- 1 Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine-Cascades (STCF)
Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine-Cascades (STCF)
The 11 Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine-Cascades (STCF) were established by Torsten Fransson and Joe Verdon in the late 1980s. The Standard Configurations are a comprehensive database of experimental data and numerical solutions for unsteady flow resulting from blade vibrations in various 2D cascade geometries. This data has proved to be an invaluable resource to manufacturers and researchers over the last 30 years. The initial website was created by Markus Joecker.
The present database contains information on 11 different two-dimensional cascade geometries and the corresponding unsteady flow established by the vibrating blades. It is believed that this database is presently the most comprehensive database related to aeroelasticity in turbomachines in the open literature.
As part of the Symposium series “Unsteady Aerodynamics and Aeroelasticity of Turbomachines and Propellers” a set of cascade standard configurations, with emphasize on the unsteady aerodynamics, was established [Bölcs and Fransson, 1986]. These have been used extensively by several authors since the “Fourth Aeroelasticity Symposium” in 1987. As both experimental and numerical procedures presently undergo a rapid development it was at that time recognized that a continuous update of the standard configurations is a necessity.
The present report gives an overview of unsteady experimental and theoretical flow models (as regards to vibrating blades in cascades) that have appeared in the open literature between the 1987 and 1991 Symposia on Aeroelasticity, together with a brief description of the major findings presented by the authors. The application domain presented for the different prediction models is pointed out, and it is concluded that the largest number of publications has appeared in the domain of development of non-linear computations. Viscous phenomena have started to be included, in different ways, in prediction models, both for actuator disk and flat plates, as well as for time- linearized and fully time-dependent methods. Many authors validate thoroughly their models against any analytical results available, as well as against existing experimental data. Unfortunately it must today be concluded that, although some well documented experiments have been presented in the last years, a large need for detailed viscous flow data through vibrating cascades exist.
The “Standard Configurations” have been updated in the sense that three cascade geometries have been reduced in importance, whereas one geometry has been extended to include experimental data at high incidence angles. The flat plate standard configuration has been extended to include two supersonic geometries that have been proven useful for comparisons in the past. Finally, a new analytical inviscid high subsonic/transonic compressor cascade geometry is proposed as “Standard Configuration 10”, with the aim of detailed studies of shock wave influences on the unsteady load on vibrating blades.
Vibration-related fatigue failures have been, and remain, a major concern for turbomachine manufacturers and operators worldwide. If such a failure appears, it has major consequences, normally in significant shut-down time of the machine and sometimes in the loss of human life, and can become extremely expensive. It is not probable that blade vibration problems will disappear in the next few years while, although the quality of design methods increases, manufacturers constantly push the aerodynamics and materials used for blades into higher performances. Modern turbomachine blades are thus constantly at the high end of possibilities of the materials employed. The two most important blade vibration problems are the forced vibration, which is a flow interaction between the rotor and the stator, and the blade flutter, which is a self-excited vibration. The correct prediction of the unsteady forces from both these phenomena is essential to an acceptable design of fans and compressors, as well as turbines. Evidence of a tremendous improvement in predicting the unsteady aerodynamic behavior of the high-speed flow through vibrating turbomachine-cascades, together with an increase in the number of well documented experimental data, can be found in the literature during recent years. Furthermore, two excellent review manuals concerning the important aeroelastic effects in axial-flow turbomachines have recently been published [Platzer and Carta; Editors, 1987, 1988]. The agreement between theoretical and experimental results in the domain of turbomachine blade aeroelasticity ranges from extremely good to extremely bad, depending on such factors as geometry and flow conditions, but also on experimental procedure and numerical method. Generally it can be concluded that the low subsonic attached flow can be reasonably well measured and predicted (whereas the transonic flow conditions on realistic profile types show discrepancies between theory and experiments) and that virtually no data or prediction models are available for separated flow conditions. A large need exists thus for both well documented experimental test cases and for appropriate prediction models. Within the framework of the symposia “Aeroelasticity in Turbomachines” [1976, 1980, 1984, 1987, 1989, 1991] a workshop, with the aim to define the state-of- the-art of prediction models and experimental test rigs for unstalled two-dimensional cascade flow, was performed with the conclusion that several successes could be found but that also some significant differences, both between theories and experiments and between different prediction models, had to be documented [Bölcs and Fransson, 1986]. At the outset of the present workshop (1980) no well- documented comparisons existed between different theoretical models and experimental data. A wide scope of different “standard configurations” was thus established, and different aeroelastic sample cases within each standard configuration were defined, with the obvious objective to better define and eventually reduce/extend the aeroelastic sample cases in a later phase of the project as possibilities and limitations of prediction models and experimental data became clearer. At the 1987 Aeroelasticity symposium a task force was thus created with the objectives to:
- follow up the literature on new experimental and theoretical procedures
- redefine the standard configurations to evolve together with the present need of aeroelastic information in transonic and high incidence flow regimes
- reduce, where possible, the number of aeroelastic sample cases for unstalled flow
- seek explanations for agreements and disagreements between prediction and experiment
- present an updated version of standard configurations at the 1991 aeroelasticity meeting.
The present note constitutes a documentation in this context. First, an attempt to give a brief, certainly non- exhaustive, overview about new experimental and numerical results on unsteady flow through vibrating axial-flow turbomachine cascades that has appeared in the open literature during the years 1987-1991 is made. The purpose of this is to guide researchers through the large amount of literature in connection with validation of experimental, theoretical and numerical procedures for the field of interest discussed here and to indicate some of the conclusions the respective authors have found important. We apologize to anyone who’s contributions have not been mentioned. Secondly, some of the standard configurations, as defined in the 1986 report [Bölcs and Fransson, 1986], have been reduced in importance . Of the remaining configurations the number of aeroelastic cases has been modified, whereas one more configuration has been added in order for the sample cases to better reflect the fields in which basic research is needed today. Furthermore, some authors have recently asked for more information on time- dependent stalled and partially stalled flow. To this end the fifth standard configuration has been extended with a few such aeroelastic sample cases. It is foreseen that the standard configurations also in the future will be extended to stalled flow conditions as soon as detailed data on separated flow becomes available. It is hoped that this will happen in the near future. Finally, as one of the objective of the present study was to solicit comparison of results during the 1991 Symposium on Aeroelasticity, some results which have been published on the standard configurations in the years 1987-1991 have also been included in the present note. It is hoped that as time goes on researchers will find it useful to compare more and more of their results on specific sets of test cases, as only through such a broad comparison will it be possible to assess possibilities and limits of different experiments and predictions. Through this the different results (experimental, numerical, analytical) can also be used towards the ultimate goals of understanding the physical phenomena involved in aeroelasticity in axial- flow turbomachines and design blades with optimal unsteady forces. To facilitate the comparisons for everyone interested, it is recommended that new results should be sent to the first author of the present report to be incorporated in the data base. This will help to judge if (and why) fundamental differences appear between experiments and predictions. The authors express their gratitude to everyone who participates in the study, and apologizes for any errors that may have slipped into the data that are represented in the appendices.
The collection of two-dimensional standard configurations, for attached flow, compiled by Bölcs and Fransson  consisted of 9 different cascade- geometries, with the objective to validate both experimental data and prediction models. To this end, two different sets of data were put forward for each class of test cases. During the project it was established that most of the data selected for purely subsonic flow gave a reasonable agreement with some prediction models, which validated both the experiments and the theories. The largest computational efforts thus went into standard configurations 1 (low subsonic flow compressor cascade), 4 (cambered transonic turbine cascade), 8 (flat plate) and 9 (double circular arc profiles with low camber), with some additional work put into configurations 5 (high subsonic compressor profile) and 7 (supersonic compressor). It was concluded from the project that certain geometries and flow conditions could be accurately predicted, whereas discrepancies existed for other sample cases. Some inconsistency has been found in the definition of the pressure coefficients (steady-state and time- dependent). These are, in the present work, defined with the compressible dynamic pressure, (pw1-p1), as non-dimensionalized value. However, some researchers have used the incompressible value, (r-_v-_2/2), instead. It has been tried to, as accurately as possibly, mention these inconsistencies in the text for the various standard configurations, but it is important to keep this eventual difference in mind for some comparisons.
As the predictions on the configurations 2, 3 and 6 (see Bölcs and Fransson ) were considerably smaller than on other cascade configurations, it is proposed that efforts for comparisons with low subsonic compressor blades and cambered transonic turbine blades should be reduced to configurations 1 and 4 (Figs. 3.1.1 and 3.4.1). Configuration 5 (Fig. 3.5.1) is today of larger interest than in the beginning of the project because of its systematic parameter- study from attached to stalled flow, although data are only available for one blade vibrating (here the question of superposition of influence coefficients in stalled flow may arise). Configuration 7, which treats supersonic inlet flow conditions for a compressor (Fig. 3.7.1), is also of present interest, especially as some major discrepancies between the data and the predictions exist. It is probable that some of these can be explained by viscous effects and by short comings in the numerical methods but that some can certainly also be found in the data. However, as no other complete data base has been found for supersonic flows to date, this configuration should be kept presently. Flat plate cascades, double circular arc profiles and other analytically defined geometries are still today of large interest and are necessary in order to compare prediction models with each other and to draw physical conclusions from the results. Furthermore, modern compressor blades in the high subsonic and supersonic flow domains are often derivatives of such profiles, and there seems to be a renewed interest in cascades with supersonic leading edge locus. The flat plate and double circular arc geometries (configurations 8 and 9) are thus kept in a redefined way (Figs. 3.8.1 and 3.9.1). Finally, a supplementary configuration is proposed, based on a modified NACA four digit series airfoil (Fig. 3.10.1) . It is important to note that the configurations are presently still limited to two-dimensional flow conditions, with mostly attached flow. Although numerical results today are available for solving the Navier-Stokes equations with different (steady-state) turbulence model assumptions there are hardly no separated experimental cascade data available (see however the extension of “Standard Configuration 5” below). Furthermore, three-dimensional unsteady cascade effects are today not taken into full account experimentally. However, it is reasonable to expect that some data for separated and three-dimensional flow will appear in the not too distant future. These will then, if possible, be incorporated in the present data base. All present sample cases are, furthermore, considered to be of uncoupled modes, although the coupling effects are of large importance for the stability of the blading. It is presently assumed that the coupled modes are obtained by superimposing the heaving and pitching motions. The number of aeroelastic sample cases in the report are still out of necessity large. This can not be otherwise as the standard configurations should cover all velocity domains from low subsonic to supersonic velocities and both compressor and turbine geometries, and as the interblade phase angle is a parameter of major importance in turbomachine applications. Furthermore, it is well known that the overall time-dependent blade lift and moment coefficients may give reasonable agreement between different prediction models and with experimental data, although the unsteady blade surface pressure coefficient results may represent quite different trends and to a certain extent may indicate different physical interpretations. It is thus today even more important than at the outset of the workshop to represent, for different interblade phase angles and for different cascade and flow configurations, the pressure and suction surface time-dependent pressure coefficients separately. For the benefit of those who may eventually be interested in comparing different results not included in the appendices, some publications treating results on the different standard configurations are given in each section below. Please also note that all airfoil coordinates as well as experimental data and numerical results presented, either in the first [Bölcs and Fransson, 1986] or the present standard configuration report, exist on computer files and can be obtained upon request. The plots of all the data obtained from different researchers are given in Appendix A4, and the corresponding data are listed in Appendix A3.
All of the data corresponding to each standard configuration is available below according to Updated report on “Standard Configurations for Unsteady Flow Through Vibrating Axial-Flow Turbomachine-Cascades“, Status as of July 1991, compiled by T. H. Fransson and J.M Verdon with two additional updates for STCF4 and STCF11 available in the appendix
The first standard configuration, included by the courtesy of Dr. Frank Carta at the United Technologies Research Center [Carta 1982a,b; 1984], and its 15 recommended aeroelastic sample cases, gives an overview of different steady-state and time- dependent flow conditions at low Mach numbers (see Fig. 3.1.1, Tables 3.1.1-2). Most prediction models give good agreement with the data, but some minor differences between the different models became apparent.
Maximum thickness at x=0.5 Vibration in pitch around (xa,ya)=(0.5,0.0115) Thickness / chord = 0.06 span=0.254 m c=0.1524m t=0.75 g=55o camber=10o i=variable (2o, 6o) Working fluid: Air a = 0.5o, 2o (=0.0087, 0.0349 rad) k=variable Fig. 3.1.1: First standard configuration: Cascade geometry [Bölcs and Fransson, 1986, p. 58] All results (experimental as well as predictions) presented on this standard configuration have been (as the flow velocity is very low) non-dimensionalized with the incompressible dynamic pressure, (r-_•v-_2/2). The most important conclusion from this standard configuration is that the detailed blade surface pressures, and thus the flutter limits, can be fairly accurately predicted for low incidence flows on this type of cascades. The reader is referred to section 7.1 in the original report on the standard configurations [Bölcs and Fransson, 1986] for details. It is however of importance to note that although the results obtained are positive, the agreement between the data and the predictions, or between the different predictions, is not as good as would be wished from a theoretical point of view. It should especially be mentioned that, in several cases, a flat plate model gives as good agreement, or better, with the data as some prediction models that consider the blade thickness.
The aeroelastic sample cases originally defined have proven their value and are thus presently kept in the data-base. It is however important to point out that some uncertainties as regards to the exact value of the inlet flow angle still exist. It has been found by different researchers that a better agreement with the steady-state blade surface pressure distribution is obtained if the inlet flow angle is modified about 2o [Bölcs and Fransson, 1986, p. 61], or if a stream-tube variation is introduced. Results on this standard configuration have been presented by Chiang and Fleeter [1989b] and Huff . These authors have, as other researchers, found a good agreement with the experimental data.
The data files can be downloaded here
File information can be found here
No modifications have been made to this standard configuration. All results, and a discussion thereof, are found in the 1986 report [Bölcs and Fransson, 1986]. A listing of all the results are found in appendix A3. As with the first standard configuration, the incompressible dynamic pressure is employed as a non-dimensionalized value for the pressure coefficients.
The data files can be downloaded here
File information can be found here
No modifications have been made to this standard configuration. All results, and a discussion thereof, are found in the 1986 report [Bölcs and Fransson, 1986]. A listing of all the results are found in appendix A3. The compressible dynamic pressure, (pw1-p1), is employed as non-dimensionalized value for the pressure coefficients.
The fourth standard configuration, with results obtained at the Swiss Federal Institute of Technology [Bölcs et al, 1985], is shown in Fig. 3.4.1, with the profile coordinates and aeroelastic sample cases given in Tables 3.4.1-2. Please note that the blade coordinates are given with more significant decimals than earlier as it was pointed out that the coordinates showed some oscillatory behavior. The Reynolds number was not given earlier and are included now as a basis for viscous calculations. Furthermore, experimental data exist for many more steady-state and time-dependent operating conditions (see for example Schläfli ). These can be obtained upon request. It is important to point out that the time-averaged dynamic pressure is used as the quantity with which the pressure coefficients are made dimensionless. This should be remembered when predictions are performed. As far as the present authors are aware of all predictions have also been presented with this dynamic pressure. The results obtained so far show a good general agreement between the data and prediction models for shock-free flows, both as regards to the time- dependent blade surface pressures as the unsteady forces. At transonic and supersonic outlet flow conditions major discrepancies are found, as presented by Bölcs and Fransson . It should however be pointed out that a re-evaluation of the original data has indicated that the experimental uncertainty for the inlet flow angle may be larger than originally thought, which may explain some differences in the experimental and computed steady- state pressure distributions, especially in the leading edge region. Most authors have thus introduced a stream-tube contraction (towards 10%) into the calculations in order to compensate for leakage flow and boundary layer growth in the test facility. A better agreement with the steady-state blade surface pressure distributions is then generally obtained. The reader is referred to section 7.4 in Bölcs and Fransson  for more details about the cascade geometry and previous results. Since the first results presented [Bölcs and Fransson, 1986], further predictions have been performed on the cascade by Whitehead , Servaty et al , Gallus an Kau , Kau and Gallus , He  and Carstens [1991a] with the general results that the predictions and experiments agree well, both for steady-state and time-dependent flow, for subsonic flow conditions whereas the predictions do not give results similar to the experiment in the neighborhood of the shock waves. It can probably be concluded that the experiments are good, but some aspects of the data can not be explained with present prediction models. Further numerical developments and experiments in transonic flow seem thus necessary for the future. It has been pointed out [Carstens, 1991a] that the position of the time-averaged shock wave at the supersonic outlet flow velocity cases can be quite accurately predicted if a sufficiently fine mesh structure is used. The predicted shock strength did however not correspond to the measured one.
While the new profile definition (which corresponds to the one after which the experimental profiles where originally manufactured) is more detailed than the one originally given, it has been found that also the new coordinates show some oscillatory behavior when a very fine mesh is used [Hoyniak, 1991; Carstens, 1991b]. This can give some spurious steady-state and unsteady results, and can be avoided by performing a smoothing of the coordinates [Carstens, 1991b]. Another problem that was discussed is the treatment of the blunt trailing edge. Most prediction models use a modified airfoil shape towards the trailing edge in order to close in towards a sharp edge. It can generally be stated that the turbine geometry defined, with its corresponding 8 aeroelastic sample cases, is still of importance for the understanding of flutter-phenomena and further developments of numerical prediction models. The original cases are thus kept in the data-base. Much more work has to be done to find explanations for the differences between the data and the predictions.
Results on the fifth standard configuration (Fig. 3.5.1, Tables 3.5.1-2) are included by the courtesy of Dr. E. Széchényi at the “Office Nationale d’Etudes et de Recherche Aerospatiale” (ONERA) [Széchényi, 1984; Széchényi et at, 1981a,b]. The original experiments treated a large domain of incidence angles, ranging from attached to stalled flow conditions. In the 1986 report on the standard configurations only the small incidence angles (i_6o) cases were included, as at that time no models for prediction of the stalled cases were proposed. In the meantime a few viscous solvers have become available, and some researchers have asked for more information on the partially and fully stalled flow conditions. An updating of the aeroelastic sample cases of the fifth standard configuration is thus of interest. These updated cases are given in Table Working fluid: Air Maximum blade thickness at x=0.67 d = 0.027 c = 0.090 m span = 0.120 m t = 0.95 camber = 0o g = 59.3o i = 2o->12o M1 = 0.5->1.0 a = 0.00524 rad s: Only one blade vibrated f = 75->550 Hz k = 0.14->1.01 Fig. 3.5.1: Fifth standard configuration: Cascade geometry [Bölcs and Fransson, 1986, p. 124]. 3.5.2, and the experimental data are shown (in listings and plots) in appendices A3 and A4 (for previous experimental results, see also section 7.5 and appendix A5 in Bölcs and Fransson ). In evaluating these data it should be kept in mind that the experimental results are obtained with only one blade vibrating. The data presented do thus not correspond to the time-dependent pressure coefficient in the traveling wave mode as for the other standard configurations, but instead to the eigen-influence of the reference blade on itself when all the other blades in the cascade are fixed. Some researchers have pointed out that the original blade coordinates seem to have some “wiggles” in them when blown up for the numerical calculations. Unfortunately, it is presently not possible to give the profile definition with a better resolution. As with the fourth standard configuration, a smoothing of the data is necessary. The question as how the pressure coefficients have been non-dimensionalized has been brought up. It has been pointed out that a better agreement between the data and one prediction model was found if the data would have been scaled with . A verification of the original results presented has shown that the experimental data have all been non- dimensionalized with the measured upstream dynamic pressure , as originally proposed. Again, as for Standard Configurations 1 and 4, an inconsistency exists between the inlet and outlet flow conditions. Some researchers have compensated this by modifying the inlet flow angle and some by an introduction of a stream tube contraction ratio. Others have left the original values given, and show therefore a less good correlation with the steady-state blade surface pressure distribution. How much these differences in the set-up of the theoretical steady-state flow conditions make out for the time-dependent flow is unclear. Please note that cases 21 and 22 below are for the same flow conditions, with the only difference being the steady-state stagnation pressure. This can give some indications about stagnation pressure influence and the experimental accuracy and should be considered while analyzing the results. Sidén [1991a,c] presents results from a Navier-Stokes solver on incidence angles 2o, 4o and 6o on this standard configuration. He shows a large unsteady pressure in the leading edge region where the experiments indicate a larger value than predictions with a linearized potential model. The viscous solver gives however a considerable overshoot compared to the data. Still, these results indicate the importance of considering viscous effects also at fairly low incidence angles on compressor blades with sharp leading edges. Széchényi  points out that the viscous separation bubble can be well trend wise predicted by a recently developed coupled inviscid/boundary layer code at ONERA [Soize, 1992]. Some of these results have been incorporated in the present data base (see appendix A4).
No modifications have been made to this standard configuration. All results, and a discussion thereof, are found in the 1986 report [Bölcs and Fransson, 1986]. A listing of all the results are found in appendix A3. The compressible dynamic pressure has been used in the definition of the pressure coefficients by all participating researchers.
The data files can be downloaded here
File information can be found here
The seventh standard configuration (Fig. 3.7.1 and Tables 3.7.1-2) was tested at Detroit Diesel Allison, and included in the workshop report by courtesy of the sponsoring agent, D. R. Boldman at NASA Lewis Research Center [Boldman, 1983; Riffel and Rothrock, 1980]. A question as regards to the validity of the profile coordinates did arise at the 1991 Aeroelasticity meeting. These have been verified [Boldman, 1991], and it is confirmed that the originally presented blade coordinates were correct. The agreement between the data and the predictions is, at the present time, not satisfactory for any of the 12 aeroelastic sample cases. It is probable that some of the discrepancies comes from the viscous effects in the experiment, some from experimental accuracy and some from the prediction models, but not enough predictions have been performed to analyze either the data or predictions for supersonic cascades with thickness. At the present time it is thus proposed to keep this standard configuration, and the corresponding aeroelastic sample cases, in its original form. It should be pointed out that, as with the other experimental Standard Configurations, the pressure coefficients are scaled with the steady-state upstream dynamic pressure . As far as the authors are aware, all predicted results have been presented with this dynamic pressure in the pressure coefficient definitions. The Reynolds number of the experiments were not given in the original report [Bölcs and Fransson, 1986], but are now included. They are situated in the range 1.1-1.6•106 [Riffel and Rothrock, 1980, p. 11] for the performed tests. Gerolymos et al  have presented calculations on this geometry. A stream sheet contraction of 0.85 was introduced for these computations in order to get a reasonable agreement with the steady-state outflow data. Trend wise agreement can be found in the unsteady pressures on the blade surfaces, and the experimental and numerical stability limits of the cascade agree fairly well.
As flat plate configurations are the most important to compare against as regards to the numerical completeness and accuracy of non-analytical prediction models, it is important that such configurations cover as wide a scope as possible, especially as regards to Mach number variations. The number of aeroelastic sample cases will thus forcibly be large, but this is not a major problem as the analytical flat plate solutions used as baseline comparisons are usually fairly fast, and researchers who may want to compare a numerical result against an analysis will only choose the domain of current interest and perform a few calculations. The 35 original aeroelastic sample cases will be kept (Fig. 3.8.1 and Table 3.8.1). The time-dependent cases 36 to 42, corresponding to some of the earlier cases but with a reduced frequency of k=0.5 instead of k=1.0, have been added. This lower reduced frequency (k=0.5) was recommended as the higher reduced frequency showed some differences, which may eventually be attributed to some numerical effects, between the different prediction models. To these aeroelastic test cases are added two supplementary steady-state conditions (Figs. 3.8.2). These, denoted as aeroelastic test cases 43-54 and suggested by Dr. Verdon, are the well known “Cascades A and B” as defined by Verdon  and Verdon and McCune . These cascade configurations were originally carefully selected to highlight wave reflections in supersonic flow and have been used frequently in the past as comparison for a number of analyses. They have provided useful insight into the physical phenomena of unsteady supersonic flow on vibrating flat plates and interesting, often positive, results from the comparisons. It is believed that they also in the future should be of special interest as baseline comparisons for numerical models for supersonic flow, also for supersonic leading edge locus configurations. As far as the present authors are aware, all pressure coefficient results have been presented with the incompressible dynamic pressure, (r-_夫-_2/2), as non-dimensionalized value.
The data files can be downloaded here
File information can be found here
The ninth standard configuration is a continuation of the eighth, but includes both thickness and camber effects. The geometry of the blades was proposed by Dr. J. M. Verdon from United Technologies Research Center (Fig. 3.9.1). At the present time it is proposed to keep the originally defined 21 aeroelastic sample cases for further studies (Table 3.9.1). However, it has been noted by the calculations done up to now that the high reduced frequency (k=1.0) gave some unexpected numerical problems which should not be the main purpose of the investigation. Furthermore, this high reduced frequency (based on half-chord) is not of extreme practical interest today. The same configurations are thus proposed, as sample cases 22-42, at the lower reduced frequency of k=0.5. The results presented are, as far as the authors’ are aware of, all presented with the incompressible dynamic pressure, (r-_•v-_2/2), as non- dimensionalized value. Among others, Whitehead , Li et al , Huff  and Verdon [1989a] have presented numerical results on unsteady flow through vibrating DCA cascades, and Buffum and Fleeter [1989a,b, 1988] and Giordano and Fleeter  have presented experimental data. The conclusions to be drawn are that promising results exist on this standard configuration, but that some unexplained effects still exist. The agreement between different prediction models is usually not as good as one would wish when the inlet flow Mach numbers are high or the blade thickness non negligible. Symmetric/flat-bottomed circular arc profiles Equation: sgn ( H ) = ± 1 for H > 0 / H < 0; ( )+ = upper surface; ( )- = lower surface Maximum thickness at x = 0.5 d = 0.01 – 0.1 c = 0.1 m t = 0.75 g = 45o, 60o camber = 0o (for symmetric profiles) i = 0o (for M1 < 1. ) a = 2.0 o M1 = variable ( 0.0 -> 1.5) k = 1.0 s = 90o Vibration in pitch around (xa,ya) = (0.5, camberline)
The data files can be downloaded here
File information can be found here
The tenth Standard Configuration, included by proposal of Dr. J. M. Verdon at the United Technologies Research Center [1987a,c], is a two- dimensional compressor cascade of modified NACA 0006 profiles that operates at subsonic inlet and exit conditions. The geometry is given by Verdon [1987a] and is repeated here for convenience. The cascade has a stagger angle, g, of 45o and a gap/chord ratio, t, of unity. The blades are constructed by superimposing the thickness distribution of a modified NACA four digit series airfoil on a circular arc camber line. The thickness distribution is given by: (3.10.1) where HT is the nominal blade thickness. The coefficient of the x4 in eq. (3.10.1) differs from that used in the standard NACA airfoil definition (i.e., – 1.015) so that the example blades will close in as wedge-shaped trailing edges. The camber distribution is given by: (3.10.2) where HC (>0) is the height of the camber-line at midchord and is the radius of the circular arc camber line. The surface coordinates of the reference blade are therefore given by: (3.10.3) where the signs + and – refer to the upper (suction) and lower (pressure) surfaces, respectively, and q=tan-1(dC/dx). For the present example we set HT=0.06 and HC=0.05 to study the unsteady aerodynamic response of a vibrating cascade of cambered NACA 0006 airfoils. We consider two different steady-state inlet operating conditions. In the aeroelastic cases 1-16 the inlet Mach number, M1, and flow angle, b1, are 0.7 and – 55o, respectively; for cases 17-32, M1=0.8 and b1=- 58o (see Table 3.10.1). The flow through the cascade is assumed to satisfy a Kutta condition at blade trailing edges and, therefore, only inlet flow information must be specified. For M1=0.7 and b1=-55o, the mean or steady flow through the cascade is entirely subsonic; for M1=0.8 and b1=-58o it is transonic with a normal shock occurring in each blade passage. As aeroelastic test cases we consider single-degree- of-freedom blade heaving, normal to chord, and pitching motions at four different frequencies, k=0.25, 0.50, 0.75 and 1.0, and at interblade phase angles lying in the range -p_s_p. The amplitude of the heaving motion, h, is 0.01; that of the pitching motion, a, is 2o. The blade pitching axis lies at midchord, i.e. (xa,ya)=(0.5,0.05). We are interested in the following aerodynamic response information for each of the two inlet operating conditions given, at reduced frequencies of k=0.25, 0.50, 0.75 and 1.0 (see Table 3.10.1 for details): 1: The time-averaged blade surface pressure coefficient, and Mach number. 2: a: Amplitude, , and phase lead angle, , of the unsteady blade surface pressure coefficient for heaving and pitching motions at s=0o and s=90o. b: Amplitude, , and phase lead angle, , of the unsteady blade surface pressure difference coefficient for heaving and pitching motions at s=0o and s=90o. 3: a: The amplitude, , and phase lead angle, , of the unsteady lift coefficient per unit amplitude vs interblade phase angle for the heaving motions at -p_s_p. b: The amplitude, , and phase lead angle, , of the unsteady moment coefficient per unit amplitude vs interblade phase angle for the pitching motions at -p_s_p. 4: The aeroelastic damping coefficient, X, vs interblade phase angle for the heaving and pitching motions at -p_s_p. Usab and Verdon [1990, 1989b, 1987a,c], and Whitehead  have already presented results on this cascade. Results from other prediction models were also recently presented [Huff, 1991; Hall, 1991]. Some very promising results have been obtained (these will be included in the complete updated report presently in preparation). When comparing these results with each other it must be considered that no analytical results exist. Only the mutual agreement between several similar theoretical methods can thus indicate the accuracy of the models. Stagger angle: g =45o Gap/chord: t =1.0 Pitch axis: (xa,ya) = (0.5,0.05).
Data file– Time averaged blade surface pressure distributions, Aerodynamic lift coefficients and phase lead, Aerodynamic moment coefficient and phase lead, time dependent blade surface mach number
Time dependent blade surface pressure distribution
Time dependent blade surface pressure difference coefficients
The data of STCF 4 is updated with additional 3D inlet and outlet boundary conditions. Steady blade surface pressures and unsteady blade surface pressures of the blades vibrating with an angle of 60.4° to chord line are only measured at midspan. For the moment the steady and unsteady data of three cases are made available, case 624, case 627 and case 628. The data was obtained at the annular test rig at the EPF Lausanne in 1986 and was recompiled for storage at this place by Dr. P. Ott , LTT, EPFL.
Some detail information needed for the 3D models of the cascade can be found here.
Note on tip clearance:
The tip clearance was estimated on the dismantled configuration by measuring the outer diameter of the cascade: largest diameter = 399.49 mm, smallest diameter = 399.32 mm.
With the inner diameter of the test section of 400.0 mm (slightly oval by 0.1 mm) this gives a tip gap size of approximately 0.3 mm.
Nomenclature– Used nomenclature and schematic view of test cascade
STCF4, Case 624
M1S=0.21, beta1=-21.4 degree
M2S=1.04, beta2=-71.3 degree
STCF4, Case 627
M1S=0.19, beta1=-15.2 degree
M2S=0.85, beta2=-71.5 degree
STCF4, Case 628
M1S=0.2, beta1=-12.0 degree
M2S=1.39, beta2=-68.3 degree
The existing set of 10 configurations for unsteady flow through vibrating axial-flow turbomachine cascades is extended by the “Standard Configuration 11”. This configuration represents a turbine blade geometry with transonic design flow conditions characterized by a normal shock impinging on 75 % real chord on the suction side. Out of a set of test cases covering all relevant flow regimes two cases were selected for publication: A subsonic, attached flow case and an off-design transonic case showing a separation bubble at about 30% real chord on the suction side. The performed tests are shown to be repeatable and suitable for code validations of numerical models predicting flutter in viscous flows. All tests were performed at the annular non-rotating test facility situated at the EPF Lausanne. The present data and geometry are given at midspan, nearly no measurements were made at other blade heights. However, the 3D shape of the blade is prismatic (which means a variable pitch-to-chord ratio over the channel height). The 3D geometry definition can be obtained by stacking the midspan plane profile in radial direction; the tip gap is 0.8mm according to the model drawings. A document available provides detailed information on the 3D geometry and the 3D blade motion as reconstructed from available drawings and reports. The data were published with the permission of ABB, which is gratefully acknowledged.
Standard Configuration 11 is introduced and discussed in a publication presented at the ASME TURBO EXPO 1998, Stockholm, Sweden (paper 98-GT-490), can be found here
Nomenclature– Used nomenclature and schematic view of test cascade