Full Paper Title (Times New Roman 14)

Proceedings of the 12th International Symposium on Experimental Computational Aerothermodynamics of Internal Flows 13-16 July 2015, Lerici, Italy _________________________________________________________________________________________________

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Aeroacoustic performance of a labyrinth seal with smooth or honeycomb land Artur Szymański 1, Sławomir Dykas 2, Włodzimierz Wróblewski 2, Mirosław Majkut 2 1 Institute of Power Engineering and Turbomachinery, Silesian University of Technology. Konarskiego 20, 44-100 Gliwice, Poland. E-mail: [email protected]

2 Institute of Power Engineering and Turbomachinery, Silesian University of Technology. Konarskiego 20, 44-100 Gliwice, Poland

Abstract This article presents a detailed Computational Fluid Dynamics (CFD) analysis of unsteady flow field behavior in labyrinth seal regions, paying special attention to vorticity and broadband noise generation. Also an impact of the sealing structure on the flow behind the rotor has been checked. For numerical calculations a commercial software Ansys CFX has been deployed. All analysis shown in this paper were performed by means of Unsteady Reynolds Averaged Navier Stokes (URANS) method coupled with the Scale-Adaptive Simulation (SAS) hybrid turbulence model. For acoustic calculations the Fast Fourier Transformation (FFT) was adopted to obtain an aeroacoustic noise spectrum. To evaluate results, aeroacoustic pressure – p’ and Sound Pressure Level (SPL) values were used. For evaluating a leakage, a discharge coefficient was also inquired and compared. The CFD results have showed an influence of honeycomb structure on pressure fluctuations and noise damping. Keywords: labyrinth, honeycomb, seal, transient, gas turbine, FFT analysis

Introduction Labyrinth seals are very critical area in turbomachinery. They separate regions with high pressure difference to avoid the leakage. The most important parts where the seals are applied are tip clearance between axial stages and casing – both in compressor and turbine vanes, as well as gap between shaft and the stator vanes. The most common sealing solution in turbomachinery is labyrinth seal both with honeycomb and smooth land. Loss caused by leakage over the row of blades is the main reason of power and efficiency decrease, fluid temperature distribution disruption and rotordynamic instability. Moreover, flow through narrow cavities is responsible for aerodynamic noise generation. Due to these phenomena, quality of tip seals is fundamental to provide safe and reliable work. This work presents detailed time-dependent flow analysis of gas turbine stage model equipped with tip labyrinth seal against honeycomb and smooth land in order to identify the noise generated aerodynamically. The computational model consists of three domains, first domain simulate conditions occurring in front of the rotor blade, the third behind the blade. The second was the sealing structure domain. Two sealing structures were investigated, namely, honeycomb and smooth land. ISAIF12

The aerodynamic sound generation is an elaborate issue that occurs in aviation and turbomachinery flows. Improvement in reduction of exhaust gases and noise emission is required to provide comfort and safety of users. It was scientifically proven [1] that aerodynamic noise is health-threatening factor to human beings. Decrease of the aerodynamic noise is closely connected with an improvement of the energy conversion efficiency. Main sources of aerodynamic noise in gas turbines are combustion, exhaust flow, interactions between fluid and blades in flows through the compressor and turbine, and flows through narrow gaps in the secondary flows system, for instance through the turbine tip sealing. Because of those facts, engineers and scientist make strenuous efforts to improve of the flow conditions in mentioned regions. Wide range of sealing solutions is being considered in turbomachinery, such as film riding face seals, finger seals or brush seals. They reduce the leakage well, however they still are vulnerable to wear and require expensive maintenance. It is proven [2], that in turbomachinery applications the ratio between leakage in commonly used labyrinth seals and modern brush seal is 3:1. Despite those facts, labyrinth seals are still the most common 1

solution applied in gas turbines. Their main advantages are low investment and maintenance costs, resistance to high temperatures and destruction resulting from rubbing (friction of labyrinth fins on the casing) [3]. Despite many advantages, labyrinth seals working under high loads tend to generate unstable rotor work resulting in vibrations [4], which affects significantly the working comfort and safety. The forces generated in this type of seal are less sensitive to clearance changes, gaps and seal details. Due to this fact, a honeycomb land is applied against labyrinth seal. In high-pressure applications, good damping and positive seal stiffness bring about better rotor stability. During start-up or shutdown, seal clearance could reduce because of thermal effects. In steady state operation, pressure differences can also affect seal geometry. It is recommended, to use damper seals, typically of the hole-pattern or honeycomb type for gas turbine internals to ensure stability when working at high pressure. Experimental work done by [5] proves that honeycomb can provide up to fourfold increase in damping properties comparing to smooth land . This solution, applied in turbomachinery contributes to the rotor vibrations decay and increase of stability. As it was mentioned before, a flow through the axial sealing is a considerable source of noise generation. In order to estimate the noise an experimental research can be conducted, although their price, level of complexity and unfavorable conditions of measurement make it very costly and difficult to perform. Nowadays, the Computational Aeroacoustics (CAA) methods analyzing the generation of noise caused by turbulent flows, are an appropriate tool to predict the aerodynamic noise sources and noise propagation. A rapid development of the Computational Fluid Dynamics (CFD) software and IT industry grant to make acoustic simulations more effective and available in comparison with experimental research. To evaluate the noise resulted by the turbulent flow, the steady state (far field noise only) or unsteady (near-field and far-field noise) flow analysis can be applied. They require further calculations by external solver to obtain acoustic behavior based on calculated pressure distribution. For estimating an unsteady flow field some numerical approaches can be applied. Direct Numerical Simulation (DNS) methods are based on

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compressible Navier-Stokes equations solved without any turbulence models. DNS is the only method that directly resolves acoustic near-field and far-field scales directly. To provide the proper solution, the whole range of time and space scales must be resolved, i.e. short time steps, and very detailed grids ought to be applied. Large differences in length scale between acoustic and flow phenomena result in large hardware requirements and long computation time. This method is unsuitable for commercial use. Large Eddy Simulation (LES) method is the second method when accuracy is taken into account. It fully resolves large turbulence scale, and models small and dissipative scale. This method is a some compromise between the solution precision and computational effort, but it is still not commonly used in engineering applications. It is only affordable in academic research. The URANS method is based on the solution of unsteady Reynolds-Averaged Navier-Stokes equations. This method is well known and widely described. It is the least accurate comparing to LES or DNS, although it provides reasonable computational requirements. In acoustic near-field applications of the URANS method may give satisfactory results [6]. This article presents a comparison of the noise generation phenomena in low-pressure turbine labyrinth tip seal with and without honeycomb land by means of URANS numerical method with SAS hybrid turbulence model. Investigated tip seal geometry Geometrical model applied in described calculations represents simplified geometry of low pressure gas turbine rotor tip seal and a part of main flow channel [7]. Mentioned geometry is shown in Figure 1. The width of computational domain is equal to two cells of honeycomb. As is was proven by Wróblewski et al. [7] this simplification allows to determine axial components and flow structures of flow with satisfactory accuracy. Moreover, it has been experimentally proven by Waschka [8] and Paolio [3] that flow through the narrow circular rotating cavities – like sealing is circumferentially averaged. Due to that fact, the calculations of higher spans of fluid domain are irrelevant. In the Figure 1 the geometry of mentioned tip seal case is presented. Two structures against the labyrinth seal has been investigated – honeycomb and smooth wall. The whole geometry has been divided in three subdomains. Sub-domain 1 simulates the flow 2

conditions at the stator blades outlet (ahead of the rotor). By using the Inlet 1 and Outlet 1 boundary conditions the inlet parameters to rotor is modelled. Sub-domain 3 simulates the conditions behind the rotor. Outlet 2 represents static pressure in front of the next stage. The geometry of the tip seal consists of two oblique fins (sub-domain 2), located at radius of 743mm. Applied honeycomb cell size was assumed on the basis of the most popular solution [9]. In the Table 1 non dimensional geometrical parameters are presented, where d denotes a honeycomb cell size, s is a clearance between fin tip and casing, b represents a fin width at tip, h is a honeycomb cell depth, H is a fin height and L is a honeycomb structure length. Table 1 Non-dimensional geometrical parameters

s/d b/d h/d H/d L/d

0,243 0,256 2,88 3,2 12,16

Presented sealing geometry is a general solution and can be also applied in other machines, such as axial compressors, steam turbines etc.

allows to precisely resolve wide range of turbulence generated during unsteady flow. At the same time SAS model can adapt itself to already simulated vortex structures yielding good results in areas with intense turbulence, separation and mixing. It compromises classic viscosity model and LES or DES methods demanding high computation time [10]. The working fluid was air ideal gas. High temperature and low pressure allow to use this simplification [11]. Physical parameters of the fluid are presented in the Table 2. Dynamic viscosity and heat conductivity change at different temperatures have been taken into account by Sutherland formula. Table 2 Thermodynamic parameter of air

Reference total temperature Gas constant Specific heat ratio Heat capacity at constant pressure Dynamic viscosity for Tref Thermal conductivity for Tref Sutherland temperature Sutherland exponent

273 K 287 J/kg·K 1.4 1004.4 J/kg·K 1.71e-5 kg/m·s 0.024 W/m·K 110.4 K 1.5

Pressure fluctuations monitoring To evaluate the near-field noise production, seven monitor points were chosen. Their location in computational domain is presented in Figure 2. Presented points are located in the midspan of computational domain (in perpendicular direction). Parameters monitored in these points were pressure and velocity, their values were used for Fast Fourier Transform to analyze the amplitude and frequencies of pressure fluctuation. The location of monitor points remain the same for honeycomb, as well as smooth land geometry. This analysis allows to compare the impact of honeycomb structure on unsteady flow pattern.

Figure 1.Computational fluid domain of labyrinth seal and main flow channel

CFD model Presented calculations were obtained by means of commercial software Ansys CFX exploiting the URANS calculation scheme with hybrid SAS (Scale Adaptive Simulation) model. SAS model is based on modified URANS method. It ISAIF12

Figure 2. Fluid domain with marked monitor points (the same location for case with honeycomb structure)

Computational grid The computational grid consists of three sub-domains. Subdomains 1, 2 (part associated with

3

labyrinth) and 3 are hex-dominant type. Honeycomb structure has been modelled as an O-grid multiblock structured mesh, as shown in figure 3. Each cell in honeycomb structure is discretized in the same manner. The main mesh is joined to the honeycomb mesh at about a third of the height of the clearance over the fins. Figure 4 shows view on honeycomb mesh merged with main mesh. The non-dimensional parameter y+ describing the size of near wall element varies. In honeycomb structure y+ < 8, in the rest of near wall regions y+ < 1. The mesh of case with smooth wall against the labyrinth is presented in figure 5. Number of mesh nodes is 3 M for case with smooth land, and 3.8 M for sealing structure with honeycomb structure.

Figure 3. View on labyrinth against honeycomb mesh

Figure 4. Labyrinth with honeycomb mesh (area over the first fin is discretized in the same manner)

Figure 5. Labyrinth without honeycomb mesh (area over the second fin is discretized in the same manner)

The solution of CFD calculation should be mesh independent. For choosing the proper discretization,

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different labyrinth and honeycomb grid sizes was tested. Investigation revealed that for grids with 2M nodes or more, the solution deviation is irrelevant. The final mesh is presented in Figures 3,4,5 Boundary conditions Boundary conditions applied are representative for conditions of flow above the tip seal in gas turbine stage, widely presented in Bochon work [14], and refer to the boundaries marked in Figure 1. Conditions at Inlet 1 and Outlet represent parameters in front of rotor blades vane. Total pressure p0 = 58kPa, total temperature T0 = 700K, turbulence intensity was 5%, stationary frame inflow direction was 20⁰ in circumferential direction. Static pressure at outlet 1 was set to 55.4 kPa, with 0.05 average over outlet profile blend. Conditions at Inlet 2 and Outlet 2 represent parameter behind the rotor blades vane. Total pressure p0 = 58 kPa, total temperature T0 = 700 K, turbulence intensity was 5%, stationary frame inflow direction was normal – 90⁰. Static pressure at outlet 2 was set to 51.6 kPa, with 0.05 average over outlet profile blend. Reference pressure was 100 kPa. Transient calculations require precisely specified initial conditions. In this case initial conditions for transient calculations were results of steady state solution. Turbulence model used in steady state calculation was Shear Stress Transport. For transient calculations Scale Adaptive Simulation method has been applied, with High Resolution advection scheme, and Second order backward Euler transient scheme. Heat transfer model was assumed as total energy with viscous work enabled. The time step in transient calculation was 1e-6 s, which corresponds with Courant Number < 1. To evaluate the flow field properly, Courant Number should be always lower than 1 [13]. All domains were set up as rotating with 839RPM on radius equal to 743mm [14]. All walls have been set as adiabatic, hydraulically smooth. Results evaluation In sealing the leakage plays an important role. The leakage can be expressed in nondimensional values. Many authors [2,3,4,5] proposes discharge coefficient cD. m cD  (1) m id Which is equal to ratio of measured/simulated mass flow rate through the seal, to the ideal mass flow rate. The ideal mass flow rate is assumed as an isentropic flow through an ideal convergent nozzle 4

with the same minimal cross section A: p m id  A  1tot T1tot

2  1   2    1    1        R    1  pr   pr    

(2)

Where p1tot is total pressure in front of the sealing, T1tot – total temperature, γ – specific heat ratio, R – gas constant, pr – pressure ratio defied as ratio of total pressure in front of the sealing to static pressure behind the sealing. Fast Fourier Transform analysis of pressure fluctuations in monitor points mentioned in figure 2 has been carried out. FFT analyses were performed using 16384 samples (time steps) of unsteady calculations. Two physical measures were taken into account: acoustic pressure p’ defined as a difference between time averaged pressure and pressure at some time step, and Sound Pressure Level (SPL) with reference pressure at 2·10-5 Pa.  p'   SPL  20  log  p   ref 

(3)

FFT analysis results Results of the FFT analysis of pressure fluctuation was presented hereafter. The most significant phenomena occurred in points 1,3,4,5 and 7. In points 2 and 6 unsteady flow behavior depended mostly on flow through the narrow cavity, although the application of honeycomb structure have brought some impact on the overall performance. In the first point, located in front of the rotor, under the inlet cavity in the main flow channel, two harmonic frequencies have been detected for the case without honeycomb, f = 6.1kHz, and f = 12.2kHz (Fig.6). The peak acoustic pressure p’ for mentioned frequencies are 270Pa and 5Pa, respectively. Application of the honeycomb structure significantly changes the acoustic pressure distribution. The drop of peak value is almost

ninefold comparing to the smooth case, and appears for higher frequency, f = 8.4kHz. The SPL values are lower for whole range of frequencies in the case with honeycomb – apart from one peak value at characteristic frequency (Fig.6). The monitor point nr. 2 is located in the middle of the inlet to the cavity of the sealing structure. For the smooth land the main frequencies are the same as for the first point, although the peak values of p’ are much lower – 167Pa and 1Pa, respectively (Fig.7). Furthermore, in the range of 9.5-10kHz some additional fluctuations appear. When the honeycomb is considered, the first harmonic frequency is higher – likewise in the first point. Contrary to the first point, the peak p’ value for sealing with honeycomb is higher than for the labyrinth with smooth land. The peak p’ value is 221Pa. For frequencies below 7,5kHz, the SPL is lower for sealing with honeycomb, then appears the peak value for honeycomb. For frequencies higher than 20kHz the SPL values are very similar. Maximum values of SPL for honeycomb and smooth solution are roughly the same SPL=140dB (Fig.7). For the third and fourth monitor points, located respectively ahead of the first fin and between the fins in the middle of the channel height, the acoustic behavior is similar. Acoustic pressure and SPL values corresponding to these points are shown in Figures 8 and 9. The sealing with smooth land characterizes with two significant harmonic frequencies; f = 6.1kHz and 12.2kHz, and one additional peak in range 9.5 - 10 kHz. The seal configuration with honeycomb land has two characteristic frequencies f = 8.2kHz and 16.4kHz, although p' peak value at 16.4 kHz is lower than nominal value with smooth land case (Fig.9). The SPL for honeycomb structure is lower for whole spectrum of frequencies, again apart from the peak value at harmonic frequency. In the third point, peak values of p’ and SPL are slightly lower than in the fourth point. This proves that the turbulence structure is similar, although its intensity is higher between the fins.

p', Pa

300

p' smooth p' honeycomb

200 100 0 0

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f, kHz

15

20

25

5

SPL, db

160 140 120 100 80 60

SPL smooth SPL honeycomb

0

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f, kHz

15

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25

p', Pa

Figure 6. FFT analysis results of acoustic pressure and SPL in the point 1 located in inlet channel, ahead the sealing structure

250 200 150 100 50 0

p' smooth p' honeycomb

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f, kHz

160 140 120 100 80 60

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SPL, db

SPL smooth SPL honeycomb

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p', Pa

Figure 7. FFT analysis results of acoustic pressure and SPL in the point 2 located in inlet cavity, ahead the sealing structure

500 400 300 200 100 0

p' smooth p' honeycomb

SPL, db

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f, kHz

160 140 120 100 80 60

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SPL smooth SPL honeycomb

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p', Pa

Figure 8. FFT analysis results of acoustic pressure and SPL in the point 3 located in front of the sealing structure.

800 600 400 200 0

p' smooth p' honeycomb

SPL, db

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f, kHz

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160 140 120 100 80 60

20 SPL smooth

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Figure 9. FFT analysis results of acoustic pressure and SPL in the point 4 located behind labyrinth fins.

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Proceedings of the 12th International Symposium on Experimental Computational Aerothermodynamics of Internal Flows 13-16 July 2015, Lerici, Italy _________________________________________________________________________________________________

p', Pa

Area behind the last labyrinth fin, where the fifth point is located, is placed where strong turbulence and sudden flow acceleration occurs. For solution with smooth land against the fins four specific frequencies are inquired. Two of them are the same as in other points – f = 6.1kHz and 12.2kHz; and also two ranges at 9.2÷10.1kHz and 18÷19kHz are noticed (Fig.10). For mentioned ranges considerable growth of SPL appears. In this area the SPL has a value of almost 160dB for f = 6.1kHz, and it is the highest value among all investigated regions. Geometry with honeycomb provides significant drop of p’, and slightly drop of SPL. Also the harmonic values moved to the higher frequencies. What is interesting, some additional frequencies range appears f = 13,6÷14,1kHz, in which SPL value rises; growth from 100dB to 120dB (Fig.10) is noticed. The peak values of SPL are roughly the same and equal to 150dB. In subcritical regions, honeycomb provides lower noise values. This complexity of flow field in this area is associated mostly with the effect of flow through the seal and swirl in outlet chamber. In the point six, located in the gap connecting the outlet sealing chamber with main flow path some interesting phenomena appear (Fig.11). In geometry with smooth land four 1200 1000 800 600 400 200 0

p' smooth p' honeycomb

0

SPL, db

noticeable frequencies appear – respectively at 6.1, 12.2, 18.3 and 24.4kHz, with peak SPL = 140dB, for first three frequencies, and 120dB for the last one. For honeycomb structure three harmonic frequencies are noticed. Unlike to the previous points, in here peak values of p’ and SPL are higher than for smooth case. Also, for f = 24.4kHz the peak p’ and SPL values are appearing despite the sealing geometry. This frequency is most likely associated with flow conditions in narrow gap. In this point an application of honeycomb does not provide considerable noise absorption. The last point located in the middle of the fluid domain, below the outlet cavity, shows quite different flow pattern than the sixth point. The first harmonic frequency is different for the smooth and honeycomb land, although the peak value of SPL is exactly the same. Similarly, as in the sixth point there are four main frequencies for smooth sealing land, and three for honeycomb. Although at f = 24.4kHz some SPL growth appears for both cases (Fig.12). As mentioned before, this is caused by turbulence consequent in flow through narrow gap. In subcritical regions the SPL for honeycomb land is somehow lower than for smooth wall case.

5

10 f, kHz

160 140 120 100 80 60

15

20

SPL smooth SPL honeycomb

0

5

10

f, kHz

15

20

Figure 10. FFT analysis results of acoustic pressure and SPL results in the point 5 located behind the sealing structure.

p', Pa

600

p' smooth p' honeycomb

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f, kHz

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25

7

SPL smooth

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SPL, db

SPL honeycomb

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Figure 11. FFT analysis results of acoustic pressure and SPL results in the point 6 located behind the sealing structure.

500 400 300 200 100 0

p', Pa

p' smooth p' honeycomb

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f, kHz

15

SPL smooth

160 140 120 100 80 60

SPL, db

20 SPL honeycomb

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f, kHz

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Figure 12. FFT analysis results of acoustic pressure and SPL results in the point 7 located in the main flow channel,.

1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0

cD Smooth

cD, -

cD Smooth average

In Figure 13, fluctuations of mass flow rate in labyrinth seal against smooth land is presented. An average value of cD for smooth land is 0.313, with frequency of oscillation at 6.1 kHz. The ratio of amplitude to average value is 1.29. On the other hand in case with honeycomb structure an average cD is 0.42 (Figure 14). 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0

cD Honeycomb cD Honeycomb avegrage

cD, -

Mass flow behavior Steady state solution gives an information of time averaged mass flow rate in analyzed domain. This information is very useful in many applications, i.e. for optimization. In this study information about unsteady flow behavior is given. For this inquiry, a dimensionless value of discharge coefficient described with equation number (1) and (2) is used. Mass flow of gas flowing through the sealing in both cases is evaluated behind the second labyrinth fin. An average value of cD is calculated as arithmetical-time average.

0

100 200 300 400 500 600 700 800

time, ns Figure 14. Time resolved discharge coefficient behavior for sealing with honeycomb land

0

100 200 300 400 500 600 700 800 time, ns

Figure 13. Time resolved discharge coefficient behavior for sealing with smooth land

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This means that applying honeycomb results in increment of the leakage, also the frequency of fluctuation is higher f = 8.2 kHz. The ratio of the cD amplitude to average is 1.85. Average leakage for 8

honeycomb structure is about 30% higher. Also the amplitude of cD changes in the sealing with honeycomb land was higher than for smooth land. This point proves that labyrinth seal work is very unstable, and results obtained from steady state calculations results may not be sufficient. Flow patterns For better understanding the impact of the honeycomb structure application, vorticity distribution (Fig. 15 and Fig. 16) are presented. In honeycomb cells, located above the fins, a strong

turbulence occurs. In the cavity between the fins the vorticity is limited. Moreover, behind the second fin the vortex structure is also present in following cells. Minor turbulence can be noticed near wall at the sealing inlet and outlet . In case without honeycomb the turbulence is more intense in cavity between the fins and behind the fins, rather than in sealing with honeycomb structure. This phenomenon is responsible for stronger pressure fluctuations and noise generation, what was already discussed for FFT analysis.

Figure 15. Vorticity structures in labyrinth seal with honeycomb

Figure 16. Vorticity structures in labyrinth seal with smooth land

Summary This paper compared transient flow patterns in two types of gas turbine sealing solutions – labyrinth seal with two oblique fins against smooth land, and honeycomb structure. For performing the calculations the URANS method applied in Ansys CFX software was employed. The turbulence was modelled by means of steady state Shear Stress Transport model, and in transient case, ScaleAdaptive Simulation hybrid model. An assessment and comparison of the unsteady flow behavior has been done. Evaluation of the turbulent noise generation by carrying out the pressure fluctuations and Sound Pressure Level in selected specific points

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(explained in figure 2), has been done by means of FFT analysis. The results allowed to make following conclusions: The SAS turbulence model allowed to capture significant number of broadband noise components. Performed analysis made it possible to determine wide range of frequencies up to 500kHz, although in range of 0–25kHz the most important phenomena occurred. The fact that human beings (1 – 20 kHz) and animals (0 – 100 kHz) hearing range is found in investigated noise range – emphasis importance of the study. Application of hole-pattern structure against rotating sealing significantly changed the flow field.

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Specific frequencies, at which the fluctuating (aeroacoustic) pressure, and mass flow amplitudes peak occurred, has moved to higher values. Namely, for sealing with smooth land three natural frequencies has been defined, at 6.1, 12.2 and 18.3kHz, whereas for honeycomb structure only two could be found - 8.2 and 16.4kHz. Observed mass flow behavior corresponds to data found in literature [8]. Applying honeycomb structure against labyrinth seal mostly increases the leakage. In this study, increscent reached up to 30%. Moreover, mass flow behavior was slightly different for two compared structures. When honeycomb was considered, the amplitude and fluctuation frequencies were higher than for smooth wall. This investigation proved that honeycomb significantly damps the pressure fluctuations which can have a serious impact on rotordynamics. Also in all concerned points honeycomb provided decrease of the noise in subcritical regions. Despite the fact that honeycomb damps pressure oscillations, the leakage is higher than in sealing with smooth land. This is caused by higher effective area of flow. This shows that some compromise between lower leakage and work stability has to be made. The future work aims further and more detailed calculations, to obtain better time discretization. References [1] K.D.Kryter, The handbook of hearing and the effects of noise: physiology, psychology, and public health., Boston: Boston: Academic Press, 1994. [2] R.C. Hendricks, Environmental and Customer-Driven Seal Requirements, Seals Flow Code Development—93, NASA CP– 10136, p. 67, 1994 [3] R.Paolio, „Rotating Seal Rig Experiments: Test Results and Analysis Modelling,” ASME Turbo Expo 2006: Power for Land, Sea and Air 3, pp. 1551-1559, 2006 [4] D.Childs, D.Elrod & K.Hale, „Annular honeycomb seals: test results for leakage and rotordynamic coefficients; comparisons to labyrinth and smooth configurations,” ASME J. Tribol. 111, 1989. [5] A.J.Smalley, M.Camatti, D.W.Childs, J.R.Hollingsworth, G.Vannini & J.J.Cartet, „Dynamic Characteristics of the Diverging Taper Honeycomb-Stator Seal,” Proceedings

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of ASME Turbo Expo 2004, Power for Land, Sea and Air, pp. 717-724, 14-17 June 2004. [6] S.Dykas, S.Rulik, W.Wróblewski & T.Chmielniak, „Numerical method for modeling of acoustic waves propagation,” Archives of Acoustics 35 (1), pp. 35-48, 2010. [7] W.Wróblewski, S.Dykas, K.Bochon & S.Rulik, „Optimization of Tip Seal with Honeycomb Land in LP Counter Rotating Gas Turbine Engine,” Task Quarterly 14 No3, pp. 189-207, 2010. [8] W. Waschka, „Zum Einfluss der Rotation auf das Durchflussverhalten und Wärmeübertragungsverhalten in Labyrinthdichtungen und Wellendurchführungen,” Dissertation, Institut für Thermische Strömungsmaschinen der Universität Karlsruhe, 1991. [9] [9] R.Hendricks, B.Steinz., „Turbomachine Sealing and Secondary Flows Part 1 - Review of Sealing Performance, Customer, Engine Designer, and Research Issues,” NASA/TM2004-211991/Part 1, 2004. [10] S.Dykas, W.Wróblewski & D.Machalica, „Numerical Analysis of the Losses in Unsteady Flow through Turbine Stage,” Open Journal of Fluid Dynamics, 3, pp. 252-260, 2013. [11] Ansys Fluent – User guide 8.16. Real gas Models. [12] W.Sutherland, „The viscosity of gases and molecular force,” Philosophical Magazine, S. 5, 36, pp. 507-537, 1893. [13] F. R. Menter, Y. Egorov, „Turbulence Models based on the Length-Scale Equation,” w Fourth International Symposium on Turbulent Shear Flow Phenomena, Williamsburg, 2005. [14] K.Bochon, „Numerical investigation of fluid flow and heat transfer phenomena in selected parts of the gas turbine stage”, Silesian University of Technology, Gliwice, 2012.