Conjugate heat transfer.pdf

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Numerical evaluation of the blade cooling for the supercriticalsteam turbine

W1odzimierz Wrblewski*

Institute of Power Engineering and Turbomachinery, Silesian University of Technology, Konarskiego 18, 44-100 Gliwice, Poland

h i g h l i g h t s

< Numerical solution of the CHT problem for the blade channel of supercritical steam turbine.

< The determination of the potential possibilities of using the martensitic steel for the first blades.

< Different cooling steam parameters, different turbulence levels of the main flow and the thermal barrier are examined.

< The obtained results determine the thermal potential of the applied method of the blade cooling.

a r t i c l e i n f o

Article history:

Received 11 June 2012

Accepted 26 October 2012

Available online 7 November 2012

Keywords:

Steam turbine

Blade cooling

Conjugate heat transfer

a b s t r a c t

Steam turbine systems for supercritical parameters are one of the most important directions of the

development of conventional power plants. A steam turbine working in such cycles has to be adjusted to

operation with higher and higher steam temperatures. The aim of this analysis is to determine the

cooling conditions of the blades of the steam turbine first stage. The cooling is supposed to ensure that

the same materials as those used for the live steam temperature of 873 K are used for the first blades

operating with the live steam temperature of 923 K. In the calculations the Conjugate Heat Transfer

(CHT) model is used to simulate the following phenomena: the fluid flow in the blade-to-blade cascade,

the heat transfer in the blade and the coolant flow in the holes. Analyses of different cooling steam

parameters and of different turbulence levels of the main flow are performed. The problem is analysed

for the steam conditions corresponding to the first blade of High Pressure (HP) and Intermediate Pressure

(IP) turbines, respectively. For the HP turbine the on-blade thermal barrier is considered as an additional

mean to reduce the metal temperature to the limit required.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

The development of modern power engineering technologies

using gas and coal fuels is motivated mainly by the increase in the

power generation efficiency and a reduction in the environmental

impact of such systems. One of the directions to achieve these

objectives is the rise in the working medium temperature at thethermal turbine inlet. This concernsboth the gas and steam turbine.

Steam turbine systems for supercritical parameters are one of

the most important directions of the development of conventional

power plants. Due to such technologies, it is possible to obtain the

efficiency of electricity generation exceeding 50% [1]. Therefore, the

steam turbine working in cycles with the steam supercritical

pressure will have to face higher and higher thermal loads. It is

anticipated that the steam temperature in the planned supercritical

power units will be by 50e100 K higher than in supercritical plants

already in service. Achieving the respective temperature and

pressure values exceeding 900 K and 30 MPa at the inlet calls for

particular attention paid to the turbine nodes operating in these

conditions. Designing them, the choice has to be made between

using a new material which is more resistant to thermal loads butexpensive, or introducing thermal screens and organising local

cooling in the flow system. The former will require a wider appli-

cation of materials made of nickel alloys. The latter might allow the

use of materials which are currently used in facilities with lower

steam parameters. The influence of thermal screens and external

cooling on the rotor thermal load in the live steam inlet area was

investigated by Kosman [2]. Design solutions specific to supercrit-

ical steam turbines make it possible to keep the thermal load and

stresses in the turbine components at a reasonable level [2].

Theapplication of convective cooling to theblades of thefirst stage

of the HP and IP parts of the steam turbine for supercritical steam* Tel.: 48 32 2371971; fax: 48 32 2372680.

E-mail address: [email protected].

Contents lists available at SciVerse ScienceDirect

Applied Thermal Engineering

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a p t h e r m e n g

1359-4311/$ e see front matter 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.applthermaleng.2012.10.048

Applied Thermal Engineering 51 (2013) 953e962
mailto:[email protected]://www.sciencedirect.com/science/journal/13594311http://www.elsevier.com/locate/apthermenghttp://dx.doi.org/10.1016/j.applthermaleng.2012.10.048http://dx.doi.org/10.1016/j.applthermaleng.2012.10.048http://dx.doi.org/10.1016/j.applthermaleng.2012.10.048http://dx.doi.org/10.1016/j.applthermaleng.2012.10.048http://dx.doi.org/10.1016/j.applthermaleng.2012.10.048http://dx.doi.org/10.1016/j.applthermaleng.2012.10.048http://www.elsevier.com/locate/apthermenghttp://www.sciencedirect.com/science/journal/13594311http://crossmark.dyndns.org/dialog/?doi=10.1016/j.applthermaleng.2012.10.048&domain=pdfmailto:[email protected]


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parameters is an additional option which may be considered for new

designs. Only convection cooling shouldbe taken into account for this

case due to the parameters of steam which are available in the steam

cycle and which may be used as the cooling agent.

In the search for solutions to problems related to the cooling of

steam turbine blades, the experience gained from research con-ducted on the cooling of gas turbines should be employed. Tracing

back the evolution of cooling techniques in these turbines, it turns

out that at first convection cooling solutions were used. More

effective cooling systems were introduced later, such as film cool-

ing or transpiration cooling. Dunn [3] analyses a wide spectrum of

problems related to the blade profile aerodynamics and the heat

transfer in various cooling methods applied in gas turbines.

To protect the gas turbine blade thermally, an on-blade thermal

barrier is used. The assessment of this solution for a selected gas

turbine was carried out in [4] using advanced numerical models.

This type of solution may also be considered as an option for steam

turbine blades.

In problems related to convection cooling of blades, the deter-

mination of theflowfieldparameters is the basis for the calculationof the heat transfer in the turbine components. Due to the very

complex flow structure and the high sensitivity of the heat transfer

conditions to changes in this structure, the accuracy of the heat

transfer coefficient calculations in the range of10% is considered

as good. In more complex areas, the differences between calcula-

tion results and measured values may reach 30% and more.

The progress in the development of computational methods in

the last dozens of years has allowed a transition from correlation

relationships on a flat plate, through the use of algorithms with

coupled solutions for the boundary layer and the main flow for

complex geometries, to methods based on solving NaviereStokes

equations. Despite that, taking account of all the flow modelling

phenomena is still a computational challenge. It is a difficult task

because in such problems the weak points of the turbulence andthe laminareturbulent transition models become more visible.

Many heat transfer problems in the turbine are analysed

assuming steady conditions. And this happens despite the fact that

the blade operating conditions are highly unsteady and the blade is

subject to the impact of the blade wake. Taking these phenomena

into account calls for a much longer computational time.

There is some hope for a more precise description of the flow

phenomena in the use of the Direct Numerical Simulation (DNS)

methods, with no application of procedures of averaging flow values.

However, these are not the methods that could be used for complex

geometrical systems in the very nearfuturefor thefluidflow problems,

especially in the coupled problems with the heat transfer in solids.

A detailed determination of flow structures is much more

signifi

cant in the case offi

lm cooling. For these problems, the

conjugate algorithm methods are extended with the Large Eddy

Simulation (LES) method, which however is much more demanding

towards the numerical mesh than the methods based on the

Reynolds-averaged NaviereStokes (RANS) equations and which

requires much longer computation times [5,6]. Coupling the LES

method with theheat transferalgorithmfor a gas turbine blade withfilm coolingis presented in [6]. However, theresults of the performed

simulations differ considerably in terms of quantity from the

experimental data obtained from the RANS computations.

Turbulence models thus remain, for the time being, the only

effective way for most analyses of technical issues. The modelling

methods which are most often used to model turbulence in fluid

flow and heat transfer problems in the blade-to-blade cascade are

the two-equation models of eddy-viscosity. These models are

a compromise between complexity and accuracy. Their usefulness

in terms of the heat transfer coefficient determination was studied

among others in [7] and [8]. In [8] comparative studies of the v2f

model were conducted in conjugate computations for a blade with

convective cooling. In [9] a comparative analysis is presented to

study the ability of three turbulence models to predict film coolingand to assess the influence of the grid type on the solution. The

results confirm that conjugate heat transfer models predict

a significant difference in the temperature predictions in compar-

ison with adiabatic models. The realizable ke 3, and the shear stress

transport keu (SST) turbulence models present a satisfactory

agreement with experimental data. The interaction between the

flow field and temperature field in the cooled blade makes it

necessary to combine the flow problem with issues related to the

heat transfer in a solid. The Conjugate Heat Transfer (CHT) calcu-

lations have their specificity and impose higher requirements,

especially on the flow part calculations. This concerns, among

others, the numerical mesh parameters near the wall to appropri-

ately determine the temperature profile of the boundary layer. The

publications presenting the solution to the Conjugate Heat Transferproblem for the turbine blade usually ignore the laminare

turbulent transition (e.g. [10e12]). The variability of the transition

models proves how difficult it is to model this phenomenon. A

comparative study of bypass transition models was presented in

[13]. The models were validated against experimental data from

different test cases including the turbine channel flow. The model

which has gained much popularity in engineering applications is

the Gammaetheta model (e.g. [14,15]). The reason for this is its

universality and availability in the ANSYS CFX software package.

Using transition models in the CHT calculations makes it

possible to obtain better results, both quantitatively and

qualitatively.

The gas turbine blade convection cooling technology may be

used for supercritical steam turbines. The modelling of thefl

ow

List of symbols

cp specific heat capacity at constant pressure, J/(kg K)

c chord, m

cx axial distance of chord, mH specific enthalpy, J/kg

h heat transfer coefficient, W/(m2 K)

k turbulence kinetic energy, J/kg

M Mach numberp static pressure, Pa

Re Reynolds number

s curvilinear coordinate from the leading edge along the

profile curve, mt/c pitch to chord ratio

T static temperature, Ky dimensionless distance

x axial coordinate, m

Greek symbols

l thermal conductivity, W/(mK)

r density, kg/m3

Indices

0 total parameters

1 inlet

2 outlet

c coolant

s isentropic

W. Wrblewski / Applied Thermal Engineering 51 (2013) 953e962954


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phenomena in such cases is more difficult due to the water vapour

parameters. Taking account of the specificity of the working and

cooling fluids by employing the appropriate real gas state equation

complicates finding the solution to the conjugate task and

lengthens the time needed for the computations. The use of the

CHT algorithm to analyse the gas turbine cooling with water vapour

is presentedin [16]. The use of the CHT algorithm for a closed steam

cooling system in a state-of-the-art steam turbine is described in

[10]. The works mentioned above use the perfect gas model with

various adjustments.

This paper formulates and solves the conjugate heat transfer

simulation task for convectively cooled blades of the steam

turbine. The aim of the analysis of the blade cooling conditions

performed for a selected configuration of cooling holes is to

provide a qualitative and quantitative assessment of the cooling

conditions of the first rings of the HP and IP parts of the turbine.

Due to the water vapour properties, it is essential to determine the

main flow field parameters in detail. In this respect, the real gas

state equation is used in the calculations and the impact of the

turbulence level at the blade channel inlet on the heat transfer

conditions is investigated. The calculations take account of the

laminareturbulent transition model. Also, the quantitative impact

of the change in the boundary layer character on temperaturedistributions on the blade is indicated. For the blade cooling

purposes, steam with various parameters (pressure and temper-

ature) which may be achieved at different points of the steam

plant cycle is assumed. The change in the cooling agent velocity is

also taken into consideration. Additionally, the effect of the

application of an on-blade thermal barrier is analysed and the

impact of the barrier on the thermal conditions is assessed. The

obtained results allow an assessment of the possibility of applying

the blade convective cooling for conditions in a supercritical

steam turbine.

The conclusions derived from the computations will make it

possible to formulate the blade geometry optimisation task with

the use of genetic algorithms according to the method described in

[17]. The optimisation algorithm used to analyse the blade coolingconfiguration of the steam turbine in [18] will be extended using

the CHT model.

2. General model description

In order to determine the temperature field of a blade washed

by water vapour with high temperature and cooled convectively by

water vapour flowing in the blade passages, it is necessary to:

- formulate the conjugate boundary value problem for the steam

flow around the blade together with conductive heat transfer

to the blade material and for the cooling steam flow in each of

the passages separately,

- to define and discretise the computational area,- to include in the analysis the laminareturbulent transition

conditions for the external flow,

- to use the real gas model.

The mathematical model that describes the fluid flow and the

heat transfer is composed of:

- the mass, momentum and energy conservation equations for

the fluid,

- the turbulence model,

- the laminareturbulent transition model equations,

- the energy conservation equation for a solid,

- the gas state equation,

- the relationships describing the material properties.

In allcases under analysis,the SSTversion of the keu turbulence

model is used. The SSTturbulence model was modified using Katoe

Launder formulation and curvature correction which are recom-

mended for such a problem. For the flow in the blade channel the

laminareturbulent transition is modelled using the Gammaetheta

model [15]. This model is related to the SST turbulence model and

consists two additional transport equations for the intermittency

and transition onset Reynolds number. The governing equations are

solved using the Ansys CFX software package procedures.

The basic equation closing the system of the conservation

equations is the gas state equation. For the validation performed for

gas turbine the ideal gas model is used. For water vapour it is

necessary to use the real gas state equation. As a result, many

relationships between thermal and calorific parameters have

a non-explicit mathematical form. This requires many additional

iterative procedures that have to be used in the solving algorithms,

which lengthens the time of computations.

The steam state equations recommended by the IAPWS (Inter-

national Association for the Properties of Water and Steam)

according to standard IAPWS-IF97 are used in the calculations.

Detailed formulae describing steam parameters may be found in

[19]. In computational programs such as Ansys-CFX, procedures are

used that make tables of steam properties in a specific range ofparameters with a pre-set accuracy.

In the CHT calculations the conduction equation in the solid

domain is included in the solver. The conduction equationis treated

as a degenerative energy equation of the fluid, where all velocities

are set to zero. This equation is solved numerically with the same

algorithm as the flow equations with the use a finite volume

approach. The CouranteFriedrichseLewy (CFL) time step condi-

tions for solving the transport equations for solid and for fluid

domains can be adjusted individually.

3. Validation test case: cooling of the gas turbine blade

Due to the lack of data for the steam turbine blade, the defined

model is verified using experimental data for the gas turbine blade.

In this case, the blade is cooled with air, using four simple holes

with a circular cross-section (Fig. 1). This configuration was

examined on the German Aerospace Center (DLR) test stand [20].

Owing to the announced experimental data, the selected profile is

a good instance for validation.

Fig.1. Mesh for validation calculations of the conjugate task for the blade with cooling

channels description.

W. Wrblewski / Applied Thermal Engineering 51 (2013) 953e962 955


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The basic turbine blade profile parameters are: the chord

c 0.0834 m, the pitch to chord ratio t/c 0.71, the blade-angle

setting in the cascade b 50.

The teststand with a cascade of profiles is fed with gas with total

temperature T0 794.5 K. The total pressure at the cascade inlet is

p0 0.15376 MPa, and the static pressure at the outlet is

p2 0.10217 MPa. These conditions correspond to the Mach

number M1 0.328 at the cascade inlet. The inlet angle of the mass

flow measured in the circumferential direction is a1 57.

The flow fluid used in the experiment is the gas obtained from

the combustion of aircraft kerosene (C14H30). The physical proper-

ties of the aircraft kerosene exhaust gases are very similar to those

of air, which results from the very high value of the air excess factor

during combustion. Therefore, it may be assumed that the exhaust

gases are replaced in the calculations with air treated as perfect gas.

For air, the dependence of specific heat on temperature is taken into

consideration.

The blade under analysis is convectively cooled with air flowing

through four holes. According to the data given by Heselhaus [21],

in the holes through which the cooling air flows, the boundary

conditions are assumed based on the values given in Table 1.

In the case under consideration, the cooling conditions are

assumed as constant, which results from the fact that the heattransfer coefficient and the cooling air temperature values are

assumed as constant, both on the hole perimeter and along the

height of the passage.

For the blade material, according to the literature data, the

following constant values of material data are assumed: density:

7900 kg/m3, specific heat: 585.2 J/kg K, conductive heat transfer

coefficient: 19 W/mK.

For the numerical calculations, the mesh (Fig. 1), containing

582,660 nodes in the flowarea and 72,072 nodes in the blade metal

area is assumed. In the boundary layer for the flow conditions

under analysis the value of y is smaller than 1.

For the turbine blade under consideration, the SST turbulence

model is used, and the laminareturbulent transition is modelled

with the Gammae

theta model.The temperature distribution on the blade surface obtained in

the experiment is used as validation data for the performed

calculations.

Fig. 2 presents a comparison of the calculated temperature

distribution on the blade surface with experimental data. It can be

seen that the temperature differences between the distributions on

the pressure side and in the first part of the suction side ranged

from15 to 30 K but the temperature differences in the secondpart

of the pressure side ranged from 55 to 2 K. Additionally, the heat

flux distribution on the blade is presented. On the suction side for s/

cw 0.65, an increase in the heat flux value is clearly visible. This

rise corresponds to the location of the laminareturbulent transi-

tion. The curvilinear coordinate s is in this case defined from the

leading edge along the profile curve. It may be assumed that thedistributions obtained near the leading and the trailing edge

feature a good concordance with the results of the experiment.

Bigger differences appear on the suction side. They may result from

the fact that the Gammaetheta model defined the beginning of the

laminareturbulent transition too early. The laminareturbulent

transition takes place on the suction side only. On the pressure

side the flow is laminar.

4. Model description for the steam turbine blade

4.1. Geometrical data

Due to the limitations on the availability of explicit experimental

and geometrical data for the real steam turbine, the task is analysed

based on the blade profile assumed for validation, adjusting its

geometry to the size which is typical of the steam turbine first stage

blade. The 0.6 scale is assumed for the profile. In each case the blade

is analysed as a cylindrical one, with a constant cross-section in theradial direction. The aimof the analysisconducted in this paper is to

indicate the potential possibilities of the steam turbine blade

cooling and to emphasise the essential problems related to this

solution. The simplifications employed at this level of thoroughness

should be considered as sufficient. This is also justified by the

relatively small Mach number and the slight change in the steam

temperature in the blade channel, which is presented below.

The computational area of the CHT task is divided into the

following (Fig. 3): the steam mainflow area (the blade channel), the

blade area (metal) and the areas of the cooling passages (passages

Table 1

Boundary conditions in the cooling holes.

Hole

number

Nu Coolant average

temperature Tav, K

Re Pr Heat transfer

coefficient h, W/m2 K

1 101.7 343.1 1.58$104 0.715 278.79

2 99.5 345.4 1.54$104 0.715 273.86

3 87.1 343.8 1.83$104 0.715 287.01

4 98.0 341.1 2.10$104 0.715 375.48

Fig. 2. Distributions of the temperature and the heat transfer on the blade surface for

validation calculations.

Fig. 3. Domains for the steam turbine blade cooling CHT task.



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in the blade and their extension), in which the heat transfer

problem is formulated separately.

The geometrical data for the blade are defined in the AutoCAD

program. The blade system geometry prepared in this way may be

directly used in programs generating a computational mesh. The

meshes are generated using the ANSYS ICEM program. The hexa

dominant type of mesh is employed in computational areas,

assuming structural meshes with clearly distinguished hexahedron

layers and elements near the walls.

The meshes in the main flow area are constructed according to

the recommendations for the appropriate boundary area model-

ling, to satisfy the needs of both the laminareturbulent transition

and the heat transfer task. Meshes with the value ofy smaller than

1, with the mesh increment rate in the range of 1.1e1.2 together

with 20e25 mesh lines in the layer area are assumed. Although

a developed turbulent flow is assumed in the cooling passages, due

to the requirements of the temperature profile, computational

meshes with similar parameters are used in the boundary layer. An

extension is added to the cooling passages at the inlet to allow the

development of the turbulent flow before the blade passage, where

the heat transfer with the solid domain of the blade takes place.

This makes it possible to improve the accuracy of the results in the

lower part of the blade.In order to reduce the task, the top and bottom surface of the

flow area, as well as the blade metal surface are assumed as

surfaces of symmetry. This makes it possible to eliminate the

boundary layer on these areas in the flow area.

The calculations are performed using the Ansys-CFX software

package. The geometry with a configuration offive holes: four non-

circular ones and one circular e GEO2 is considered.

4.2. Selected physical properties of the blade material

The selection of the assumed physical properties of the blade

material, apart from the correct determination of the fluid ther-

modynamic properties, is of fundamental importance in the

calculations of the flow field with heat transfer.In the conjugate heat transfer task under consideration it is

assumed that the blades are made of martensitic steel.The material

data for this type of steel are assumed based on the average values

given for steel used for turbine construction and designed for

operation in the analysed temperature range [22].

The martensitic steel density is assumed as r 7850 kg/m3, and

the specific heat is defined by the dependence:

c 0:46 0:000177T 4:67e 7T2; J=kg K (1)

The heat conductivity coefficient is approximated with the

function:

l 0:01801T 23:88; W=mK (2)

4.3. Formulation of boundary conditions

The conditions for the blade channel flow domain in the HP

turbine row are selected assuming that the isentropic drop in

enthalpy in the stator is DHs 15 kJ/kg. This results from the

distribution of the enthalpy drop in the HP turbine into 18 stages

and from the assumption that a stage reactivity is at the level of 0.4.

Taking account of the following steam parameters at the turbine

inlet: total pressure:p0 30 MPaand total temperature t0 650 C,

the value of static pressure after the blade row is assumed as

p1 28.82 MPa. It is assumed in the calculations that the pressure

value in the outlet cross-section is an average value. A similar

assumption is made for the inlet cross-section. The average total

parameters in the cross-section are constant.

Different values of total pressure and total temperature at the

inlet are assumed forthe cooling passages in order to determinethe

potential of the used steam for the purposes of blade cooling. At the

inlet, static pressure values are selected as they ensure moderate

velocity values in the cooling passage of approximately M 0.5. The

impact of the steam velocity in the cooling passage is analysedbelow.

Table 2 lists all the variants of the cooling passage geometry and

of the cooling steam parameters for the conditions corresponding

to the first blade row of the HP turbine.

The following marking convention is adopted for the variants:

WP_GEO2_yy_zzz_n_aaaawhere WP stands for the HP turbine,

GEO2 is the geometry symbol, yy is the total pressure at the cooling

passage inlet (bar), zzz is the total temperature at the cooling

passage inlet (C), n is the number of holes and aaaa provides

additional information concerning flow conditions.

For the first blade row of the IP part, the following total

parameters are assumed at the inlet: pressure p0 5.9 MPa and

temperature t0 670 C, which correspond to the parameters of

a supercritical thermal cycle. At the outlet, the selected staticpressure value is p1 5.695 MPa and it is assumed that this is the

average value in the outlet cross-section. This results from the

assumption that the isentropic drop in enthalpy at the stator is the

same as for the HP turbine DHs 15 kJ/kg. In the inlet cross-

section, the total parameters do not change along the blade height.

Table 3 lists all the variants of the cooling steam parameters for

the conditions corresponding to the first blade row of the IP

turbine. SP stands for the intermediate pressure part and the other

elements of the marking are the same as those for the HP turbine.

5. Calculation results for the HP turbine blade

The distributions of the main flow parameters in the blade-to-

blade channel of HP turbine do not vary significantly during thetesting. There are bigger changes only in the turbulence level

resulting from changes in the boundary conditions. The obtained

maximum values of the Mach number are about 0.3, which indi-

cates a subsonic flow with relatively small velocities.

Assuming that the turbulence level is 1%, at the passage inlet the

laminareturbulent transition is located quite early on the suction

Table 2

List of variants for the HP turbine blade.

No. Var ia nt T0c,C p0c, bar p2c, bar

1. WP_GEO2_50_310_5 310 50 42

2. WP_GEO2_50_327_5 327 50 42

3. WP_GEO2_64_330_5 330 64 54.2

4. WP_GEO2_64_390_5 390 64 54.2

5. WP_GEO2_95_360_5 360 95 80.1

6. WP_GEO2_95_450_5 450 95 80.57. WP_GEO2_95_360_5_Ma075 360 95 65.6

8. WP_GEO2_95_360_5_Tu01 360 95 80.1

9. WP_GEO2_95_360_5_Tu02 360 95 80.1

10. WP_GEO2_95_360_5_Tu05 360 95 80.1

11. WP_GEO2_95_360_5_Tu12 360 95 80.1

12. WP_GEO2_95_315_5_Tu12_Ma070 315 95 80.1

Table 3

List of variants calculated for the IP turbine blade.

No. Variant T0c,C p0c, bar p2c, bar

1. SP_GEO2_95_360_5 360 95 80.1

2. SP_GEO2_50_327_5 327 50 42

3. SP_GEO2_50_327_5_Tu12 327 50 42



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side of the blade (for x/cx about 0.2) (Fig. 4). Also on the pressure

side of the blade, the laminareturbulent transition is observed in

the front part of the blade. The character of the steam flow for the

assumed parameters differs from what is obtained from the vali-

dation calculations described in Section 3.

Fig. 5 presents the contours of the steam temperature distri-

bution in the blade channel during expansion. A slight difference in

temperature can be noticed, which is included in the range of 6 K.

This points to very similar thermal conditions on the whole blade

perimeter, which translates into strict requirements concerning the

blade cooling organisation in the entire cross-section.

After preliminary calculations, a configuration of 5 cooling

passages with an irregular cross-section is assumed for a further

analysis. The configuration of passages and the computational

mesh are presented in Fig. 6. The passages are placed in a relatively

uniform manner along the profile to achieve an appropriate cooling

effect in the entire cross-section. Passage 1 is moved closer to the

profile leading edge to ensuremore intense cooling in this area. The

circular passage is located as close to the trailing edge as possible to

limit the temperature rise in the trailing edge area. The numerical

mesh has 630,318 nodes in the main flow area, 488,649 nodes for

the five passages of the cooling steam area and 66,429 nodes in the

blade metal area.

5.1. The impact of the cooling steam parameters

Six variants of parameters of cooling steam with high pressure

are analysed. The steam pressureis selected based on a power plant

cycle for steam parameters of 30 MPa and 650 C. The selected

variants are those with possibly highest pressure and possibly low

temperature values. The temperature selection is limited by the

need to guarantee superheated steam in the cooling passages,i.e. to

eliminate the possibility of steam condensation. The variants under

analysis are listed in Table 4.

The blade temperature contour for the selected WP_GEO2_95_

360_5 variant is presented in Fig. 7. The chart in Fig. 8 compares the

temperatures on the wall blade in its tip cross-section. The differ-ences between the maximum temperaturesare not big and amount

to several kelvins. The laminareturbulent transition occurs in each

case at the same place, but for variants where the lowest temper-

atures are achieved it is observed that the temperature curve after

the laminareturbulent transition, despite the occurrence of the

turbulent boundary layer, is lowered further at a certain section of

Fig. 4. The turbulence level Tu contour (no cooling).

Fig. 5. Distribution of the steam temperature in the blade-to-blade channel (no

cooling).

Fig. 6. Cooling passages geometry and numerical mesh for the GEO2 confi

guration.



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the contour. This is evidence of intense cooling in this area of the

blade. The steam parameters of 95 bar and 360 C turn out to bethe

most favourable ones in terms of the obtained maximum blade

temperature. For these cooling steam parameters the maximum

blade surface temperature of 880 K is obtained.

5.2. The impact of the cooling steam velocity

Assuming an increased steam flow in the cooling passages,

calculations are performed for the cooling steam parameters:

p0c 95 bar, T0c 360 C, selected in the previous analysis. The

static pressure at the outlet is lowered from p1c 80.1 bar to the

value ofp1c 65.6 bar. The coolantflow is faster, reaching the Machnumber values of 0.6e0.75, depending on the heat transfer in

individual passages. Fig. 9 compares the distribution curves of the

temperature on the blade surface for different conditions of the

cooling steam flow in the passages. An increase in the mass flow

resulted in a slight reduction in the surface temperature by a few

kelvins only. In the trailing edge area, the obtained drop in

temperature is about 7 K. The maximum temperature on the blade

surface is on the suction side with the coordinate of about

x/cx 0.55. In terms of improvement in the cooling conditions, the

effect of a substantial rise in the coolant mass flow velocity is not

too big.

5.3. The impact of the main flow turbulence level

In the next step, the impact of the main flow turbulence level

on the blade cooling conditions is studied. The calculations

are performed for the following cooling steam parameters:

p0c 95 bar, T0c 360

C andp1c 80.1 bar. The basic case, in whichthe turbulence level before the passage is about 1%, and cases with

the turbulence level at the inlet of 2%, 5% and 12% are also

considered are shown in Fig. 10.

For the turbulence level of 12% the temperature is higher in the

front part of the blade near the edge. The temperature in the

remaining fragments of the cross-section changes only slightly.

Increasing turbulence to just 2% results in a shift in the laminare

turbulent transition towards the blade leading edge and a rise in

the minimum temperature by approximately 30 K. For higher

turbulence level values before the blade, the boundary layer is

turbulent on the whole perimeter of the blade. This causes a rise in

temperature on the leading edge by 20e25 K. The temperature of

the blade contour in the trailing part is only slightly higher, by a few

kelvins.Fig. 11 compares the heat transfer coefficient distribution on the

blade surface for the variants with the turbulence level of Tu 1%

Table 4

The set of cooling steam parameters for the GEO2 passage configuration.

No. Variant T0c,C p0c, bar p2c, bar

1 WP_GEO2_50_310_5 310 50 42

2 WP_GEO2_50_327_5 327 50 42

3 WP_GEO2_64_330_5 330 64 54.2

4 WP_GEO2_64_390_5 390 64 54.2

5 WP_GEO2_95_360_5 360 95 80.1

6 WP_GEO2_95_450_5 450 95 80.5

Fig. 7. Distribution of the blade temperature (variant WP_GEO2_95_360_5).

Fig. 8. Distribution of temperature on the blade profile for different parameters of the

coolant.



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and Tu 12%. The coefficient is determined based on the heat flux

in the blade surface at the assumed value of the fluid temperature

of Tbulk 923 K. The heat transfer coefficient for steam is very

high; for the Tu 12% variant it reaches values of approximately

65,000 W/m2 K in the leading edge area. The difference

between the coefficient distributions is significant and reaches

30,000 W/m2

K.

5.4. The impact of the thermal barrier

As presented above, the cooling of the HP turbine first blade is

not an easy task. The cooling has to be rather intense in the entire

cross-section, and the steam and metal properties cause substantial

temperature gradients in the blade. Therefore, the application of

the thermal barrier on the blade surface is considered.

One of the methods of blade protection used in gas turbines is

a thermal barrier in the form of a ZrO2 coating. Zirconium dioxide,

as a ceramic material, features a low heat transfer coefficient of

0.8e3 W/(mK). It is assumed for a comparative analysis that on the

blade surface there is a zirconium dioxide coating which creates

heat transfer resistance

R d=l 5e 5

m2K.

W; (3)

where d is the coating thickness. The calculations are performed for

the variant WP_GEO2_95_360_Tu12. A much better temperature

equalizing is visible than in the case of the variants analysed

previously. The metal maximum temperature is substantially lower.

This can be seen in Fig. 12, which compares the blade surface

Fig. 9. Distribution of temperature on the blade profile for different mass flow values

of the coolant.

Fig.10. Distribution of temperature on the blade profile for different turbulence levels.

Fig. 11. The heat transfer coefficient distribution on the blade surface (variants

WP_GEO2_95_360_5, WP_GEO2_95_360_Tu12).

Fig. 12. Temperature distributions for variants WP_GEO2_95_360_Tu12 and

WP_GEO2_95_360_Tu12_coating.

Fig.13. Distribution of temperature on the blade profile for different flow parameters

(IP turbine).



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temperature distributions in the tip area for the variants with and

without the thermal barrier. The use of a ceramic coating causes

a drop in the blade surface temperature by 60e80 K.

The obtained temperature level after the application of the

thermal barrier for the assumed cooling parameters turns out to be

lower than required. Consequently, it is possible to limit the blade

cooling by: reducing the cooling steam mass flow, raising the

cooling steam temperature or changing the thermal barrier

parameters. The cooling steam temperature of 733 K makes it

possible to obtain maximum temperatures lower than 870 K.

6. Calculation results for the IP turbine blade

The calculations for the IP turbine blade are conducted for the

GEO2 geometrical configuration of the cooling passages. The IP

turbine blade is about four times higher than the HP turbine blade.

The boundary conditions for the calculations are presented in

Section 4, and the cooling steam parameters are listed in Table 3.

The assumed drop in enthalpy in the stage is the same as the

enthalpy drop in the HP turbine stage. Because of that, the distri-

butions of relative flow parameters in the blade channel are very

similar. The change in the pressure value is included in the range of

0.3 MPa, and the maximum Mach number in the channel reachesa moderate value of 0.29.

Three variants of the flow conditions analysed for the IP part

blade are selected as characteristic after the testing conducted for

the HP turbine. Consequently, in the first variant the comparative

conditions for the cooling steam assumed for the HP turbine,

namely p0c 50 bar, T0c 327 C and the turbulence level Tu 1%,

are considered. The next analysed variant is the one with

p0c 95 bar, T0c 360 C and Tu 1%, and then the first variant

with the turbulence level at the inlet increased to 12%. Quantita-

tively changes in temperature can be examined in more detail in

Fig. 13. For flows in which the laminareturbulent transition occurs

on the blade, the blade surface reaches the lowest temperature

values at the level of 710 K. The part of the blade with a laminar

flow is cooled down very intensely. In the trailing edge area, themaximum temperature reaches 835 K. Such temperature values are

lower than 873 K e the value assumed as permissible for metals. It

can be seen that in all these cases the blade material temperature is

relatively low. So, it is much easier to cool the IP turbine blade than

the HP turbine one. Therefore, the appropriate level of maximum

temperature may be obtained reducing the cooling steam mass

flow. In the temperature distributions locations can easily be

noticed where the laminareturbulent transition occurs:x/cx 0.1

for the pressure side and x/cx 0.6 for the suction side.

For the variant with a high level of turbulence, the blade surface

temperature is higher and reaches the maximum value of 851 K on

the leading edge of the profile.

7. Conclusions

The subject matter of this analysis is the determination of the

potential possibilities of using the same materials for the first

blades of a steam turbine with the live steam temperature of 923 K

as those used for the live steam temperature of 873 K.

The employed computational conjugate heat transfer simula-

tion model for the steam flow in the blade channel, of the heat

transfer in the blade and of the cooling steam flow in the passages

allows a comprehensive assessment of the phenomenawhich occur

during the heat transfer.

Analyses of different cooling steam parameters and of different

turbulence levels of the main flow are performed. The presented

results of the analyses indicate that the steam expansion conditions

in thefi

rst blade row cause that the blade operates in very balanced

thermal conditions on the entiresurface. The cooling of the blade of

the HP turbine using 5 cooling passages is a complex task due tothe

relatively large fluxes of transferred heat and to the material

properties of water vapour and metal: very high heat transfer

coefficients for steam and a high heat conductivity coefficient for

metal. It is shown that it is possible, from the thermal point of view,

to select such geometry of passages and such steam parameters

that the temperature in the blade is kept below 873 K. The most

critical points that need particular attention in the blade cooling are

the leading edge and the trailing edge.

The cooling of the IP part blades is a much easier task compared

to the cooling of the HP turbine blades. The required cooling effect

may be achieved with more moderate parameters of the cooling

steam. This allows a much easier matching of the cooling condi-

tions to the temperature level, avoiding significant temperature

gradients.

The character of the flow in the blade channel, the location of

the laminareturbulent transition and the turbulence level all have

a substantial impact on the heat transfer conditions.

The obtained results determine the thermal potential of the

applied method of the blade cooling. However, due to significant

temperature gradients, they require a strength verification. In order

to reduce the temperature gradients, solutions should be found tosupplement the cooling, such as a replacement of the material with

one that features a reduced heat conductivity coefficient (in the

calculations the average value from the different material data is

assumed) or an introduction of the thermal barrier at the places

most exposed to high temperatures, i.e. in the leading and trailing

edge areas.

The results of the analysis can be use to formulate assumptions

and boundary conditions for the blade geometry optimisation task.

Acknowledgements

The results presented in this paper were obtained from research

work co-financed by the Polish National Centre of Research and

Development in the framework of Contract SP/E/1/67484/10 eStrategic Research Programme e Advanced technologies for

obtaining energy: Development of a technology for highly efficient

zero-emission coal-fired power units integrated with CO2 capture.

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