CENTRIFUGAL COMPRESSOR DESIGN AND TESTING IN THE FINNISH HIGH SPEED TECHNOLOGY J. Larjola, J. Backman, H. Esa, H. Pitkänen, P. Sallinen and J. Honkatukia Lappeenranta University of Technology, Department of Energy Technology P.O. Box 20 , 53851 Lappeenranta, Finland E-mail:
[email protected]
ABSTRACT This paper reports on the work carried out in the Laboratory of Fluid Dynamics, at Lappeenranta University of Technology (LUT), which has been designing and testing compressors, turbines and pumps since 1982. The Laboratory has been responsible of large number of centrifugal compressor design and testing in Finland. These compressors are usually directly connected to a high speed electric motor. Speed control is used instead of IGV and diffuser vane control and this sets some additional requirements e.g. for compressor performance map shape. One dimensional computation, giving the basic geometry and performance map of compressor, is made with a program developed by LUT. Then a three-dimensional program, developed also by LUT is used to define the whole compressor wheel geometry. The wheel geometry data is used in the flow and the structure analyses. The compressor flow is calculated with a three-dimensional CFD-program (Finflo), which has been designed by Helsinki University of Technology and modified for centrifugal compressor flow together with LUT. The final compressor geometry is measured in the test facility at Lappeenranta University and the test results are used to develop the design loop. Up to this date, around 15 high speed compressors have been aerodynamically designed and tested in this design loop. Typical pressure ratio of the compressors ranges from 1.6 to 2.5.
NOMENCLATURE e specific internal energy u,v,w Cartesian velocity components x,y,z Cartesian coordinates p pressure r r radius t time y+ non-dimensional distance E total internal energy F,G,H inviscid flux vectors Fv,Gv,Hv viscous flux vectors Pinput input power Q source term R residual S cell face area U solution vector V volume r V absolute velocity R density γ ratio of specific heats π pressure ratio Ω angular velocity
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INTRODUCTION In the centrifugal compressor the flow enters axially, but is then turned radially out from the impeller. The static pressure rises due to the decrease of the relative velocity, but also due to the centrifugal forces. After the impeller, the flow enters a radially annular vaned or vaneless diffuser. In vaneless diffuser, the flow is slowed by the free vortex. The compressor needs a gathering body, volute, to assemble the flow to the next stage or to the outlet piping. The first part of the paper deals how the design of a centrifugal compressor starts with the definition of the initial parameters, which are used to calculate the one-dimensional flow in the corresponding program. This program, developed by LUT, uses empirical data from literature and test results from previous design to give preliminary results about the compressor performance. Compressors, which design is presented here, are usually directly connected to a high speed electric motor. Speed control is used instead of IGV and diffuser vane control and this sets some additional requirements e.g. for compressor performance map shape. Benefits of this High Speed Technology are presented in details in Larjola (1986 and 1988), Larjola and Backman (1995) and Larjola et al. (1995). It is required, that at the design pressure ratio the compressor has an operating range 1:2 in mass flow, when optimal speed control is used. It is also required, that the high efficiency range of compressor is as wide as possible. The initial parameters of compressor impeller geometry and flow are used in the three-dimensional program, which is used to define the whole compressor wheel geometry. This program, developed also by LUT, calculates the blades and wheel passages in details, which can be examined in more details to find any non-conformity and to optimize the blade thickness distribution. The wheel geometry data is used in the flow and the stress and vibration analyses. The compressor flow is calculated with three-dimensional CFD-program (Finflo), which has been designed by Helsinki University of Technology and modified for centrifugal compressor flow together with LUT. The program also calculates the flow in the stator of the compressor. Normally the computation is made time-averaged, but also some timedependent calculations have been made. Results of CFDcalculation and one-dimensional calculation are compared, and the design procedure repeated, if necessary, see Pitkänen et al. (1999a, 1999b and 1999c). The high complexity of the flow, especially in the rotating impeller, makes the CFD modeling very difficult. There has been done much research in analysing the flow and the different viscous phenomena, but there are still no programmes that can calculate the time dependent flow explicitly. The final compressor geometry is tested in the test facilities at Lappeenranta University and the test results are used to develop the design loop. Up to this date, around 15 high speed
compressors have been aerodynamically designed and tested in this design loop. 1. ONE-DIMENSIONAL FLOW DESIGN In the early 80’s the first compressor design was based on the theory of one-dimensional flow in centrifugal compressors. The design team gathered data from literature and visited to other universities and was convinced that the design of a centrifugal compressor starts with the definition of the initial parameters, which are used to calculate the one-dimensional flow in the corresponding program. Gradually, we were able to have data also from our own measurements and the team developed the program design principles further.
Fig. 1 Result window of the one-dimensional flow design program The one-dimensional flow design program, developed by LUT, uses empirical data from literature and test results from previous design to give preliminary results about the compressor performance as well as some impeller and diffuser geometrical parameters. The calculation routine is sequential, iterative and quick with modern personal computers. The input data includes compressor pressure ratio, inlet temperature, inlet pressure, fluid (humid air is the most frequently used fluid), rotational speed and mass flow. The program includes variables that can later be altered: specific speed, different geometrical ratios, number of blades in the impeller and diffuser, loss constants, inlet flow angles, volute pressure recovery factor, etc. Although the program has been programmed in the DOS environment, it has all the results onscreen (Fig. 1) and the main calculation results are: Pressure, temperature, enthalpy, specific volume in the inlet (1) and outlet (2) of the impeller wheel, outlet of the diffuser (3) and volute (4). Pressure, temperature and enthalpy are given with the static and stagnate conditions (1 and 01) Main geometry parameters for the impeller, diffuser and volute. Also, compressor specific speed and power consumption Isentropic efficiency and pressure ratio in each point, pressure recovery in the diffuser and volute
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Velocity triangles, deviation angle and relative Mach number in the impeller wheel inlet and outlet The program calculates the off-design performance automatically and produces the compressor performance map for further studies on the performance. 2. THREE-DIMENSIONAL GEOMETRY DESIGN The high-speed research team has been involved in the impeller research since 1982, first with radial turbines and then with centrifugal compressors. The full geometry design is vital for CFD analysis and manufacturing and predicting the operational strength of the impeller. The impeller blade geometry for centrifugal compressors is generated using a software developed by LUT. Before the year 1998 the three-dimensional geometry modeling program developed by LUT has been used in minicomputers. The need for using microcomputers for impeller blade design arose after the mid-1990’s and thus a new software for microcomputers was developed at LUT.
When the blade designer accepts the blade geometry the numerical geometry data can then be generated for compressor flow CFD analysis, finite element method (FEM) based stress and vibration analysis (FEM) and computer aided manufacturing (CAM). If any non-conformity is found in blade geometry or the results from either CFD or FEM analysis do not meet the requirements, the design procedure must be repeated partially or totally, even starting from one-dimensional flow design.
Fig. 3. View of one flow passage (full blade suction side to splitter pressure side) of an impeller.
Fig. 2. Axial view of an impeller blade. Generating the impeller blade geometry for centrifugal compressors proceeds as follows. The main geometry data of the impeller, such as the main dimensions and the blade angles obtained from one-dimensional flow design (see chapter 1), is used as input data for three-dimensional modeling. Blade design is started with defining the camber lines for the hub and shroud of an impeller blade. The three-dimensional modeling software provides a graphical blade design environment for modifying camber line geometry. The next stage is to define the thickness distributions for the hub and shroud of the blade and they can be modified graphically, as well. Based on the camber lines and the thickness distributions the suction and pressure side coordinates for the hub and shroud are finally calculated. The blade can be displayed using various projections (Fig. 2 and 3).
3. THREE-DIMENSIONAL FLOW DESIGN Modern computers and softwares have made the numerical testing of the compressor geometry design possible. Generally, it is much more economical to find out the locations in the geometry needing some modifications compared to the real laboratory experiments. The computational fluid dynamics (CFD) has been a part of the radial compressor design process at Lappeenranta University of Technology since 1995. The result of the 3D design program, i.e., the boundary curves of the full and splitter blades, can directly be read into the pre-processor, which converts the data into the Cartesian coordinate system. Both the full and splitter blades consist of four boundary curves: the hub and shroud curves on pressure and suction surfaces, respectively.
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solution of the Reynolds averaged Navier-Stokes equations with Cartesian velocity components
∂ U ∂ ( F − Fv ) ∂ ( G − Gv ) ∂ ( H − H v ) + + + =Q ∂t ∂x ∂y ∂z
(1)
where the solution vector U = [ ρ , ρ u, ρ v , ρ w, E ] , and F, G, T
H are the flux vectors in each coordinate direction, respectively. r r r r Here ρ is the density, V = ui + vj + wk is the absolute velocity, and E is the total internal energy. The rotational speed of the r r T domain is Ω × r = [0, − Ωz , Ωy] and the convective, i.e. the r r r relative speeds are V − Ω × r . In the case of the steady or quasiFig. 4. One impeller passage. Splitter blade in the middle. The grid generation is made by an automatic generation tool of a commercial turbomachinery oriented software, IGG (1997). The main input parameters for the grid generation besides of the blade geometry data are the number of cells at each block, and the type of the grid clustering near the solid walls. The tip-clearance size and the leading edge rounding are specified also at the input data file. The grid covers also part of the inlet duct and the vaneless diffuser. Typically only single impeller passage is modeled, Fig. 4. The effect of the grid quality has to be known in the CFD simulations. In order to capture the real physical phenomena, e.g., boundary layer thickness and secondary vortices in the blade passage, the number of cells should be large enough. But, when the number of cells grows, the calculation time increases rapidly. The grid size is, therefore, a compromise between time and resolution of the result. Most of the radial compressor impeller simulations have been made by using a grid, where the size of the cross-sectional grid of the blade passage between two adjacent full blades is 64x32x64 in azimuth, spanwise and streamwise directions, respectively. Besides the grid size, height of the first cell on the solid surface is important. The size has to be set in order to get the y+ value near unity. If first cell is bigger, the solution could underestimate the losses. After the grid has been generated, the boundary conditions for the flow solver have to be defined. The values for rotational speed, mass flow rate, total inlet temperature, and static pressure at vaneless diffuser outlet are taken from 1D program. Thus, inlet pressure, as well as the outlet temperature, are the results of the CFD analysis. All the solid walls at the impeller are defined as rotating wall excluding the shroud surface. The flow solver FINFLO, developed in Helsinki University of Technology, has been used in the compressor simulations, Siikonen and Pan (1992). It has been applied for many kind of both internal and external flow simulations. In the steady-state solution as well as in the time-accurate simulation the impeller is assumed to rotate around the x-axis with an angular velocity Ω. The simulation is based on the
steady computation a source term Q = [0, 0, ρ Ωw, − ρ Ωv , 0] is T
introduced, but in the time-accurate calculation Q = 0. The quasi-steady calculations are performed in the rotating coordinate system with Cartesian velocity components and modified convective speeds. In the case of the time-accurate solution the convective speeds are identical to those in a rotating coordinate system. Hence, the only difference between these two approaches concerns the source term Q. The pressure is calculated from an equation of state. For a perfect gas p = (γ − 1) ρ e , where γ is the ratio of specific heats
and e is the specific internal energy. The molecular viscosity is calculated from Sutherland's formula. The Reynolds stresses in the viscous fluxes Fv, Gv and Hv are modeled using Boussinesq's approximation. The algebraic turbulence model developed by Baldwin and Lomax (1978) is applied in order to calculate turbulent viscosity. The implementation of the model is given in Reunanen (2000). The quasi-steady approach and the time-accurate solution utilize the same basic steady-state algorithm. In the present solution, a finite-volume technique with a structured grid is applied. The flow equations have a discrete form Vi
dU i = dt
∑ − S ( F$ − F$v ) + Vi Qi = Ri
(2)
faces
where the sum is taken over the faces of the computational cell. In the evaluation of the inviscid fluxes in a moving grid, Roe's method, Roe (1981) is applied. A MUSCL-type approach has been adopted for the evaluation of the primary flow variables (ρ, u, v, w, p) on the cell surfaces. The viscous fluxes are evaluated using a thin-layer approximation. The thin-layer model is activated in all coordinate directions. Equation (2) is integrated in time implicitly by applying the DDADI-factorization, Lombard et al. (1983). The resulting implicit stage consists of a backward and forward sweep in every coordinate direction. The boundary conditions are treated explicitly, and a spatially varying time step is utilized. Furthermore, a multigrid acceleration of convergence is utilized.
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The time-accurate simulation is based on a dual timestepping, i.e. it shares the same basic features described above, but now the pseudo time-integration is performed inside a physical time step and a true time derivative is added on the right-hand side of Eq. (2). A three-level fully implicit scheme is applied for the time-integration, Hoffren et al. (1995). More details of the solution methods are given in Siikonen (1995) and Reunanen (2000). Two multigrid levels are typically used in the simulation. The first few hundred iterations are calculated using a coarse grid, which contains only half of the grid points at each gridindex direction. The result of the coarse grid is used as the starting point for the dense-grid simulation. It is practical to start the CFD analysis from the nearoptimum operating point locating at the middle of the performance map. If the simulation converges normally, the result is saved, and the next operating point can be simulated for instance using the same speed and outlet pressure, but little bigger or smaller mass flow rate until the operating limits are reached. The calculation time is strongly related to the grid, and computer speed. Usually the simulation of one operating point can be done overnight with a modern workstation without using parallelization. The CFD result is mainly used for the preliminary verification of the compressor impeller performance. It gives estimations for the pressure ratio and efficiency levels at selected operation points. It also predicts the operation range between stall and choking limits. According to the CFD results, it is possible to make modifications to the geometry. It should be noted that the full stage performance estimation with CFD would need also the volute analysis. However, it is not always modeled due to the complicated and time-consuming grid generation process. If the volute is analyzed separately, the combination of the impeller and volute results is possible but then some simplifications have to be accomplished Pitkänen et al (1999c). The full stage simulation is often too complex and slow task for design purposes, but it will come more common in future. Currently the volute is taken into account roughly by using an estimated pressure recovery coefficient. Result of that method is shown in Fig. 5. In practice, experimental studies can not be fully replaced by the numerical simulations because there are always some options, which may have an effect to the result, e.g. grid density, grid quality, and models of turbulence. At present, performance of the manufactured devices, which are going to be installed into the plant, is always verified by the measurements. CFD results have to be compared with that data.
Fig. 5. Comparison between CFD predicted and measured data of the centrifugal compressor stage.
4. TEST FACILITIES The high-speed technology compressors have been commercially manufactured since 1996 in Finland. The LUT research group has designed hundreds of different compressor wheels with the one-dimensional flow design program for different production plans. From previous basic design, 35 have been designed with full geometric details and 20 have been gone through Finflo calculations. The commercial compressors have been tested both for general and individual performance. The test facility for general performance is situated at LUT and it is built to give accurate information from compressor inlet and outlet conditions. The compressor test facility can be used both for overpressure and vacuum compressors. In a standard measuring procedure the compressor thermal efficiency, compressor total efficiency, mass flow rate, pressure differential produced by compressor and the electric input power are measured. Main parts of the measuring arrangements are described in figures 6 and 7. The fluid flow is measured with standard orifice and nozzle. Mass flow measurement is measured by means explained standards ISO 5167, VDI 2041 chapter 5.2. VDI 2041 standard tells the special measurement of the gas flow. It gives technique how to measure the mass flow of the gas when the orifice or nozzle is at the beginning of a pipeline. The compressor performance is measured by means explained standards ISO 5389, VDI 2045 and ASME Power Test Code. The measured values are corrected to the same inlet, temperature and air humidity.
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Fig. 6. Compressor test facility layout. When the compressor is used with different inlet conditions, the aerodynamical performance differs from that on the test facility. This will be taken into account with calculation in which similarity laws are used. Conversion of the test results from test conditions to the specified conditions, assuming constant polytropic efficiency.
Fig. 7. Schematic of compressor test facility.
Previously mentioned assumption is generally only possible when similarity of the flow is assured for the conversion of a test point to specified conditions, i.e. when the following main requirements are fulfilled /ISO 5389 Annex D, Similarity of the flow, Similar velocity triangles/, a) geometrical similarity b) equal isentropic exponent c) equal enthalpy rise coefficients and flow coefficients d) equal Mach numbers e) equal Reynolds numbers
All measuring data is collected with data logger into a computer in which the needed parameters are calculated. The measured signals are analyzed with PC-program that saves the original data into a file, calculates the compression process and shows the most significant process parameters. The program also saves the stationary measured data points into a file that can be utilized by other program to show the compressor map. Absolute pressure and pressure difference are measured by Rosemount and Druck transmitters. Temperatures are measured by K-type thermocouples. Relative humidity is measured by Vaisala humidity sensor. Compressor shaft speed is measured with magnetic pulse generator installed permanently to the compressor shaft and compressor electrical input power is measured with LEM Norma D4000 power analyzer. The uncertainty of the mass flow measurement can be determined with the help of the standards /ISO 5167/ and /ISO 5168/. Performing partial differentiation uncertainties of the other terms can be calculated. Current uncertainties of the various terms are: - uncertainty at the 95.4% confidence level in input power measurements is about ± 0.3% - uncertainty of the electromechanical efficiency is about ± 0.9% when Pinput is 45 kW and electromechanical efficiency is 88% - uncertainty of the flow rate is about ± 0.9% - uncertainty of the pressure ratio is about ± 0.6%, - uncertainty of the isentropic efficiency is about ± 1.2%, - uncertainty of the compressor total efficiency is about ± 0.9%. 5. CONCLUSIONS This paper reports on the work carried out in the Laboratory of Fluid Dynamics, at Lappeenranta University of Technology (LUT), which has been designing and testing compressors, turbines and pumps since 1982. The Laboratory has been responsible of large number of centrifugal compressor design and testing in Finland. These compressors are usually directly connected to a high speed electric motor. Instead of IGV and diffuser vane control speed control is used, which sets some additional requirements e.g. for compressor performance map shape. It is required, that at the design pressure ratio the compressor has an operating range 1:2 in mass flow, when optimal speed control is used. It is also required, that the high efficiency range of compressor is as wide as possible. Efficiencies obtained are from 80 to 82% in this operating range (vaneless diffuser). Calculated values with the own programs used in design are within 2 to 4% from the measured ones in most cases. The final compressor geometry is tested in the test facilities at Lappeenranta University and the test results are used to develop the design loop. Up to this date, around 15 high speed compressors have been aerodynamically designed and tested in this design loop. Typical pressure ratio of the compressors
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ranges from 1.6 to 2.5 and rotational speed from 25,000 rpm to 40,000 rpm. ACKNOWLEDGMENTS
The authors wish to acknowledge the Technology Development Centre of Finland and High Speed Tech Oy LTD for the financial support for this work. The authors also wish to thank Professor T. Siikonen of Helsinki University of Technology for providing the basic solver for CFD-calculations. REFERENCES Baldwin B., Lomax H., 1978, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows”, AIAA Paper 78-275. IGG, 1997, Interactive Geometry Modeller and Grid Generator, User Manual, Version 3.6, NUMECA International Hoffren J., Siikonen T., Laine S., 1995, ”Conservative Multiblock Navier-Stokes Solver for Arbitarily Deforming Geometries”, Journal of Aircraft, Vol. 32, No. 6, pp. 1342-1350 Larjola J., Backman J., 1995, ”Oil free bearings in high speed technology". Stockholm Power Tech, June 18-22, 1995, International Symposium on Electric Power Engineering, invited speakers' sessions, pp. 63-68 Larjola J., Alamäki J., Sallinen P., 1995, ”High speed pumps in water jet cutting and in water jetting”. - Proceedings of the 4th Pacific Rim International Conference on Water Jet Technology, April 20-22, 1995, Shimizu, Japan. Part l: Future applications of the jetting technology (Invited papers), pp. 4756 Larjola J. (editor), 1988, ”Proceedings of Conference on High Speed Technology”, August 21-24, 1988, Lappeenranta, Finland. Lappeenranta University of Technology, Department of Energy Technology, publ. No ENTE D-15, 288 p. Larjola, J., 1986, ”High-Speed Turbomachinery and Its Application in the Conversion of Energy”, ASME Winter Annual meeting, Anaheim, December 7-12, 1986. ASME publ. 86-WA/FE-4 Lombard C., Bardina J., Venkapathy E., Oliger J., 1983, “Multi-Dimensional Formulation of CSCM – An Upwind Flux Difference Eigenvector Split Method for the Compressible Navier-Stokes Equations”, 6th AIAA Computational Fluid Dynamics Conference, Massachusetts, pp. 649-664. Pitkänen H., Esa H., Sallinen P., Larjola J., Heiska H., Siikonen T., 1999a, ”Time-accurate CFD analysis of a centrifugal compressor”. Fourth Int. Symposium on Experimental and Computational Aerodynamics of Internal Flows, Dresden August 31 to September 2. Proceeding Vol. 2, pp. 130-139 Pitkänen H., Esa H., Reunanen A.., Sallinen P., Larjola J., 1999b, ”Experimental and numerical investigation of a centrifugal compressor volute”. Fourth Int. Symposium on Experimental and Computational Aerodynamics of Internal Flows, Dresden August 31 to September 2. Proceeding Vol. 2, pp. 120-129
Pitkänen, H. Esa H., Sallinen P., Larjola J., 1999c, ”CFD analysis of a centrifugal compressor impeller and volute”. Int. Gas Turbine & Aeroengine Congress, Indianapolis, June 7 June 10. ASME publ. 99-GT-436, 8 p. Reunanen A., Pitkänen H., Siikonen T., Heiska H., Larjola J., Esa H., Sallinen P., 2000, “Computational and experimental Comparison of different volute geometries in a radial compressor,” Accepted to: Int. Gas Turbine & Aeroengine Congress, May 8-11, 2000, Munich, Germany, ASME Paper 2000-GT-0469 Roe P., 1981, “Approximate Riemann Solvers, Parameter Vectors and Difference Schemes”, Journal of Computational Physics, Vol. 43, pp. 357-372. Siikonen T., 1995, ”An Application of Roe’s FluxDifference Splitting for the k-ε Turbulence Model”, International Journal for Numerical Methods in Fluids, Vol. 21, pp. 1017-1039 Siikonen T., Pan H., 1992, "Application of Roe's Method for the Simulation of Viscous Flow in Turbomachinery," Proceedings, First European Computational Fluid Dynamics Conference, Ch. Hirsch et al., ed., Brussels, Belgium, pp. 635641
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