.155 -0.608 -0.54 -0.768

0.264 -0.351 -0.47 -0.563

0.445 -0.459 -0.3 -0.421

0.564 -0.580 -0.36 -0.464

0.700 -1.159 -0.53 -0.652

The comparison of the computational values of profile losses over the

measuring plane for smooth profile 6030 with the experimental values of

Samsher [1] is shown in Table 4.1 and comparison of the computational values

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of specific pressure coefficient Cp over the blade surface for smooth profile

6030 with the experimental values of Samsher [1] is shown in Table 4.2. The

experimental and computational values match well with each other for

validation purpose.For the profile 6030, which is a reaction profile, the profile losses match

well with the experimental results. However, the velocity angles observed in the

experimental values show a large variation, but in computational values there is

not much variation. There is slight variation in the velocity angles in the wake

region in the computational values but variation in the velocity angle in the

experimental results is quite substantial. The results for static pressure

coefficient Cp match very well between the experimental results and the

computational values. These values also obey the expected theoretical trends.

For the profile 5530, this is also a reaction profile, the profile losses

match well to the experimental results. The experimental results are slightly on

the higher side. The velocity angles observed in the experimental results show

a large variation but the velocity angles observed in the computational results

does not vary much but there is small increase in the wake region. The velocity

angle was experimentally checked again and it was observed that the

maximum variation in the velocity angle is only 5 for profile 5530 with smooth

surface. Thus experimental results were not repetitive. The results for the

computational static pressure coefficient Cp match with the experimental

results. There are very few values of experimental results in the leading and

the trailing edges of the blades, due to difficulty in providing probes in very thin

region. So the trends in these regions cannot be compared with the

experimental results. However, these trends match well with the published

literature.

The profile 3525 is the impulse profile; the computational values of the

profile losses match with the trends of experimental results; however the losses

observed in the experiment are quite less than the losses obtained in the

computational values. The velocity angle in this profile matches better than the

earlier two profiles. In some computational results the velocity angle follows

quite closely the experimental results and also there is a large variation in the

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velocity angles which are not observed in the computational results earlier. The

static pressure coefficient varies quite closely in the experimental as well as the

computational results. These also match well with published literature.

4.3.1 Effect of change in Mach number for smooth profile

The experimental work on wind tunnel was done at Mach number

ranging from 0.3 to 0.4; however the modern steam turbine runs at much

higher Mach number ranging from 0.6 to supersonic values. The profile 6030

under consideration has optimum values of Mach number from 0.65 to 0.95

and the best point lies at 0.8 Mach number. Similarly the profile 3525 has

optimum values of Mach number from 0.85 to 1.1 and the best point lies at

0.85 Mach number. So the computations are carried around these Mach

numbers.

Profile3525

0.4

0.5

0.6

0.7

0.8

0.9

-0.5 0 0.5 1 1.5x/l values

MachNo.atMP

MP at 5% of Chord MP at 15% of Chord

Figure 4.6 Comparison of Mach number at different position of measuringplane.

Comparison of Mach number at different positions of the measuring

plane is shown in Figure 4.6. When the measuring plane is at the distance of

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15 % of the chord length from the trailing edge of the cascade, the Mach

number varies from 0.65 to 0.77 and when the measuring plane is at distance

of 5 % of the chord length from the trailing edge of the cascade, the Mach

number varies from 0.71 to 0.86, which is very close to the optimum value ofthe profile which is 0.85. However, as in the experimental work the measuring

plane was considered at 15 % of the chord length and the profile losses,

velocity angle are compared at the same position.

For comparing results at higher Mach number the total pressure is

increased from 105.184 kPa to 150 kPa while keeping the static pressure

100.458 kPa. The total pressure distribution in computation domain for smooth

blade at 150 kPa inlet total pressures is shown in Figure 4.7. Here the total

pressure is constant up to the blade cascade then after passing through the

cascade, there is large drop in total pressure at the outer bend, where the flow

is maximum, but the pressure drop in the wake region is small at inner blades.

Figure 4.7 Total pressure distributions in Pa fo

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