New generation of universal modeling for centrifugal compressors calculation

Transcription

1 IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS New generation of universal modeling for centrifugal compressors calculation To cite this article: Y Galerkin and A Drozdov 015 IOP Conf. Ser.: Mater. Sci. Eng Related content - Compressor map prediction tool Arjun Ravi, Lukasz Sznajder and Ian Bennett - Scroll Compressor Oil Pump Analysis S Branch - Development of a J-T Micro Compressor P Champagne, J R Olson, T Nast et al. View the article online for updates and enhancements. This content was downloaded from IP address on 15/07/018 at 1:57

2 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 NEW GENERATION OF UNIVERSAL MODELING FOR CENTRIFUGAL COMPRESSORS CALCULATION Y. GALERKIN, A. DROZDOV R&D Laboratory Gas dynamics of turbo machines Peter the Great St.Petersburg Polytechnic University, Polytechnical st. 9, St.Petersburg, Russia Abstract: The Universal Modeling method is in constant use from mid 1990 TH. Below is presented the newest 6 th version of the Method. The flow path configuration of D impellers is presented in details. It is possie to optimize meridian configuration including hub/shroud curvatures, axial length, leading edge position, etc. The new model of vaned diffuser includes flow non-uniformity coefficient based on CFD calculations. The loss model was built from the results of 7 experiments with compressors stages of different flow rates and loading factors. One common set of empirical coefficients in the loss model guarantees the efficiency definition within an accuracy of 0.86 % at the design point and 1. % along the performance curve. The model verification was made. Four multistage compressors performances with vane and vaneless diffusers were calculated. As the model verification was made, four multistage compressors performances with vane and vaneless diffusers were calculated. Two of these compressors have quite unusual flow paths. The modeling results were quite satisfactory in spite of these peculiarities. One sample of the verification calculations is presented in the text. This 6th version of the developed computer program is being already applied successfully in the design practice. Nomenclature b - ade non-dimensional height c absolute velocity, m/s c u tangential velocity, m/s c velocity in view of a ade ockage factor, m/s c velocity in a ade row throat, m/s D - diameter, m D - impeller diameter, m D - hub non-dimensional diameter h D0 - impeller inlet non-dimensional diameter i - incidence angle l - non-dimensional length of a ade - non-dimensional length of a ade in meridian plane lm L m - non-dimensional axial length of impeller l imp - non-dimensional length in meridian section l t av - solidity of the vane cascade М - Mach number u M u krt t inl m - mass flow rate, kg/s Re - Reynolds number doi: / x/90/1/0100 Content from this work may be used under the terms of the Creative Commons Attribution.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Puished under licence by Ltd 1

3 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 u p D t inl Reu RT inl t inl Rh - hub non-dimensional radius of curvature R - shroud non-dimensional radius of curvature s S - non-dimensional ade surface area S - non-dimensional average area of hub and shroud o V inl - inlet flow rate, m /min X ( i) - empirical coefficient in the math model z - number of ades - absolute flow angle - vane angle (to tangential direction), 0 v - relative flow angle - impellers ade angle to tangential direction, 0 - non-dimensional ade s thickness v - non-dimensional vane s thickness - flow coefficient - angle of a shroud straight part - densities ratio at inlets of VD and of an impeller - densities ratio at outlet of VD and of an impeller inlet - velocity coefficient u u u k RT k 1 p t inl out - pressure ratio p inl - ade ockage factor hp p - polytrophic head coefficient u i - work coefficient T cu / u - loading factor - angle of ade generatrix inclination to radial direction, 0 p - polytropic efficiency i - flow rate coefficient doi: / x/90/1/0100 Subscripts 1 impeller ade row inlet impeller outlet - vaned diffuser inlet - vaned diffuser outlet av average ade calc calculated corr - corrected cr - critical des design exp experiment

4 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 h hub init initial imp impeller inc - incidence mean mean max maximum opt optimum out outlet s shroud doi: / x/90/1/ INTRODUCTION The complex of computer programs for gas dynamic design and flow path optimization named Universal Modeling method is in constant use from mid 1990TH [1, ]. The results of application and the process of the Method improvement are presented at conferences since 1995 []. Math model is the set of algebraic equations for calculation of head loss and mechanical work transmitted to gas. By means of th version math model several dozens of successful gas dynamic designs were created and realized by compressor manufacturers of Russia, Ukraine and Poland. The disadvantage of the model was that to calculate a stage performance with good accuracy an individual set of empirical coefficients must be applied. Different sets for stages with different design flow rate and loading factors were necessary. The proem was overcome in 5th version of the math model [, 5]. The presented 6th version extends 5th version advantages on stages with D impellers and vaned diffusers (VD). Below is presented the main features of the 6th version of the Method.. D IMPELLERS CALCULATION The new, 6 th version expands the 5 th version model achievements [, 6, 7, 5, 8] on D impellers and vaned diffusers. Calculation algorithm used in the 6 th version suggests more detailed calculation of head losses in D impellers. An important part is the more accurate definition of the hub/shroud surfaces and ades surface area. Blades surface area is of the same order as hub/shroud surfaces area unlike D impellers. It is important to calculate ades surface area precisely. The previous, th version treated the proem in the very simplified way [9]. As it is shown at Figure 1 (left) only three geometry parameters specified a meridian shape: non-dimensional impeller inlet diameter D 0, non-dimensional hub diameter D h,outlet height of ades b. Not universal empirical formulas were applied to surface area calculations. Hub and shroud non-dimensional area in th model: Shs Shs 1 D1 1 8 (1) D Blades surface area is defined as the product of ade length l and average ades height of an impeller: 1 The empirical formula for a ade length: S 0,5l b b () l D0 1.5Dh sin sin 1 ()

5 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 doi: / x/90/1/0100 Figure 1. D impeller meridian section by the th program version (left) and the 6 th version (right) This approach does not allow estimate accurately friction losses on all surfaces of an impeller. It also does not give an opportunity to optimize geometric dimensions of the D impeller by candidates comparison. Figure 1 (right) demonstrates the set of geometry parameters that completely describe an impeller meridian shape in 6 th version. This set is identical to one used for QD non-viscid calculations in the design process [1]. These parameters are: D 0, D h, b, a non-dimensional axial length of the impeller L m, hub and shroud curvature radius R h and R s, the angle of a shroud straight part. Position of the ade leading edge is determined too by the parameter l / l. The inlet ade height b 1 and diameter D 1 are calculated from the set of geometric quantities and is not user-defined. The surface area of a ade in 6 th version is: m imp S i lmi bi () 0 sin cos i Figure. Schematization of ade angle along ade meridian length To calculate ade area, it is necessary to know the function f lm. The analysis of ade angle variation with the length for several versions of D impellers is made, and as a result the schematic linear approximation is proposed. The D impellers designed in accordance with [1], in most cases,

6 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 doi: / x/90/1/0100 have firstly an increasing ade angle, a middle part with practically constant angles and descending angles near the outlet: - the initial portion lminit / l m = 0 0.5, assuming a linear angle increase from 1 to max ; - middle portion from lm mean / l m = 0.5-0,75, assuming constant ade angle max =1.5 ; - outlet portion from lm outl / l m = , assuming a linear angle decrease from max to. The graphical view of such schematization is shown in Figure. To calculate the ade surface area an impeller meridian length is divided into 0 sections. Figure demonstrates position of a ade surface generatrix on a conical surface a-a. Figure. Blade meridian cross section (left) and ade generatrix position on a conical surface a-a The angle of an inclination of a generatrix to a meridian plane on a surface a-a is not the independent design parameter. The angle varies along ade length and its value at a leading edge is equal sometimes. Big increases ade surface area and a ade ockage factor. It is taken into account in a simplified way - the angle average value is assuming to be equal to 0 0 for all D impellers. In accordance with loss model the friction force is proportional to average area of hub and shroud S 0.5 S S. The equation for calculations is: surfaces 0 h mean S S l 1 D z o 0 m av D sin av (5) CFD calculations of stages with different D impellers have demonstrated that correct calculation of surface area is important. For instance, D impellers with slightly excessive number of ades are much less effective than could be expected.. VANED DIFFUSER LOSS MODEL The sixth version uses a new algorithm for calculation the parameters in vaned diffusers. The vaneless part of greater or lesser extent is located before vaned diffuser. This is done to reduce the negative impact of uneven flow after impeller for vaned diffuser. Mechanical considerations are obvious. In this element, the approach presented in [, 5, 6, 7, 8] is applied with some modifications in case of D impeller. Some equations of the mathematical modeling for the vane part of the diffuser are presented below. Flow coefficient at vanes inlet is: D b X ( i) (6) 5

7 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 doi: / x/90/1/0100 The math model empirical coefficient X ( i ) takes into account a boundary layer ockage factor. The ade ockage factor is a geometry parameter: zvd vvd 1 K D sin (7) v The coefficient K is different for vanes of different shape airfoil type or other. The non-incidence inlet condition and incidence losses are determined with taking into account vanes load. The crucial factor is a direction of a streamline that goes to a critical point on a ade surface. Near a vane cascade a critical streamline deviates to a suction side of vanes where pressure is less. The scheme of this streamline behavior is presented in Figure. Figure. Velocity triangles at VD inlet The critical streamline increases its velocity tangential component on c u under an influence of vanes load. Non incidence condition is: The angle of a critical streamline is defined by the formula: (8) v cr cr arctg c c u u (9) To calculate a critical streamline deviation the scheme from [1] is applied: c u c D c D z ( D D ) u u VD (10) If a critical streamline direction does not correspond to vane inlet angle then incidence losses take place. The analogy with sudden expansion losses is used. The losses are proportional to difference of vectors c cr and c (velocity of inlet flow turned to direction of vanes) - Figure : cinc cu cu (11) tg v 6

8 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 doi: / x/90/1/0100 Formula for calculating efficiency losses incvd due to incidence inlet is similar to the corresponding formula in th version [10]: c X ( i) inc incvd X ( i)(1 X ( i)( u c ) ) (1) T The exit angle of the flow differs from the ade angle v on a deviation angle : (1) v Deviation angle, according to [, 11] is defined by the formula: v v l / t av (1) The optimum solidity of the vane cascade according to [1] is defined by the formula: l tav opt z VD D log D.7sin v v (15) Measurements of flow structure at diffuser exit demonstrated sufficient non-uniformity. Kinetic energy of flow is bigger than by 1D calculation (1D representation corresponds to uniform flow). Kinetic energy influences head loss in the following element return channel or scroll. Calculations by ANSYS CFX programs of a performance of the stator of the medium specific speed centrifugal stage have presented information on flow structure [9, 1]. The values of cd were averaged by energy m 0.5c D dm 0.5c at nine flow rates, i.e., at nine incidence angles i v. The same element was calculated by 6 th version computer program and c 1D values at the same conditions were defined. The ratio of the calculated by CFD velocity c D to velocity by 1D mode c1d is presented in Figure 5 ack square. Coefficient outlet: Knu takes into account flow non-uniformity at a vane cascade K nu cd. (16) c 1D Minimum of Knu corresponds to zero incidence angle i. The corrected value of non-dimensional velocity c corr is used in formula for head loss calculation in the element after vaned diffuser: c corr Presented in Figure 5 calculations were approximated by the formula: / sin K (17) nu 7

9 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 K doi: / x/90/1/0100 nu sin i (18) The Eq. (18) approximates results of the numerical experiment data satisfactory in the practically important part of the performance. Figure 5. Non-uniformity coefficient versus the incidence angle i Black square CFD/6 th version calculations, solid line simulation by eq. (18). MATHEMATICAL MODELLING VERIFICATION Test results of 8 model stages were used for 6 th version loss model identification (9 basic stages and their variants). The range of the main parameters of the model stages: des = , T des 6 6 = , D h = , D = , M u = , Re u = All stages consist of an impeller, vaneless or vaned diffuser and return channel. The basic stages were tested with varied hub ratio, vaneless diffusers (VLD) width, ade trailing edge configuration. Each test consisted of six different flow rate regimes. Thus, the identification process was made on the base of 8 empirical efficiency values. The identification process consists of search of empirical coefficients values that satisfy the condition: d Z exp calc 1 av Z 0 (19) After identifying the average error in calculating the maximum efficiency for all stages with vaned and vaneless diffusers which is equal to Average calculation error for six points on efficiency performance curves is Average calculation error for five points (except the highest flow rate regime) is Several model stages test performance curves and results of their simulation by the 6 th version model are presented at Figure 6. Verification of a mathematical model was made by comparison of calculated efficiency performance curves with measured ones for several industrial compressors designed by the Universal modeling method and by other designer design procedure is unknown. Test data are presented by manufacturers as results of official plant tests. There is one sample below. The flow path scheme drawings of two pipeline booster compressors 16 MW with a delivery pressure of 7.5 MPa and pressure ratio = 1.7. The designs of both compressors were made in due time by th version of the Method. Two-stage compressor flow path was places in the body of the standard pipeline compressor with = 1.. The elevated pressure ratio was achieved by increasing of impeller diameters and loading factor Т des =0.8. Low flow rate coefficient and big loading factor limited the efficiency by level of 80% - that is good for given non-dimensional parameters Figure 7. 8

10 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 doi: / x/90/1/0100 Figure 6. Five model stages test performance curves and results of their simulation by the 6th version model, dashed line test, solid line - simulation Figure 7. Performance curves of the 16 MWt four-stage pipeline booster compressor with VLD (air plant test). Solid line test, dashed line 6 th version Math model calculation Figure 8. Performance curves of the 16 MWt two-stage pipeline booster compressor with VD (air plant test). Solid line test, dashed line 6 th version Math model calculation The four-stage compressor with the same dimensional parameters has optimal non-dimensional parameters. The loading factor at the design flow rate is slightly less than 0.5. The optimal design flow rate coefficient of stages with D impellers lies in range Kinetic energy and surface area corresponds to minimum loss of a head in this case. Design flow rate coefficients of the compressor stages lie in this range. According to the official test maximum efficiency is 87.6%. Calculated and measured performance curves are compared at Figure 8. Simulation results are good in main part of performances. Maximum flow rate corresponds to a compressor operation with low pressure ratio. Compressors do not operate at these regimes in practice. Poor simulation result at the maximum flow rate has no practical significance. 9

11 IOP Conf. Series: Materials Science and Engineering 90 (015) 0100 doi: / x/90/1/0100 The analogy results were obtained for three more centrifugal compressors with significantly different parameters. CONCLUSION The new 6th version of the math model demonstrated ability to predict centrifugal stages and compressors gas dynamic performances with good accuracy. Precise calculations of stages and compressors with quite different design flow rate coefficients and loading factors are made by one common set of the empirical coefficients. Elevated power of modern PC opens way to further improvements of math modeling. One of evident ways is QD approach for modeling of D impellers that is inside visie future of the authors. ACKNOWLEDGMENT Work is performed with support of a Grant of the President of the Russian Federation for young PhD MK REFERENCE [1] Galerkin Y. Turbo compressors. [text] / Galerkin Y. // LTD information and puishing center. - Moscow. 010 [Russian]. [] Galerkin, Y. B., Soldatova, K.V. Operational process modeling of industrial centrifugal compressors. Scientific bases, development stages, current state. Monograph. [text] / Galerkin Y., Soldatova K.// Sankt-Peterburg. - SPbTU [Russian]. [] Galerkin Y.B., Popova E.Y., Danilov К.А., Mitrofanov V.P. Quasi-d Calculations in Centrifugal Impeller Design. VDI Berichte. 15. Hannover [] Galerkin, Y. B., Soldatova, K.V. Operational process modeling of industrial centrifugal compressors. Scientific bases, development stages, current state. Monograph. [text] / Galerkin Y., Soldatova K.// Sankt-Peterburg. - SPbTU [Russian]. [5] Galerkin, Y. B., Soldatova, K.V. The application of the Universal Modeling Method to development of centrifugal compressor model stages. [text] / Galerkin Y., Soldatova K.// International Conference Compressors and their Systems. London. 01. P [6] Galerkin Y., Drozdov A., Gas dynamic performances simulation of centrifugal compressor stages with D impeller. [text] / Galerkin Y., Rekstin A. // Scientific and technical transactions of the TU SPb. 01. No.. Page 5-5. [Russian]. [7] Y. Galerkin, A. Drozdov, K.Soldatova Centrifugal compressor efficiency types and rational application. [text] / Galerkin Y., Drozdov A., Soldatova K.// International Conference on Compressors and their systems. London: City University, UK. 01. [8] Galerkin, Y. B., Soldatova K.V., Drozdov A.A. New version of the Universal modeling for centrifugal compressor gas dynamic design. [text] / Galerkin Y., Drozdov A., Soldatova K.// Purdue Conference 01. USA. [9] Galerkin, Y. B., Marenina L.A. Research and improvement of centrifugal stages fixed elements by methods of computational dynamics. Part 1. / Galerkin Y., Marenina L.// Compressors and pneumatics, P [Russian]. [10] Galerkin Y. Danilov K., Popova E. Design philosophy for industrial centrifugal compressor. [text] / Galerkin Y., Danilov K., Popova E. // International Conference on Compressors and their systems. London: City University [11] Den G.N. Mechanic of a stream in centrifugal compressors. [text] / Den G. // Leningrad. Mechanical engineering [Russian]. [1] Ris V. Centrifugal compressors. [text] / Ris V. // - Leningrad [Russian]. [1] Galerkin, Y. B., Marenina L.A. Research and improvement of centrifugal stages fixed elements by methods of computational dynamics. Part. / Galerkin Y., Marenina L.// Compressors and pneumatics, 01.. P [Russian]. 10