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Experimental and theoretical rotordynamic stiffness coefficients for a three-stage brush seal
Mechanical Systems and Signal Processing 31 (2012) 143–154
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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Experimental and theoretical rotordynamic stiffness coefficients for a three-stage brush seal A.O. Pugachev a,n, M. Deckner b a b
Institute of Energy Systems, Technische Universit¨ at M¨ unchen, Garching, Germany Eta Energieberatung GbR, Pfaffenhofen a.d. Ilm, Germany
a r t i c l e i n f o
abstract
Article history: Received 23 September 2011 Received in revised form 22 February 2012 Accepted 24 March 2012 Available online 5 April 2012
Experimental and theoretical results are presented for a multistage brush seal. Experimental stiffness is obtained from integrating circumferential pressure distribution measured in seal cavities. A CFD analysis is used to predict seal performance. Bristle packs are modeled by the porous medium approach. Leakage is predicted well by the CFD method. Theoretical stiffness coefficients are in reasonable agreement with the measurements. Experimental results are also compared with a three-teeth-on-stator labyrinth seal. The multistage brush seal gives about 60% leakage reduction over the labyrinth seal. Rotordynamic stiffness coefficients are also improved: the brush seal has positive direct stiffness and smaller cross-coupled stiffness. & 2012 Published by Elsevier Ltd.
Keywords: Brush seal Labyrinth seal Rotordynamics Measurement Numerical analysis
1. Introduction Brush seals are well-known for their superior leakage performance when comparing with conventional labyrinth seals. Brush seals have already found an application in gas turbines and are now being introduced in steam turbines [1–3]. The leakage reduction in a brush seal over a labyrinth seal can be expected to be as high as 80% [4], though it depends on the brush seal and labyrinth seal designs, operating conditions, and applications. Brush seal consists of a large number of fine bristles angled to the shaft and closely packed between front and backing plates. In contrast to the simple rigid geometry of labyrinth seals, compliant structure of the bristle pack causes a number of phenomena that makes behavior of the brush seal far more complex. The most important of these phenomena are blowdown effect (closing the radial clearance between the shaft surface and the bristle tips due to the radial pressure gradient), bristle lift-off (opening the radial clearance due to the aerodynamic forces), stiffening (compression of the bristle pack due to the axial pressure gradient), and hysteresis (the leakage characteristics depends on the loading history due to the friction between the bristles and the backing plate). Many works were published studying these phenomena experimentally and theoretically. Several reviews can be found in [5–7]. Widening operating range in terms of pressure differential and superficial velocity, endurance of brush seals, and their rotordynamic characteristics are among the current challenges in brush seal technology. Installing brush seals in a row (a multiple brush seal) brings an additional issue regarding pressure reduction across the sealing configuration. The experience shows that the last bristle pack can face almost the whole pressure differential, the bristle packs upstream reduce pressure insignificantly [8]. Similar behavior was observed in brush-labyrinth sealing
n
Corresponding author. E-mail address: [email protected] (A.O. Pugachev).
0888-3270/$ - see front matter & 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.ymssp.2012.03.015
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Nomenclature a b bb cu0 d e F r ,F t hb I K,k N n p Q R t v
viscous resistance (1/m2) inertial resistance (1/m2) bristle pack thickness (m) inlet swirl (m/s) bristle diameter (m) eccentricity of the shaft (m) radial and tangential components of the seal reaction (N) brush seal radial clearance (m) inflow swirl force (kg m/s2) direct and cross-coupled stiffness coefficients (N/m) bristle packing density (bristles/m) shaft rotational speed (rpm) pressure (Pa) mass flow rate (kg/s) shaft radius (m) cavity length (m) flow velocity (m/s)
a e m r j O
o
angular coordinate (rad) porosity (–) dynamic viscosity (Pa s) density (kg/m3) lay angle (rad) whirl speed (rad/s) shaft rotational speed (rad/s)
Superscripts 0, 1, 2, 3 sealing cavities Subscripts 0
inlet
Abbreviations BBB SSS
three-stage brush seal three-teeth-on-stator staggered labyrinth seal
configurations [9]. Brush seals located upstream or labyrinth teeth are seen as a backup solution in such arrangements. ¨ Buscher [10] reported on the opposite effect when the first bristle pack in a multiple brush seal could have the maximal local pressure drop at certain operating conditions and loading cycle. Influence of brush seal on the rotordynamics is far less known comparing with labyrinth seals. Available field experience and laboratory-scale results demonstrate partially opposite results. Conner and Childs [11] presented the experimental results for the direct and cross-coupled stiffness and direct damping coefficients obtained on a laboratoryscale test rig for a four-stage brush seal with zero cold clearance at rotational speed range of 5000–16,000 rpm and inlet pressure range of 0.79–1.83 MPa. Direct damping increased slightly with rotational speed; otherwise, the rotordynamic coefficients were relatively insensitive to changes in the test parameters. Cross-coupled stiffness was very low and virtually unchanged by increasing the inlet swirl. Comparison of the four-stage brush seal with an eight-cavity tooth-onrotor labyrinth seal with the radial clearance of 0.24 mm showed improved rotordynamic performance for the brush seal, i.e. larger direct stiffness and lower cross-coupled stiffness. Pugachev and Deckner [12] presented the experimental and CFD-predicted results for rotordynamic coefficients of clearance brush-labyrinth gas seals for pressure differentials up to 0.9 MPa. The brush seal improved the rotordynamic characteristics in most cases comparing to three-tooth-on-stator staggered labyrinth seal with the clearance of 0.27 mm. In contrast to the results of Conner and Childs, the cross-coupled stiffness of brush-labyrinth seals was changing with the inlet swirl similar to labyrinth seals. San Andre´s et al. [13] presented the rotordynamic force coefficients of a hybrid brush seal, a second generation shoed-brush seal where seal pads are connected to the seal housing by spring lever elements with low radial and high axial stiffness. This hybrid brush seal demonstrated very low cross-coupled stiffness coefficients and rapid reduction of the seal equivalent viscous damping with increasing the excitation frequency. Experimental results presented in [14] showed that the hybrid brush seal reduced leakage rates by about 30% in comparison with a conventional brush seal. In this work, a three-stage brush seal with clearance is studied experimentally and theoretically to obtain rotordynamic stiffness coefficients as well as leakage. The scheme of the tested brush seal is shown in Fig. 1. The seal consists of three
Fig. 1. Three-stage brush seal (BBB seal).
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Table 1 Bristle pack parameters. Bristle Bristle Bristle Bristle Bristle
pack diameter ðmmÞ length (mm) packing density (bristles/mm) lay angle (1) tip cold clearance (mm)
70.0 10.3 200 45 0.31
Fig. 2. Cross-section of the no-whirl test rig.
identical MTU standard brush seals with cold free radial clearance. The bristle pack parameters are summarized in Table 1. Stiffness coefficient test results are obtained from integrating circumferential pressure distribution measured in the seal cavities at different shaft eccentricities. A full three-dimensional eccentric RANS analysis is used to predict performance of the multistage brush seal. The bristle packs are modeled by the porous medium approach, a computationally efficient method to predict leakage and, to some extent, rotordynamic coefficients of the brush seals. The model coefficients in the expressions describing the resistance of the porous medium were derived from the empirical data, therefore, the porous medium model of a bristle pack must be calibrated against the experimental data for at least one operating point, otherwise the model parameters have to be selected based on the experience of modeling similar brush seals. Modeling of multistage brush seals is more complex than one-stage brush seals due to increased number of model parameters of bristle packs. Unknown functions of bristle pack thickness and radial clearance under pressurization and swirl cause high degree of uncertainty. An additional single brush seal is studied experimentally and theoretically to estimate the blow-down effect and the bristle pack stiffening versus the pressure differential across the brush seal. The experimental performance of the BBB seal is compared with the performance of a three-teeth-on-stator staggered labyrinth seal (SSS seal). 2. Experimental setup The experimental results presented in this paper are obtained on the no-whirl test rig (former static test rig for the identification of local stiffness coefficients, see [15–17]). The identification procedure is similar to that in [18,19]. This test rig and identification procedure are briefly described below. 2.1. No-whirl test rig Fig. 2 shows a schematic of the no-whirl test rig. A symmetrical rigid rotor is supported by ball bearings and driven by a variable-speed direct-current motor with the maximum rotational speed of 12,000 rpm. The maximum pressure differential is 0.9 MPa. The stator can be moved by hydraulic cylinders to preset position of the rotor with respect to the tested seals. The value of rotor eccentricity is measured by eight eddy current displacement sensors with 0.01 mm uncertainty. Sealing medium is air. As opposed to the dynamic test rig (another test rig for studying seal rotordynamics at ¨ Munchen), ¨ the Institute of Energy Systems, Technische Universitat the shaft does not undergo whirling motion in the nowhirl test rig, the shaft rotates on its axis only. Therefore, only stiffness coefficients can be identified by integrating the measured circumferential pressure distribution.
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The testing assembly consists of the inflow casing and two identical seals. The double-flow configuration of the testing assembly compensates axial forces. Compressed air is injected at the center of the testing assembly into the swirl chamber to generate the inflow swirl. Depending on the control parameters of the valve system, one part of inlet air discharges axially through the tested sealing configurations to ambient. The rest flows through the bypass channels back into the air supply line. A single preswirl ring is used, but the inflow swirl value can be set between 30 m/s and 300 m/s by changing the mass flow rate through the bypass channels. Due to the arrangement of the inflow vane with the bypass channels the inflow swirl value can be set nearly independent of the inlet pressure. Static pressure measurements are performed with the Scanivalve pressure sensor with forty eight measuring points. Pressure taps are evenly distributed on circumference in the seal cavities 1 and 2 (see Fig. 1) to measure circumferential pressure distribution. There are 10 pressure taps in each cavity. The measurement planes are located in the middle of the cavities (see bore holes in Fig. 1). In addition, static pressure is measured in the cavity 0 at the tightest and largest clearances respectively. The exit static pressure is measured in the cavity 3. Total pressure measurement is performed with a Pitot tube and is used to calculate the inflow swirl (preswirl). One pressure tap is used to measure the ambient pressure. Uncertainty of pressure measurements is 0.06%. Leakage is measured by Rheonik Coriolis mass flow meter with uncertainty of 0.3%. 2.2. Identification procedure Along with measuring leakage and pressure distribution, the no-whirl test rig is used to identify local (former static) aerodynamic direct K and cross-coupled k stiffness coefficients of the seal. The local stiffness coefficient of the seal is made up of stiffness coefficients in cavities 1 and 2: K ¼ K1 þ K2,
1
2
k ¼ k þk
ð1Þ
Assuming the constant circumferential pressure distribution in the cavity along its axial length, the stiffness coefficients in each cavity are calculated from the measured circumferential pressure distribution pðjÞ in this cavity and known shaft eccentricity e ( ) Z K cos a 1 F r Rt 2p ¼ p ð2Þ da ¼ Ft e e 0 sin a k The experimental procedure consists in performing several measurements at different shaft positions for each operating point. Three to five different shaft eccentricity values including concentric position are used. A least-squares method is applied to approximate the radial and tangential force components as functions of the eccentricity and to obtain the stiffness coefficients. The drawback of this identification procedure is that the upstream and downstream regions as well as regions under the bristle packs are not taken into account in the determination of the local stiffness coefficients. Nevertheless, the local stiffness coefficients provide critical information on rotordynamic behavior of a seal. 3. CFD model of the three-stage brush seal ANSYS CFX 13 software is used to model the flow through the BBB seal. ANSYS CFX is a commercial general-purpose CFD code based on the conservative finite-element-based control volume method and coupled multigrid solution methodology [20]. A compressible Reynolds-Averaged Navier–Stokes approach with the Total Energy model is applied. Air is modeled as an ideal gas. Turbulence modeling is performed using the SST (Shear-Stress-Transport) model with automatic wall functions. As flow in the seal can be highly swirled (at least in the inflow cavity), the curvature correction option in the turbulence model [21] is switched on. The bristle packs are modeled using the porous medium model (see description below). 3.1. Seal geometry and boundary conditions Fig. 3 shows a schematic of the BBB seal. Dark gray regions are bristle packs. The computational domain consists of the upstream region, seal, and downstream region. The configuration of the upstream region is similar to the inflow cavity of the testing assembly, however the inlet boundary is simplified to reduce the computation effort. Rotor diameter is 180.05 mm. Seal diameter is 192 mm. Stator diameter in the upstream and downstream regions is 210 mm. Two fluid boundary conditions are defined in the upstream region to simulate the inlet flow conditions correctly. At the inlet, axial and circumferential components of the velocity are set to simulate the inlet swirl. Static pressure is set at the bypass to control the inflow pressure. At the outlet, pressure boundary condition is used. Shaft surface is modeled as an adiabatic rotating wall. Dimension of the brush seal is shown in Fig. 4. Each brush seal consists of two subregions: idealized bristle pack region and free radial clearance region. The radial length and axial thickness of the bristle pack change during the operation. These changes must be taken into account in the CFD model (see Section 4).
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Fig. 3. BBB seal scheme (all dimensions are in mm).
Fig. 4. Brush seal scheme (all dimensions are in mm).
Fig. 5. Computational grid of the BBB seal.
The local stiffness coefficients are calculated in the same way as in the experimental procedure using Eq. (2) and 10 pressure values per cavity. Forces obtained from the pressure distribution on the whole shaft surface can differ from the local forces significantly depending on the operating parameters. As this study is aimed at comparing predictions with the experimental data, only predictions of local coefficients are shown and discussed. 3.2. Computational grid ANSYS ICEM CFD 13 software is used to generate three-dimensional hexahedral O-grids with eccentric shaft (Fig. 5). The height of the free radial clearance region and thickness of the bristle pack are varying with the pressure drop across the brush seal and the inflow swirl. This fact means that an individual grid is needed for each operating point. One approach to reduce effort on grid generation is to use very fine meshing of the brush seal region. In this case, only one grid is necessary. The changes in the dimensions of the bristle pack are captured during the simulation by defining two analytical expressions to control bristle pack dimensions. This approach was used in [12]. In this work, computational grids are generated for each operating point to accelerate the convergence and avoid very fine meshing. However, when the free radial clearance is below certain value (0.2 mm) an analytical expression is used to avoid elements with very high aspect ratio. Results of the grid independence study are provided in the corresponding section below. 3.3. Porous medium model The bristle packs are included into the CFD model as porous regions. This approach is computationally simple and quite efficient. The main characteristic of the porous medium is its porosity e. For the bristle pack of width bb composed of bristles with diameter d and aligned at the lay angle j with packing density N, the expression for the porosity is
e ¼ 1
pd2 N 4bb cos j
ð3Þ
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The resistance of the porous medium to the flow is described by the following equation:
@p ¼ ai mvi þ bi rJvi Jvi @xi
ð4Þ
The behavior of the porous medium is determined by the viscous resistance coefficient a (inverse of the permeability) and inertial resistance coefficient b. ANSYS CFX code is capable of modeling porous regions, therefore, expressions for the resistance coefficients can be directly set during the pre-processing. Inclination of the bristle pack is taken into account in the theoretical model by specifying resistance directions (bristle lengthwise s and bristle normal n directions) of the porous region. In this work, the following expressions for the resistance coefficients in bristle lengthwise and normal to bristles directions are used: an ¼ 80C, bn ¼ 1:16D,
as ¼ 32eC, bs ¼ 0,
C¼
ð1eÞ2
e 3 d2
1e D¼ 3 e d
ð5Þ
¨ The expressions in Eq. (5) are taken from Prostler [22] who extended the original model of Chew et al. [23,24] and demonstrated their adequacy for the leakage prediction. Discussion of different expressions for the resistance coefficients in the porous medium model can be found in [25]. The expressions in Eq. (5) were derived from empirical data. Hence, in most cases, the porous medium model for a particular brush seal must be calibrated for at least one operating point. Calibration means an adjustment of one or more model parameters to get a correct (measured) output value. The described porous medium model was used in previous studies [9,12,26] and proved suitable for prediction of leakage, pressure and swirl distribution, rotordynamic coefficients for different brush-labyrinth seals and different bristle packs. However, as mentioned in [12], prediction of rotordynamic stiffness and damping coefficients using the porous medium approach is a lot more challenging than prediction of leakage because of high sensitivity of rotordynamic coefficients to the model parameters. 4. Calibration of the porous medium model Due to the empirical nature of Eq. (5) the porous medium model must be calibrated. Calibration means that the predicted seal operating characteristics should be adjusted to experimental data by varying bristle pack dimensions or porous medium model parameters. The one-point calibration could provide reasonable leakage and pressure drop predictions for the whole range of operating parameters [9]. The porous medium model of Eqs. (3)–(5) has only one uncertain parameter, the bristle pack thickness bb, which depends on the operating conditions, first of all on the pressure drop through the bristle pack. The measurements of the bristle pack thickness during the operation is difficult. The value can be estimated and, therefore, must be adjusted. Schwarz et al. [27] used glass segments embedded in a non-rotating shaft and a microscope to estimate compression of the bristle pack depending on the pressure drop. Increasing pressure drop from zero to four bar resulted in decrease of the bristle pack thickness of up to 0.38 mm depending on the brush seal design. In the clearance brush seals, a free radial clearance hb between the bristle tips and the rotor surface is the second uncertain parameter to be adjusted. The brush seal radial clearance depends strongly on the pressure drop. Several experimental studies revealed that the brush radial clearance variation could be approximated with a logarithmic or power function of the pressure drop [9,27]. In this work, the calibration against pressure drop across the bristle packs is used. Additionally, the aerodynamic force sensitivity on model parameters is monitored and used in some cases to adjust the values of bb and hb. 4.1. Experimental and theoretical results for a single brush seal An additional investigation of a brush seal configuration with only one bristle pack (B seal) is performed to estimate the dependence of the bristle pack thickness on the pressure drop across the bristle pack. Fig. 6(a) shows a schematic of the single brush seal arrangement. This seal is tested on the no-whirl test rig. Axial pressure distribution, leakage, and free radial clearance are measured for the inlet pressure range of 0.2–1.0 MPa. The values of the free radial clearance are estimated by optical measurements using a digital camera similar to the approach described in [28]. Using the experimentally obtained values of the free radial clearance, the CFD calculations are performed to calibrate the theoretical leakage performance of the B seal for each pressure drop by changing the bristle pack thickness. The results obtained experimentally and theoretically for the B seal are shown in Fig. 6(b). The blow-down effect can be clearly identified. However, a residual free radial clearance remains for all measured pressure drops. The optical measurement results are consistent with the data for a similar bristle pack presented in [9]. Regarding the results for the bristle pack thickness, the bristle pack shrinks at small pressure differentials and then remains almost constant at the value of 1.3 mm. A theoretical estimation of the minimal pack thickness using Eq. (6) from [22] is 1.21 mm. The larger value of predicted minimal pack thickness is in agreement with the observation that the bristle pack thickness does not
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Fig. 6. Single brush seal (B seal) scheme and results. (a) Schematic of the B seal and (b) experimental free radial clearance and predicted bristle pack thickness for the B seal.
Fig. 7. Experimental leakage performance for the BBB and SSS seals.
reach its theoretical minimum even at high pressure drops [22,29]. pffiffiffi 3d dN min 1 bb ¼ d þ 2 cos j
ð6Þ
4.2. Calibration of the BBB seal Having the results for the single brush seal, one can adjust the parameters of three bristle packs in the BBB seal depending on their individual pressure drops. However, as shown below, the pressure drop after the first and second brushes can be less than 0.1 MPa which lies outside of the measured range for the B seal (see Fig. 6(b)). Additionally, the free radial clearance and the bristle pack thickness are believed to depend on the flow swirl. This dependence is not investigated for the single brush seal. All this brings a degree of uncertainty in the determination of the operating parameters for the bristle packs 1 and 2. 5. Results and discussion 5.1. Experimental results The short three-teeth-on-stator staggered labyrinth seal with a band on rotor under the second tooth (SSS seal) is used for comparison. The SSS seal has the same dimensions as the BBB seal and was tested on the same no-whirl test rig [17]. The tooth clearance is 0.27 mm. Fig. 7 shows the measured leakage performance of the BBB and SSS seals versus pressure differential. The BBB seal demonstrates up to 60% leakage reduction comparing to the SSS seal. Table 2 compares the local pressure ratios for the SSS and BBB seals at different pressure differentials calculated as follows:
dploc i ¼
pcav i , pcav i1
i ¼ 1, . . . ,3
ð7Þ
Both seals demonstrate similar pressure reduction capability through the stages at small pressure differentials. With increasing the inlet pressure, this capability deteriorates for the first and second brushes in the BBB seal (the local pressure ratio for the first bristle pack increases from 0.86 to 0.92), while the two upstream teeth in the SSS seal show nearly constant local pressure ratios for different pressure differentials (0.85 for the first tooth).
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Table 2 Experimental local pressure ratio. Pressure differential (MPa)
Chamber number 0
1
2
3
0.10 0.11
SSS BBB
1 1
0.84 0.86
0.84 0.85
0.68 0.66
0.35
SSS BBB
1 1
0.85 0.84
0.79 0.92
0.32 0.28
0.85 0.90
SSS BBB
1 1
0.85 0.92
0.79 0.93
0.15 0.11
Fig. 8. Experimental local stiffness coefficients under non-rotating conditions.
Fig. 9. Experimental local stiffness coefficients in the BBB seal versus rotational speed for p0 ¼ 0:4 MPa and three inlet swirl velocities (46 m/s, 217 m/s, and 306 m/s).
The experimental local direct and cross-coupled stiffness coefficients are shown in Fig. 8. The cross-coupled stiffness is shown as a function of the inflow swirl force, a product of the mass flow rate and the inlet swirl. The error bars represent the maximal positive and negative difference between the individual measurements taken at different shaft eccentricities and the averaged coefficients. In contrast to the SSS seal, the BBB seal has a positive direct stiffness. Regarding the crosscoupled coefficients, performance of the BBB seal is better than performance of the SSS seal for the majority of operating conditions because at the same pressure differential and preswirl the inflow swirl force is lower for the BBB seal due to the smaller leakage [16]. Fig. 9 shows the effect of shaft rotational speed on the stiffness coefficients of the BBB seal for three preswirl velocities. At the high inlet swirl values, the local direct stiffness is almost insensitive to the shaft rotational speed. For the low inlet swirl, the value of K is doubled when the rotational speed is increased from 1500 rpm to 12,000 rpm. The local crosscoupled stiffness decreases with increasing the shaft rotational speed. This behavior of the BBB seal is similar to the results obtained for the SSS seal in [17]. The maximal deviations (the error bars in Fig. 9) appear at high inlet swirl and high rotational speed. The experimental data for the BBB seal under non-rotating conditions are tabulated in Appendix A. 5.2. Predicted performance of the BBB seal The CFD calculations are performed using the second order advection scheme. The convergence rate is checked by setting targets for the root mean square equation residuals (5 10 6) and global balances (1%), as well as by observing
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Fig. 10. Results of the mesh density study for the BBB model.
Fig. 11. Experimental and predicted leakage performance and local pressure drops for the BBB seal. (a) Leakage performance and (b) local pressure drop.
convergence history of leakage, pressure at several probes, and stiffness coefficients. The observed convergence behavior is rather not consistent. To improve convergence, the calculation is started with the low blend factor value of 0.2. The blend factor is then gradually raised to the final value of 1.0. The preset RMS residual target could not be reached for all operating conditions. In this case, the history of the stiffness coefficients is considered as a main convergence criterion with the equation RMS residuals below 1 10 4. The mesh density study is performed for the following operating parameters: p0 ¼ 10 bar, cu0 ¼ 42 m=s, e¼0.106 mm. Fig. 10 shows the effect of the computational mesh on the leakage and local stiffness coefficients. Various meshes are tested ranging from 3 million cells to 13 million cells. The local direct stiffness demonstrates the largest deviation up to 30%. The local cross-coupled stiffness remains virtually constant for all meshes at the tested operating conditions. The mesh with about 5.5 million cells and the smallest deviation for the direct stiffness is used in the further calculations. Fig. 11(a) shows comparison between experiments and predictions for the leakage of the BBB seal. As expected, the CFD model with porous medium approach predicts leakage of the BBB seal reasonably well. Comparison between the experimental and predicted local pressure drop is shown in Fig. 11(b) for the low-pressure, low-preswirl case (left y-axis) and the high-pressure, high-preswirl case (right y-axis) respectively. The bristle packs 1 and 2 demonstrate a considerably smaller pressure drop in comparison with the last bristle pack. Though there is a noticeable discrepancy in the low ðp0 ,cu0 Þ case, the stiffness coefficients predictions are in a sufficient agreement with the experimental data (see below). The small deviations in the high ðp0 ,cu0 Þ case are the result of detailed calibration which is necessary to obtain consistent predictions for the local stiffness coefficients. Fig. 12 compares experimental and predicted local stiffness coefficients. The actual values of deviation bars, which appear small in Fig. 8 because of scale of the y-axis, are clearly seen. As shown in Appendix A, cases with the high inlet swirl in combination with the moderate to high inlet pressure values have the largest deviations. The absolute deviations for the local cross-coupled stiffness are comparable with those for the local direct stiffness, but due to the higher averaged values of k the relative uncertainty is lower and more consistent. Dependence of the stiffness coefficients on the shaft eccentricity can be explained by the blow-down effect in the bristle packs. Apart from the concentric case, the shaft eccentricity values are varied from 0.100 mm to 0.205 mm. The function of free radial clearance along the circumference under the bristle pack depends on both shaft eccentricity and blow-down. Formation of the radial force occurs in the regions of high eccentricity ratio e=hb , i.e. under the bristle tips, therefore, the dependence of the direct stiffness values on the shaft eccentricity are more explicit comparing with the cross-coupled stiffness. Experiments have also shown that using small shaft eccentricity of 0.055 mm could clearly increase deviation from averaged values due to higher sensitivity of the testing procedure to operating parameters and testing arrangement. The predictions shown in Fig. 12 follow the experimental data. The parameters bb and hb are set for the last brush using the functions shown in Fig. 6 in accordance with the local axial pressure differential. The pressure drop across the bristle
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Fig. 12. Comparison between experiments and predictions for the local stiffness coefficients of the BBB seal (non-rotating conditions).
Table 3 Deviation between experiments and predictions for the low pressure/swirl and high pressure/swirl cases. Case:
Low p0 and cu0 High p0 and cu0
Average
K, e ¼0.104 mm
k, e¼ 0.104 mm
K
k
Cav 1
Cav 2
Sum
Cav 1
Cav 2
Sum
0.22 0.20
0.12 0.20
0.39 0.54
0.45 10.54
0.07 0.07
0.16 0.15
0.11 0.14
0.05 0.08
packs located upstream is in most cases less than 0.1 MPa. Hence, the results from Fig. 6 cannot be used directly. The final values of these parameters for the first and the second bristle packs are determined by applying pressure drop calibration. 1;2 1;2 The initial estimations of bb and hb provide satisfactory results for the low-preswirl cases. The high preswirl can significantly change the condition of the bristle pack 1 which makes the calibration procedure difficult due to uncertainty 1;2 1;2 about the values of bb and hb . Table 3 shows a detailed comparison between the experiments and the simulations for the low ðp0 ,cu0 Þ and high ðp0 ,cu0 Þ cases. The first two sets represent the deviation between the predicted stiffness coefficients and the averaged experimental values which are presented in Fig. 12 and Appendix A. Then the comparison with the experimental stiffness coefficients of the individual cavities and the total values are presented for a particular shaft eccentricity as used in the calculation. Regarding the total local coefficients, the cross-coupled stiffness is overpredicted in both cases, while the direct stiffness is overpredicted in the case of low ðp0 ,cu0 Þ and underpredicted in the case of high ðp0 ,cu0 Þ. The discrepancy between the experiments and predictions is below 22%. As expected, the agreement is better when comparing with the experimental data set at the same shaft eccentricity (e¼ 0.104 mm). However, comparison of the direct stiffness coefficients in the individual cavities reveals much greater deviation between the experiments and predictions. At high preswirl, the experimental direct stiffness in the second cavity is ten times the predicted value. Nevertheless, the combined effect of two cavities results in a reasonable agreement between the experiment and the prediction. The predicted cross-coupled stiffness of the individual cavities has a similar level of agreement with the experimental values as the total coefficients.
6. Conclusions The three-stage brush seal with non-zero cold clearance is studied experimentally and theoretically in regard of leakage performance and local rotordynamic stiffness coefficients. The experimental local stiffness coefficients are obtained by integrating measured circumferential pressure distribution in the two sealing cavities between the bristle packs.
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The multistage brush seal has the leakage characteristics half as much as the three-tooth-on-stator staggered labyrinth seal with the radial clearance of 0.27 mm. The local direct stiffness is positive for the multistage brush seal and negative for the labyrinth seal. Both seals have similar local cross-coupled stiffness coefficients which clearly depend on the inflow swirl. Such behavior of the brush seal is explained by the residual free clearance which exists at all tested pressure differentials. Due to the blow-down effect, the local stiffness coefficients depend on the shaft eccentricity. Theoretical predictions are obtained for the multistage brush seal using a 3D CFD model where the bristle packs are represented as porous media. In spite of the obtained functions for the free radial clearance and the bristle pack width, the multistage brush seal model must be calibrated because of the very low pressure drop across the two bristle packs located upstream. The predictions of the total stiffness coefficients are in reasonable agreement with the experimental data. The discrepancy between the experiments and CFD-based predictions increases for the operating conditions with high inlet swirl. In this case, a more sophisticated calibration is needed. Also, a direct modification of the porous medium model expressions in Eq. (5), e.g. taking into account the flow swirl, would be an option for improvement of the brush seal model. This, however, requires an extensive experimental investigation. Comparing with single brush seals, modeling of multistage brush seals is considerably more complicated. The presented three-stage brush seal model depends heavily on the experimental data, especially for the high-preswirl cases. Nevertheless, CFD modeling based on the porous medium approach helps to understand the formation of rotordynamic stiffness in brush seals, and, with further refinement using accumulated experimental and theoretical data, can be efficiently applied to multistage brush seals.
Acknowledgement Experimental part of this work was funded by Bayerische Forschungsstiftung and Siemens PG.
Appendix A. Experimental data for stationary tests (n ¼ 0) Table A1 provides data of non-rotating tests for the BBB seal. The signs ‘‘ þ’’ and ‘‘ ’’ represent maximum positive and negative deviations of individual measurements for various shaft eccentricities from the average value.
Table A1 Experimental data of stationary tests (n ¼0) on the no-whirl test rig for the BBB seal, ambient pressure 0.96 bar. prel (bar)
cu0 (m/s)
0
1
2
0.20 0.20 0.20 0.19 0.19 1.07 1.05 1.06 1.06 1.07 3.53 3.54 3.56 3.54 3.55 3.53 6.55 6.56 6.58 9.04 9.04 9.01
0.13 0.12 0.11 0.08 0.07 0.83 0.76 0.74 0.70 0.66 3.19 3.03 2.85 2.96 2.59 2.71 5.92 5.51 4.86 8.35 8.26 8.00
0.07 0.07 0.06 0.04 0.04 0.57 0.50 0.50 0.45 0.43 2.82 2.55 2.43 2.57 2.22 2.36 5.38 4.96 4.28 7.65 7.64 7.37
37.40 129.52 181.03 237.41 283.24 54.49 152.18 207.78 255.66 306.10 45.98 55.10 216.25 217.80 307.11 311.56 43.84 212.89 295.42 41.88 129.60 190.48
Q (g/s)
7.50 7.80 7.30 6.80 5.60 18.50 20.20 19.70 19.80 19.60 31.50 39.90 41.60 35.10 40.50 35.30 53.70 56.70 59.00 65.10 71.50 73.20
Local K (N/mm)
Local k (N/mm)
Value
þ
Value
þ
2.71 4.39 4.94 5.75 4.47 10.93 17.61 20.68 26.54 28.61 15.85 21.15 47.51 43.01 54.32 49.95 22.63 60.11 66.43 23.39 40.86 52.76
0.53 0.50 0.71 0.83 0.69 1.69 0.98 1.46 2.82 1.33 1.83 0.33 2.86 4.09 3.03 3.17 1.93 1.25 5.02 1.89 1.37 1.73
0.27 0.30 0.39 0.59 0.26 1.07 0.80 0.91 1.27 1.68 2.94 1.85 1.99 1.93 13.36 3.70 6.29 2.17 16.74 2.80 2.27 8.53
6.60 14.47 18.16 19.13 17.55 24.17 46.79 56.28 65.60 70.72 39.39 50.92 109.13 97.87 124.22 118.75 56.73 129.98 145.59 65.66 103.35 136.34
1.14 3.04 4.30 3.15 2.81 1.96 9.35 10.15 12.31 9.16 3.92 6.84 16.69 18.31 7.06 11.96 7.29 10.45 14.53 2.24 8.74 18.23
0.55 1.44 1.78 1.44 0.56 1.11 4.21 4.83 5.19 4.83 1.05 3.13 7.15 8.53 2.99 5.27 2.14 4.31 5.28 0.92 3.22 7.51
The signs ‘‘þ ’’ and ‘‘ ’’ represent maximum positive and negative deviations of individual measurements for various shaft eccentricities from the average value.
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References [1] D. Stephen, S. Hogg, Development of brush seal technology for steam turbine retrofit applications, in: Proceedings of ASME International Joint Power Generation Conference (IJPGC2003-40103), Atlanta, Georgia, USA, 2003, doi:10.1115/IJPGC2003-40103. URL /http://link.aip.org/link/abstract/ ASMECP/v2003/i36924/p505/s1S. [2] N. Turnquist, M. Burnett, F. Baily, F. Rivas, A. Bowsher, P. Crudgington, Brush seals for improved steam turbine performance, in: IMechE Seminar on Retrofitting Steam Power Generating Plant, London, UK, 2005. [3] P. Hurd, F. Truckenmueller, N. Thamm, H. Pollak, M. Neef, M. Deckers, Modern reaction HP/IP turbine technology advances and experiences, in: Proceedings of ASME Power Conference (PWRC2005-50085), Chicago, Illinois, USA, 2005, doi:10.1115/PWR2005-50085. URL /http://link.aip.org/ link/abstract/ASMECP/v2005/i41820/p425/s1S. [4] R. Flitney, Seals and Sealing Handbook, fifth ed., Elsevier, 2007. [5] P. Basu, A. Datta, R. Loewenthal, J. Short, R. 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Helm, Calibration of porous medium models for brush seals, Proc. Inst. Mech. Eng. A: J. Power Energy 223 (1) (2009) 83–91, http://dx. doi.org/10.1243/09576509JPE641. URL /http://pia.sagepub.com/cgi/content/abstract/223/1/83S. ¨ ¨ ¨ Dampfturbinen, Ph.D. Thesis, Technische Universitat ¨ Braunschweig, Germany, [10] S. Buscher, Untersuchung von mehrstufigen Burstendichtungen fur 2010. [11] K. Conner, D. Childs, Rotordynamic coefficient test results for a four-stage brush seal, J. Propul. Power 9 (3) (1993) 462–465, http://dx.doi.org/ 10.2514/3.23644. [12] A. Pugachev, M. Deckner, CFD prediction and test results of stiffness and damping coefficients for brush-labyrinth gas seals, in: Proceedings of ASME Turbo Expo 2010 (GT2010-22667), Glasgow, Scotland, 2010, doi:10.1115/GT2010-22667. URL /http://link.aip.org/link/abstract/ASMECP/v2010/ i44014/p175/s1S. [13] L. San Andre´s, J. Baker, A. Delgado, Rotordynamic force coefficients of a hybrid brush seal: measurements and predictions, J. Eng. Gas Turbines Power 132 (4) (2010) 042503, http://dx.doi.org/10.1115/1.3159377. URL /http://link.aip.org/link/?GTP/132/042503/1S. [14] L. San Andre´s, Z. Ashton, Comparison of leakage performance in three types of gas annular seals operating at a high temperature (300 1C), Tribol. Trans. 54 (3) (2010) 463–471, http://dx.doi.org/10.1080/10402000903420803. [15] K. Kwanka, W. Ortinger, J. Steckel, Calculation and measurement of the influence of flow parameters on rotordynamic coefficients in labyrinth seals, in: Proceedings of a Workshop on Rotordynamic Instability Problems in High-performance Turbomachinery, Texas A&M University, USA, 1993, pp. 209–218. ¨ ¨ Turbomaschinen, Ph.D. Thesis, Technische Universitat ¨ Munchen, ¨ [16] M. Deckner, Eigenschaften kombinierter Labyrinth-Burstendichtungen fur Germany, 2010. [17] A. Pugachev, M. Deckner, Analysis of the experimental and CFD-based theoretical methods for studying rotordynamic characteristics of labyrinth gas seals, in: Proceedings of ASME Turbo Expo 2010 (GT2010-22058), Glasgow, Scotland, 2010, doi:10.1115/GT2010-22058. URL /http://link.aip. org/link/abstract/ASMECP/v2010/i44014/p11/s1S. [18] K. Millsaps, M. Martinez-Sanchez, Rotordynamic forces in labyrinth seals: theory and experiment, in: Proceedings of a Workshop on Rotordynamic Instability Problems in High-Performance Turbomachinery, Texas A&M University, USA, 1993, pp. 179–207. [19] T. Iwatsubo, K. Fukumoto, H. Mochida, An experimental study of dynamic characteristics of labyrinth seals, in: Proceedings of a Workshop on Rotordynamic Instability Problems in High-performance Turbomachinery, Texas A&M University, USA, 1993, pp. 219–237. [20] ANSYS, Inc., Release 12.1, ANSYS CFX-Solver Theory Guide, 2009. [21] P.R. Spalart, M. Shur, On the sensitization of turbulence models to rotation and curvature, Aerosp. 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Neef, Breaking the swirl with brush seals: numerical modeling and experimental evidence, in: Proceedings of ASME Turbo Expo 2008 (GT2008-50257), Berlin, Germany, 2008, doi:10.1115/GT2008-50257. URL /http://link.aip.org/link/abstract/ASMECP/v2008/i43147/ p1387/s1S. ¨ von Burstendichtungen ¨ ¨ Dampfturbinen, in: [27] H. Schwarz, G. Kosyna, J. Flegler, Experimentelle Untersuchungen zur radialen Adaptivitat fur ¨ Proceedings of VGB Conference on Steam Turbines and Operation of Steam Turbines (V11), Lubeck, Germany, 2010. [28] P. Helm, H. Spliethoff, M. Neef, Closing the gap: measuring bristle blow down of brush seals, in: Proceedings of the 19th International Conference on Fluid Sealing, Poitiers, France, 2007. [29] G. Holle, R. Chupp, C. Dowler, Brush seal leakage correlations based on effective thickness, in: Proceedings of the 4th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC-4), vol. A, Honolulu, Hawaii, USA, 1992, pp. 296–304.
Contents lists available at SciVerse ScienceDirect
Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Experimental and theoretical rotordynamic stiffness coefficients for a three-stage brush seal A.O. Pugachev a,n, M. Deckner b a b
Institute of Energy Systems, Technische Universit¨ at M¨ unchen, Garching, Germany Eta Energieberatung GbR, Pfaffenhofen a.d. Ilm, Germany
a r t i c l e i n f o
abstract
Article history: Received 23 September 2011 Received in revised form 22 February 2012 Accepted 24 March 2012 Available online 5 April 2012
Experimental and theoretical results are presented for a multistage brush seal. Experimental stiffness is obtained from integrating circumferential pressure distribution measured in seal cavities. A CFD analysis is used to predict seal performance. Bristle packs are modeled by the porous medium approach. Leakage is predicted well by the CFD method. Theoretical stiffness coefficients are in reasonable agreement with the measurements. Experimental results are also compared with a three-teeth-on-stator labyrinth seal. The multistage brush seal gives about 60% leakage reduction over the labyrinth seal. Rotordynamic stiffness coefficients are also improved: the brush seal has positive direct stiffness and smaller cross-coupled stiffness. & 2012 Published by Elsevier Ltd.
Keywords: Brush seal Labyrinth seal Rotordynamics Measurement Numerical analysis
1. Introduction Brush seals are well-known for their superior leakage performance when comparing with conventional labyrinth seals. Brush seals have already found an application in gas turbines and are now being introduced in steam turbines [1–3]. The leakage reduction in a brush seal over a labyrinth seal can be expected to be as high as 80% [4], though it depends on the brush seal and labyrinth seal designs, operating conditions, and applications. Brush seal consists of a large number of fine bristles angled to the shaft and closely packed between front and backing plates. In contrast to the simple rigid geometry of labyrinth seals, compliant structure of the bristle pack causes a number of phenomena that makes behavior of the brush seal far more complex. The most important of these phenomena are blowdown effect (closing the radial clearance between the shaft surface and the bristle tips due to the radial pressure gradient), bristle lift-off (opening the radial clearance due to the aerodynamic forces), stiffening (compression of the bristle pack due to the axial pressure gradient), and hysteresis (the leakage characteristics depends on the loading history due to the friction between the bristles and the backing plate). Many works were published studying these phenomena experimentally and theoretically. Several reviews can be found in [5–7]. Widening operating range in terms of pressure differential and superficial velocity, endurance of brush seals, and their rotordynamic characteristics are among the current challenges in brush seal technology. Installing brush seals in a row (a multiple brush seal) brings an additional issue regarding pressure reduction across the sealing configuration. The experience shows that the last bristle pack can face almost the whole pressure differential, the bristle packs upstream reduce pressure insignificantly [8]. Similar behavior was observed in brush-labyrinth sealing
n
Corresponding author. E-mail address: [email protected] (A.O. Pugachev).
0888-3270/$ - see front matter & 2012 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.ymssp.2012.03.015
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Nomenclature a b bb cu0 d e F r ,F t hb I K,k N n p Q R t v
viscous resistance (1/m2) inertial resistance (1/m2) bristle pack thickness (m) inlet swirl (m/s) bristle diameter (m) eccentricity of the shaft (m) radial and tangential components of the seal reaction (N) brush seal radial clearance (m) inflow swirl force (kg m/s2) direct and cross-coupled stiffness coefficients (N/m) bristle packing density (bristles/m) shaft rotational speed (rpm) pressure (Pa) mass flow rate (kg/s) shaft radius (m) cavity length (m) flow velocity (m/s)
a e m r j O
o
angular coordinate (rad) porosity (–) dynamic viscosity (Pa s) density (kg/m3) lay angle (rad) whirl speed (rad/s) shaft rotational speed (rad/s)
Superscripts 0, 1, 2, 3 sealing cavities Subscripts 0
inlet
Abbreviations BBB SSS
three-stage brush seal three-teeth-on-stator staggered labyrinth seal
configurations [9]. Brush seals located upstream or labyrinth teeth are seen as a backup solution in such arrangements. ¨ Buscher [10] reported on the opposite effect when the first bristle pack in a multiple brush seal could have the maximal local pressure drop at certain operating conditions and loading cycle. Influence of brush seal on the rotordynamics is far less known comparing with labyrinth seals. Available field experience and laboratory-scale results demonstrate partially opposite results. Conner and Childs [11] presented the experimental results for the direct and cross-coupled stiffness and direct damping coefficients obtained on a laboratoryscale test rig for a four-stage brush seal with zero cold clearance at rotational speed range of 5000–16,000 rpm and inlet pressure range of 0.79–1.83 MPa. Direct damping increased slightly with rotational speed; otherwise, the rotordynamic coefficients were relatively insensitive to changes in the test parameters. Cross-coupled stiffness was very low and virtually unchanged by increasing the inlet swirl. Comparison of the four-stage brush seal with an eight-cavity tooth-onrotor labyrinth seal with the radial clearance of 0.24 mm showed improved rotordynamic performance for the brush seal, i.e. larger direct stiffness and lower cross-coupled stiffness. Pugachev and Deckner [12] presented the experimental and CFD-predicted results for rotordynamic coefficients of clearance brush-labyrinth gas seals for pressure differentials up to 0.9 MPa. The brush seal improved the rotordynamic characteristics in most cases comparing to three-tooth-on-stator staggered labyrinth seal with the clearance of 0.27 mm. In contrast to the results of Conner and Childs, the cross-coupled stiffness of brush-labyrinth seals was changing with the inlet swirl similar to labyrinth seals. San Andre´s et al. [13] presented the rotordynamic force coefficients of a hybrid brush seal, a second generation shoed-brush seal where seal pads are connected to the seal housing by spring lever elements with low radial and high axial stiffness. This hybrid brush seal demonstrated very low cross-coupled stiffness coefficients and rapid reduction of the seal equivalent viscous damping with increasing the excitation frequency. Experimental results presented in [14] showed that the hybrid brush seal reduced leakage rates by about 30% in comparison with a conventional brush seal. In this work, a three-stage brush seal with clearance is studied experimentally and theoretically to obtain rotordynamic stiffness coefficients as well as leakage. The scheme of the tested brush seal is shown in Fig. 1. The seal consists of three
Fig. 1. Three-stage brush seal (BBB seal).
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145
Table 1 Bristle pack parameters. Bristle Bristle Bristle Bristle Bristle
pack diameter ðmmÞ length (mm) packing density (bristles/mm) lay angle (1) tip cold clearance (mm)
70.0 10.3 200 45 0.31
Fig. 2. Cross-section of the no-whirl test rig.
identical MTU standard brush seals with cold free radial clearance. The bristle pack parameters are summarized in Table 1. Stiffness coefficient test results are obtained from integrating circumferential pressure distribution measured in the seal cavities at different shaft eccentricities. A full three-dimensional eccentric RANS analysis is used to predict performance of the multistage brush seal. The bristle packs are modeled by the porous medium approach, a computationally efficient method to predict leakage and, to some extent, rotordynamic coefficients of the brush seals. The model coefficients in the expressions describing the resistance of the porous medium were derived from the empirical data, therefore, the porous medium model of a bristle pack must be calibrated against the experimental data for at least one operating point, otherwise the model parameters have to be selected based on the experience of modeling similar brush seals. Modeling of multistage brush seals is more complex than one-stage brush seals due to increased number of model parameters of bristle packs. Unknown functions of bristle pack thickness and radial clearance under pressurization and swirl cause high degree of uncertainty. An additional single brush seal is studied experimentally and theoretically to estimate the blow-down effect and the bristle pack stiffening versus the pressure differential across the brush seal. The experimental performance of the BBB seal is compared with the performance of a three-teeth-on-stator staggered labyrinth seal (SSS seal). 2. Experimental setup The experimental results presented in this paper are obtained on the no-whirl test rig (former static test rig for the identification of local stiffness coefficients, see [15–17]). The identification procedure is similar to that in [18,19]. This test rig and identification procedure are briefly described below. 2.1. No-whirl test rig Fig. 2 shows a schematic of the no-whirl test rig. A symmetrical rigid rotor is supported by ball bearings and driven by a variable-speed direct-current motor with the maximum rotational speed of 12,000 rpm. The maximum pressure differential is 0.9 MPa. The stator can be moved by hydraulic cylinders to preset position of the rotor with respect to the tested seals. The value of rotor eccentricity is measured by eight eddy current displacement sensors with 0.01 mm uncertainty. Sealing medium is air. As opposed to the dynamic test rig (another test rig for studying seal rotordynamics at ¨ Munchen), ¨ the Institute of Energy Systems, Technische Universitat the shaft does not undergo whirling motion in the nowhirl test rig, the shaft rotates on its axis only. Therefore, only stiffness coefficients can be identified by integrating the measured circumferential pressure distribution.
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The testing assembly consists of the inflow casing and two identical seals. The double-flow configuration of the testing assembly compensates axial forces. Compressed air is injected at the center of the testing assembly into the swirl chamber to generate the inflow swirl. Depending on the control parameters of the valve system, one part of inlet air discharges axially through the tested sealing configurations to ambient. The rest flows through the bypass channels back into the air supply line. A single preswirl ring is used, but the inflow swirl value can be set between 30 m/s and 300 m/s by changing the mass flow rate through the bypass channels. Due to the arrangement of the inflow vane with the bypass channels the inflow swirl value can be set nearly independent of the inlet pressure. Static pressure measurements are performed with the Scanivalve pressure sensor with forty eight measuring points. Pressure taps are evenly distributed on circumference in the seal cavities 1 and 2 (see Fig. 1) to measure circumferential pressure distribution. There are 10 pressure taps in each cavity. The measurement planes are located in the middle of the cavities (see bore holes in Fig. 1). In addition, static pressure is measured in the cavity 0 at the tightest and largest clearances respectively. The exit static pressure is measured in the cavity 3. Total pressure measurement is performed with a Pitot tube and is used to calculate the inflow swirl (preswirl). One pressure tap is used to measure the ambient pressure. Uncertainty of pressure measurements is 0.06%. Leakage is measured by Rheonik Coriolis mass flow meter with uncertainty of 0.3%. 2.2. Identification procedure Along with measuring leakage and pressure distribution, the no-whirl test rig is used to identify local (former static) aerodynamic direct K and cross-coupled k stiffness coefficients of the seal. The local stiffness coefficient of the seal is made up of stiffness coefficients in cavities 1 and 2: K ¼ K1 þ K2,
1
2
k ¼ k þk
ð1Þ
Assuming the constant circumferential pressure distribution in the cavity along its axial length, the stiffness coefficients in each cavity are calculated from the measured circumferential pressure distribution pðjÞ in this cavity and known shaft eccentricity e ( ) Z K cos a 1 F r Rt 2p ¼ p ð2Þ da ¼ Ft e e 0 sin a k The experimental procedure consists in performing several measurements at different shaft positions for each operating point. Three to five different shaft eccentricity values including concentric position are used. A least-squares method is applied to approximate the radial and tangential force components as functions of the eccentricity and to obtain the stiffness coefficients. The drawback of this identification procedure is that the upstream and downstream regions as well as regions under the bristle packs are not taken into account in the determination of the local stiffness coefficients. Nevertheless, the local stiffness coefficients provide critical information on rotordynamic behavior of a seal. 3. CFD model of the three-stage brush seal ANSYS CFX 13 software is used to model the flow through the BBB seal. ANSYS CFX is a commercial general-purpose CFD code based on the conservative finite-element-based control volume method and coupled multigrid solution methodology [20]. A compressible Reynolds-Averaged Navier–Stokes approach with the Total Energy model is applied. Air is modeled as an ideal gas. Turbulence modeling is performed using the SST (Shear-Stress-Transport) model with automatic wall functions. As flow in the seal can be highly swirled (at least in the inflow cavity), the curvature correction option in the turbulence model [21] is switched on. The bristle packs are modeled using the porous medium model (see description below). 3.1. Seal geometry and boundary conditions Fig. 3 shows a schematic of the BBB seal. Dark gray regions are bristle packs. The computational domain consists of the upstream region, seal, and downstream region. The configuration of the upstream region is similar to the inflow cavity of the testing assembly, however the inlet boundary is simplified to reduce the computation effort. Rotor diameter is 180.05 mm. Seal diameter is 192 mm. Stator diameter in the upstream and downstream regions is 210 mm. Two fluid boundary conditions are defined in the upstream region to simulate the inlet flow conditions correctly. At the inlet, axial and circumferential components of the velocity are set to simulate the inlet swirl. Static pressure is set at the bypass to control the inflow pressure. At the outlet, pressure boundary condition is used. Shaft surface is modeled as an adiabatic rotating wall. Dimension of the brush seal is shown in Fig. 4. Each brush seal consists of two subregions: idealized bristle pack region and free radial clearance region. The radial length and axial thickness of the bristle pack change during the operation. These changes must be taken into account in the CFD model (see Section 4).
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147
Fig. 3. BBB seal scheme (all dimensions are in mm).
Fig. 4. Brush seal scheme (all dimensions are in mm).
Fig. 5. Computational grid of the BBB seal.
The local stiffness coefficients are calculated in the same way as in the experimental procedure using Eq. (2) and 10 pressure values per cavity. Forces obtained from the pressure distribution on the whole shaft surface can differ from the local forces significantly depending on the operating parameters. As this study is aimed at comparing predictions with the experimental data, only predictions of local coefficients are shown and discussed. 3.2. Computational grid ANSYS ICEM CFD 13 software is used to generate three-dimensional hexahedral O-grids with eccentric shaft (Fig. 5). The height of the free radial clearance region and thickness of the bristle pack are varying with the pressure drop across the brush seal and the inflow swirl. This fact means that an individual grid is needed for each operating point. One approach to reduce effort on grid generation is to use very fine meshing of the brush seal region. In this case, only one grid is necessary. The changes in the dimensions of the bristle pack are captured during the simulation by defining two analytical expressions to control bristle pack dimensions. This approach was used in [12]. In this work, computational grids are generated for each operating point to accelerate the convergence and avoid very fine meshing. However, when the free radial clearance is below certain value (0.2 mm) an analytical expression is used to avoid elements with very high aspect ratio. Results of the grid independence study are provided in the corresponding section below. 3.3. Porous medium model The bristle packs are included into the CFD model as porous regions. This approach is computationally simple and quite efficient. The main characteristic of the porous medium is its porosity e. For the bristle pack of width bb composed of bristles with diameter d and aligned at the lay angle j with packing density N, the expression for the porosity is
e ¼ 1
pd2 N 4bb cos j
ð3Þ
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The resistance of the porous medium to the flow is described by the following equation:
@p ¼ ai mvi þ bi rJvi Jvi @xi
ð4Þ
The behavior of the porous medium is determined by the viscous resistance coefficient a (inverse of the permeability) and inertial resistance coefficient b. ANSYS CFX code is capable of modeling porous regions, therefore, expressions for the resistance coefficients can be directly set during the pre-processing. Inclination of the bristle pack is taken into account in the theoretical model by specifying resistance directions (bristle lengthwise s and bristle normal n directions) of the porous region. In this work, the following expressions for the resistance coefficients in bristle lengthwise and normal to bristles directions are used: an ¼ 80C, bn ¼ 1:16D,
as ¼ 32eC, bs ¼ 0,
C¼
ð1eÞ2
e 3 d2
1e D¼ 3 e d
ð5Þ
¨ The expressions in Eq. (5) are taken from Prostler [22] who extended the original model of Chew et al. [23,24] and demonstrated their adequacy for the leakage prediction. Discussion of different expressions for the resistance coefficients in the porous medium model can be found in [25]. The expressions in Eq. (5) were derived from empirical data. Hence, in most cases, the porous medium model for a particular brush seal must be calibrated for at least one operating point. Calibration means an adjustment of one or more model parameters to get a correct (measured) output value. The described porous medium model was used in previous studies [9,12,26] and proved suitable for prediction of leakage, pressure and swirl distribution, rotordynamic coefficients for different brush-labyrinth seals and different bristle packs. However, as mentioned in [12], prediction of rotordynamic stiffness and damping coefficients using the porous medium approach is a lot more challenging than prediction of leakage because of high sensitivity of rotordynamic coefficients to the model parameters. 4. Calibration of the porous medium model Due to the empirical nature of Eq. (5) the porous medium model must be calibrated. Calibration means that the predicted seal operating characteristics should be adjusted to experimental data by varying bristle pack dimensions or porous medium model parameters. The one-point calibration could provide reasonable leakage and pressure drop predictions for the whole range of operating parameters [9]. The porous medium model of Eqs. (3)–(5) has only one uncertain parameter, the bristle pack thickness bb, which depends on the operating conditions, first of all on the pressure drop through the bristle pack. The measurements of the bristle pack thickness during the operation is difficult. The value can be estimated and, therefore, must be adjusted. Schwarz et al. [27] used glass segments embedded in a non-rotating shaft and a microscope to estimate compression of the bristle pack depending on the pressure drop. Increasing pressure drop from zero to four bar resulted in decrease of the bristle pack thickness of up to 0.38 mm depending on the brush seal design. In the clearance brush seals, a free radial clearance hb between the bristle tips and the rotor surface is the second uncertain parameter to be adjusted. The brush seal radial clearance depends strongly on the pressure drop. Several experimental studies revealed that the brush radial clearance variation could be approximated with a logarithmic or power function of the pressure drop [9,27]. In this work, the calibration against pressure drop across the bristle packs is used. Additionally, the aerodynamic force sensitivity on model parameters is monitored and used in some cases to adjust the values of bb and hb. 4.1. Experimental and theoretical results for a single brush seal An additional investigation of a brush seal configuration with only one bristle pack (B seal) is performed to estimate the dependence of the bristle pack thickness on the pressure drop across the bristle pack. Fig. 6(a) shows a schematic of the single brush seal arrangement. This seal is tested on the no-whirl test rig. Axial pressure distribution, leakage, and free radial clearance are measured for the inlet pressure range of 0.2–1.0 MPa. The values of the free radial clearance are estimated by optical measurements using a digital camera similar to the approach described in [28]. Using the experimentally obtained values of the free radial clearance, the CFD calculations are performed to calibrate the theoretical leakage performance of the B seal for each pressure drop by changing the bristle pack thickness. The results obtained experimentally and theoretically for the B seal are shown in Fig. 6(b). The blow-down effect can be clearly identified. However, a residual free radial clearance remains for all measured pressure drops. The optical measurement results are consistent with the data for a similar bristle pack presented in [9]. Regarding the results for the bristle pack thickness, the bristle pack shrinks at small pressure differentials and then remains almost constant at the value of 1.3 mm. A theoretical estimation of the minimal pack thickness using Eq. (6) from [22] is 1.21 mm. The larger value of predicted minimal pack thickness is in agreement with the observation that the bristle pack thickness does not
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Fig. 6. Single brush seal (B seal) scheme and results. (a) Schematic of the B seal and (b) experimental free radial clearance and predicted bristle pack thickness for the B seal.
Fig. 7. Experimental leakage performance for the BBB and SSS seals.
reach its theoretical minimum even at high pressure drops [22,29]. pffiffiffi 3d dN min 1 bb ¼ d þ 2 cos j
ð6Þ
4.2. Calibration of the BBB seal Having the results for the single brush seal, one can adjust the parameters of three bristle packs in the BBB seal depending on their individual pressure drops. However, as shown below, the pressure drop after the first and second brushes can be less than 0.1 MPa which lies outside of the measured range for the B seal (see Fig. 6(b)). Additionally, the free radial clearance and the bristle pack thickness are believed to depend on the flow swirl. This dependence is not investigated for the single brush seal. All this brings a degree of uncertainty in the determination of the operating parameters for the bristle packs 1 and 2. 5. Results and discussion 5.1. Experimental results The short three-teeth-on-stator staggered labyrinth seal with a band on rotor under the second tooth (SSS seal) is used for comparison. The SSS seal has the same dimensions as the BBB seal and was tested on the same no-whirl test rig [17]. The tooth clearance is 0.27 mm. Fig. 7 shows the measured leakage performance of the BBB and SSS seals versus pressure differential. The BBB seal demonstrates up to 60% leakage reduction comparing to the SSS seal. Table 2 compares the local pressure ratios for the SSS and BBB seals at different pressure differentials calculated as follows:
dploc i ¼
pcav i , pcav i1
i ¼ 1, . . . ,3
ð7Þ
Both seals demonstrate similar pressure reduction capability through the stages at small pressure differentials. With increasing the inlet pressure, this capability deteriorates for the first and second brushes in the BBB seal (the local pressure ratio for the first bristle pack increases from 0.86 to 0.92), while the two upstream teeth in the SSS seal show nearly constant local pressure ratios for different pressure differentials (0.85 for the first tooth).
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Table 2 Experimental local pressure ratio. Pressure differential (MPa)
Chamber number 0
1
2
3
0.10 0.11
SSS BBB
1 1
0.84 0.86
0.84 0.85
0.68 0.66
0.35
SSS BBB
1 1
0.85 0.84
0.79 0.92
0.32 0.28
0.85 0.90
SSS BBB
1 1
0.85 0.92
0.79 0.93
0.15 0.11
Fig. 8. Experimental local stiffness coefficients under non-rotating conditions.
Fig. 9. Experimental local stiffness coefficients in the BBB seal versus rotational speed for p0 ¼ 0:4 MPa and three inlet swirl velocities (46 m/s, 217 m/s, and 306 m/s).
The experimental local direct and cross-coupled stiffness coefficients are shown in Fig. 8. The cross-coupled stiffness is shown as a function of the inflow swirl force, a product of the mass flow rate and the inlet swirl. The error bars represent the maximal positive and negative difference between the individual measurements taken at different shaft eccentricities and the averaged coefficients. In contrast to the SSS seal, the BBB seal has a positive direct stiffness. Regarding the crosscoupled coefficients, performance of the BBB seal is better than performance of the SSS seal for the majority of operating conditions because at the same pressure differential and preswirl the inflow swirl force is lower for the BBB seal due to the smaller leakage [16]. Fig. 9 shows the effect of shaft rotational speed on the stiffness coefficients of the BBB seal for three preswirl velocities. At the high inlet swirl values, the local direct stiffness is almost insensitive to the shaft rotational speed. For the low inlet swirl, the value of K is doubled when the rotational speed is increased from 1500 rpm to 12,000 rpm. The local crosscoupled stiffness decreases with increasing the shaft rotational speed. This behavior of the BBB seal is similar to the results obtained for the SSS seal in [17]. The maximal deviations (the error bars in Fig. 9) appear at high inlet swirl and high rotational speed. The experimental data for the BBB seal under non-rotating conditions are tabulated in Appendix A. 5.2. Predicted performance of the BBB seal The CFD calculations are performed using the second order advection scheme. The convergence rate is checked by setting targets for the root mean square equation residuals (5 10 6) and global balances (1%), as well as by observing
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Fig. 10. Results of the mesh density study for the BBB model.
Fig. 11. Experimental and predicted leakage performance and local pressure drops for the BBB seal. (a) Leakage performance and (b) local pressure drop.
convergence history of leakage, pressure at several probes, and stiffness coefficients. The observed convergence behavior is rather not consistent. To improve convergence, the calculation is started with the low blend factor value of 0.2. The blend factor is then gradually raised to the final value of 1.0. The preset RMS residual target could not be reached for all operating conditions. In this case, the history of the stiffness coefficients is considered as a main convergence criterion with the equation RMS residuals below 1 10 4. The mesh density study is performed for the following operating parameters: p0 ¼ 10 bar, cu0 ¼ 42 m=s, e¼0.106 mm. Fig. 10 shows the effect of the computational mesh on the leakage and local stiffness coefficients. Various meshes are tested ranging from 3 million cells to 13 million cells. The local direct stiffness demonstrates the largest deviation up to 30%. The local cross-coupled stiffness remains virtually constant for all meshes at the tested operating conditions. The mesh with about 5.5 million cells and the smallest deviation for the direct stiffness is used in the further calculations. Fig. 11(a) shows comparison between experiments and predictions for the leakage of the BBB seal. As expected, the CFD model with porous medium approach predicts leakage of the BBB seal reasonably well. Comparison between the experimental and predicted local pressure drop is shown in Fig. 11(b) for the low-pressure, low-preswirl case (left y-axis) and the high-pressure, high-preswirl case (right y-axis) respectively. The bristle packs 1 and 2 demonstrate a considerably smaller pressure drop in comparison with the last bristle pack. Though there is a noticeable discrepancy in the low ðp0 ,cu0 Þ case, the stiffness coefficients predictions are in a sufficient agreement with the experimental data (see below). The small deviations in the high ðp0 ,cu0 Þ case are the result of detailed calibration which is necessary to obtain consistent predictions for the local stiffness coefficients. Fig. 12 compares experimental and predicted local stiffness coefficients. The actual values of deviation bars, which appear small in Fig. 8 because of scale of the y-axis, are clearly seen. As shown in Appendix A, cases with the high inlet swirl in combination with the moderate to high inlet pressure values have the largest deviations. The absolute deviations for the local cross-coupled stiffness are comparable with those for the local direct stiffness, but due to the higher averaged values of k the relative uncertainty is lower and more consistent. Dependence of the stiffness coefficients on the shaft eccentricity can be explained by the blow-down effect in the bristle packs. Apart from the concentric case, the shaft eccentricity values are varied from 0.100 mm to 0.205 mm. The function of free radial clearance along the circumference under the bristle pack depends on both shaft eccentricity and blow-down. Formation of the radial force occurs in the regions of high eccentricity ratio e=hb , i.e. under the bristle tips, therefore, the dependence of the direct stiffness values on the shaft eccentricity are more explicit comparing with the cross-coupled stiffness. Experiments have also shown that using small shaft eccentricity of 0.055 mm could clearly increase deviation from averaged values due to higher sensitivity of the testing procedure to operating parameters and testing arrangement. The predictions shown in Fig. 12 follow the experimental data. The parameters bb and hb are set for the last brush using the functions shown in Fig. 6 in accordance with the local axial pressure differential. The pressure drop across the bristle
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Fig. 12. Comparison between experiments and predictions for the local stiffness coefficients of the BBB seal (non-rotating conditions).
Table 3 Deviation between experiments and predictions for the low pressure/swirl and high pressure/swirl cases. Case:
Low p0 and cu0 High p0 and cu0
Average
K, e ¼0.104 mm
k, e¼ 0.104 mm
K
k
Cav 1
Cav 2
Sum
Cav 1
Cav 2
Sum
0.22 0.20
0.12 0.20
0.39 0.54
0.45 10.54
0.07 0.07
0.16 0.15
0.11 0.14
0.05 0.08
packs located upstream is in most cases less than 0.1 MPa. Hence, the results from Fig. 6 cannot be used directly. The final values of these parameters for the first and the second bristle packs are determined by applying pressure drop calibration. 1;2 1;2 The initial estimations of bb and hb provide satisfactory results for the low-preswirl cases. The high preswirl can significantly change the condition of the bristle pack 1 which makes the calibration procedure difficult due to uncertainty 1;2 1;2 about the values of bb and hb . Table 3 shows a detailed comparison between the experiments and the simulations for the low ðp0 ,cu0 Þ and high ðp0 ,cu0 Þ cases. The first two sets represent the deviation between the predicted stiffness coefficients and the averaged experimental values which are presented in Fig. 12 and Appendix A. Then the comparison with the experimental stiffness coefficients of the individual cavities and the total values are presented for a particular shaft eccentricity as used in the calculation. Regarding the total local coefficients, the cross-coupled stiffness is overpredicted in both cases, while the direct stiffness is overpredicted in the case of low ðp0 ,cu0 Þ and underpredicted in the case of high ðp0 ,cu0 Þ. The discrepancy between the experiments and predictions is below 22%. As expected, the agreement is better when comparing with the experimental data set at the same shaft eccentricity (e¼ 0.104 mm). However, comparison of the direct stiffness coefficients in the individual cavities reveals much greater deviation between the experiments and predictions. At high preswirl, the experimental direct stiffness in the second cavity is ten times the predicted value. Nevertheless, the combined effect of two cavities results in a reasonable agreement between the experiment and the prediction. The predicted cross-coupled stiffness of the individual cavities has a similar level of agreement with the experimental values as the total coefficients.
6. Conclusions The three-stage brush seal with non-zero cold clearance is studied experimentally and theoretically in regard of leakage performance and local rotordynamic stiffness coefficients. The experimental local stiffness coefficients are obtained by integrating measured circumferential pressure distribution in the two sealing cavities between the bristle packs.
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The multistage brush seal has the leakage characteristics half as much as the three-tooth-on-stator staggered labyrinth seal with the radial clearance of 0.27 mm. The local direct stiffness is positive for the multistage brush seal and negative for the labyrinth seal. Both seals have similar local cross-coupled stiffness coefficients which clearly depend on the inflow swirl. Such behavior of the brush seal is explained by the residual free clearance which exists at all tested pressure differentials. Due to the blow-down effect, the local stiffness coefficients depend on the shaft eccentricity. Theoretical predictions are obtained for the multistage brush seal using a 3D CFD model where the bristle packs are represented as porous media. In spite of the obtained functions for the free radial clearance and the bristle pack width, the multistage brush seal model must be calibrated because of the very low pressure drop across the two bristle packs located upstream. The predictions of the total stiffness coefficients are in reasonable agreement with the experimental data. The discrepancy between the experiments and CFD-based predictions increases for the operating conditions with high inlet swirl. In this case, a more sophisticated calibration is needed. Also, a direct modification of the porous medium model expressions in Eq. (5), e.g. taking into account the flow swirl, would be an option for improvement of the brush seal model. This, however, requires an extensive experimental investigation. Comparing with single brush seals, modeling of multistage brush seals is considerably more complicated. The presented three-stage brush seal model depends heavily on the experimental data, especially for the high-preswirl cases. Nevertheless, CFD modeling based on the porous medium approach helps to understand the formation of rotordynamic stiffness in brush seals, and, with further refinement using accumulated experimental and theoretical data, can be efficiently applied to multistage brush seals.
Acknowledgement Experimental part of this work was funded by Bayerische Forschungsstiftung and Siemens PG.
Appendix A. Experimental data for stationary tests (n ¼ 0) Table A1 provides data of non-rotating tests for the BBB seal. The signs ‘‘ þ’’ and ‘‘ ’’ represent maximum positive and negative deviations of individual measurements for various shaft eccentricities from the average value.
Table A1 Experimental data of stationary tests (n ¼0) on the no-whirl test rig for the BBB seal, ambient pressure 0.96 bar. prel (bar)
cu0 (m/s)
0
1
2
0.20 0.20 0.20 0.19 0.19 1.07 1.05 1.06 1.06 1.07 3.53 3.54 3.56 3.54 3.55 3.53 6.55 6.56 6.58 9.04 9.04 9.01
0.13 0.12 0.11 0.08 0.07 0.83 0.76 0.74 0.70 0.66 3.19 3.03 2.85 2.96 2.59 2.71 5.92 5.51 4.86 8.35 8.26 8.00
0.07 0.07 0.06 0.04 0.04 0.57 0.50 0.50 0.45 0.43 2.82 2.55 2.43 2.57 2.22 2.36 5.38 4.96 4.28 7.65 7.64 7.37
37.40 129.52 181.03 237.41 283.24 54.49 152.18 207.78 255.66 306.10 45.98 55.10 216.25 217.80 307.11 311.56 43.84 212.89 295.42 41.88 129.60 190.48
Q (g/s)
7.50 7.80 7.30 6.80 5.60 18.50 20.20 19.70 19.80 19.60 31.50 39.90 41.60 35.10 40.50 35.30 53.70 56.70 59.00 65.10 71.50 73.20
Local K (N/mm)
Local k (N/mm)
Value
þ
Value
þ
2.71 4.39 4.94 5.75 4.47 10.93 17.61 20.68 26.54 28.61 15.85 21.15 47.51 43.01 54.32 49.95 22.63 60.11 66.43 23.39 40.86 52.76
0.53 0.50 0.71 0.83 0.69 1.69 0.98 1.46 2.82 1.33 1.83 0.33 2.86 4.09 3.03 3.17 1.93 1.25 5.02 1.89 1.37 1.73
0.27 0.30 0.39 0.59 0.26 1.07 0.80 0.91 1.27 1.68 2.94 1.85 1.99 1.93 13.36 3.70 6.29 2.17 16.74 2.80 2.27 8.53
6.60 14.47 18.16 19.13 17.55 24.17 46.79 56.28 65.60 70.72 39.39 50.92 109.13 97.87 124.22 118.75 56.73 129.98 145.59 65.66 103.35 136.34
1.14 3.04 4.30 3.15 2.81 1.96 9.35 10.15 12.31 9.16 3.92 6.84 16.69 18.31 7.06 11.96 7.29 10.45 14.53 2.24 8.74 18.23
0.55 1.44 1.78 1.44 0.56 1.11 4.21 4.83 5.19 4.83 1.05 3.13 7.15 8.53 2.99 5.27 2.14 4.31 5.28 0.92 3.22 7.51
The signs ‘‘þ ’’ and ‘‘ ’’ represent maximum positive and negative deviations of individual measurements for various shaft eccentricities from the average value.
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