IJSRD - International Journal for Scientific Research & Development Vol. 3, Issue 03, 2015 ISSN (online): 2321-0613 Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale Samkit V Shah 1 Prof. Nilesh R.Sheth 2 Prof. Samip P.Shah 3 1 ME Student 2,3 Professor 1 Department of Energy Engineering 1,2 GEC Valsad 3 C.K.P.C.E.T Surat Abstract This paper investigates the development of a preliminary design method for centrifugal compressors. The analysis and design of Turbo-machines, at any level of sophistication, must ultimately be based on an understanding of the thermodynamics and fluid mechanics processes which take place in the machine. On the simplest level a preliminary design may consist of no more than the application of the basic equations to estimate the magnitude of overall design parameters, while on more complex level the design methods will attempt to simulate more closely the actual flow. The present work describes the simplified approach to optimum design of centrifugal compressor stage with the help of fundamental equations, which describe thermodynamics, and aero-fluid dynamic flow process in Turbo-machines. Key words: Conceptual Design for Centrifugal Compressor Impeller, aero-fluid dynamic flow NOMENCLATURE: 1) SYMBOLS A- Flow area section of impeller, diffuser & volute channels a -Speed of sound C- Absolute velocity of gas (Air) W- Relative velocity of gas with respect to rotating element D 2 -Impeller exit (tip) diameter i -Blade incidence angle M u -Blade Mach number M, M - Absolute & Relative Mach number m -Mass flow rate N - Rotational speed of Impeller P - Fluid static pressure PR - Stage total pressure ratio P o - Fluid Stagnation pressure R - Universal gas constant, Radius t b - Impeller blade thickness U 2 -Blade tip speed x- Meridional (axial) distance from axis of rotation Z b - Number of Impeller blades z -Axial meridional distance along axis of rotation SPECIAL CHARACTERS α - Absolute flow angle w.r.t meridional (flow) direction β -Relative flow angle w.r.t flow direction β B -Blade angle λ -Work input coefficient γ -Isentropic index for air ν -Impeller eye hub to shroud diameter ratio μ -Slip factor η -Efficiency φ -Flow co-efficient 2) SUBSCRIPT I -Impeller Total to Total S -Stage Total to Total 01-Stagnation state at inlet to eye 02 -Stagnation state at impeller exit 1 -Static state at impeller eye 2 -Static state at impeller exit 1s - State at shroud of impeller eye inlet 1h -State at hub of impeller eye inlet 1m -State at mean section of impeller eye inlet a -Axial meridional component m -Radial meridional component θ -Tangential component I. INTRODUCTION Centrifugal compressor, also called radial compressor, are critical equipment in a wide variety of application in the chemical process industries, power plant etc. As their name suggest, their primary process is to compress a fluid in to smaller volume while simultaneous increasing pressure and temperature of fluid. In other words, compressor accepts a mass of gas at some initial pressure and temperature and rise pressure and temperature of a gas. A Solid foundation for turbo machinery design must comprise basic fundamentals and useful experience. Both the basic principles of fluid mechanics and thermodynamics on the one hand and appropriate design data on the other hand are essential. If these two resources are utilized effectively, very fine design can be prepared for new application. There are, however probably as many different design techniques as there are designers in the world. Each designer undoubtedly uses similar basic principles with a different combination of experimental data to achieve the desire result. II. CONCEPTUAL DESIGN FOR CENTRIFUGAL COMPRESSOR IMPELLER The main requirement from an impeller design procedure is the computation of the overall principal dimensions and the inlet and discharge blade angles. Impeller design procedure is carried out applying non dimensional parameters thermodynamic correlation which disregard actual size of machine and more general compared to dimensional quantities. A. Impeller Design Steps: Impeller design has been accomplished systematically for complete control of aerodynamic parameters within optimum recommended range. Input parameter are as follows Power (P) Stagnation Pressure ratio (PR) from 1.5 to 5 bar [9] Gas constant (R=287 kj/kg. K) Specific heat ratio (ϒ=1.4) At inducer eye hub to shroud diameter ratio (D1h/D1s) from 0.3 to 0.6 [9] shroud inlet diameter to Outlet diameter (D1s/D2) from 0.4 to 0.9 [9] Impeller Total to Total Efficiency (η I ) All rights reserved by www.ijsrd.com 839
Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale Stage Total to Total Efficiency (η S ) Inlet blade angle at shroud (β1s) from 560 to 640 [9] Inlet absolute Flow angle (α1) outlet Blade angle (β2 ) from 00 to -600 [9] outlet absolute flow angle (α2) from 600 to 700 [9] 1) Step: 1 Determination of Blade Mach number (M u ) It is governing parameter to decide the size and rotational speed of impeller. Correlation between M u and stagnation pressure ratio is given as Fig. 2.2: Velocity Triangle At Outlet [5] For radial impeller β B2 = 0o, So λ=μ= 0.8 to 0.9 [3] For high speed compressor developing high pressure ratio, maximum allowable value of M u would be under 2. [4] 2) Step 2: Determination of stagnation temperature ratio and pressure ratio (T o2 /T 01 & P 02 /P 01 ) Generally, inlet stagnation condition is known to designer. So knowledge of Mu gives the value of developed stage total stagnation temperature. Fig. 2.1: Main Component Of Centrigugal Compressor With Velocity Triangle At Inlet And Exit [9] 3) Step 3: Determination of Absolute Impeller Exit Mach number (M 2 ) It depends on M u and absolute exit flow angle α 2. Johnston and Dean (1966) showed that an optimum swirl angle α 2, for design purposes, lies between 63 to 68 degrees. Similarly Rodger and Sapiro (1972) considered the optimum flow angles to lie between 60 to 70 degrees w.r.t radial direction. [9] 4) Step 4: Determination of Relative outlet Mach number ( ' M 2 ) at shroud All rights reserved by www.ijsrd.com 840
Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale 6) Step 6: Determination of Non-dimensional mass flow rate, flow co-efficient Impeller Blade height to outlet radius ratio. Flow co-efficient: 5) Step 5: Determination of absolute and Relative ' inlet Mach number ( M 1s & M 1s ) at shroud Non-dimensional Mass flow rate ratio: In actual case blade height at impeller exit (b 2 ) is higher than above calculated value due to consideration of hub thickness of each vane, therefore let actual blade height be found assuming b2 = 1.1 b 2. 7) Step 7: Now specify the mass flow rate and inlet stagnation condition to convert the Nondimensional geometry of impeller in to absolute dimension Density at inlet of impeller Fig. 2.3: Inlet Velocity Triangle At Hub Shroud And Mean [5] Sound velocity at inlet Outlet flow area from impeller Outlet radius of impeller All rights reserved by www.ijsrd.com 841
Width of impeller blade flow passage at outlet Inlet shroud radius Inlet hub radius Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale Where, K 1 = 0.28 and K 2 = 0.8 For hub, a = -Z 1h, b = Z 2h (L)-Z 1h, c = -X 2h, d = X 1h - X 2h For shroud, a = -Z 1s, b = Z 2s -Z 1s, c = -X 2s, d = X 1s - X 2s ; p 2 3 2 3 q 1 1 2 2 p = 3 and q = 2 value is applied as it gives slight long axial path inducer without prewhirl. 8) Step 8: Determination of Impeller blade numbers and maximum hub thickness (Z b, t bh ) Various correlations for estimation of slip factor (μ) have been developed by many researchers applied for wider range of impeller vane no.(z b ), vane exit angle (β B2 ) and radius ratio. Stodala equation:[13,14] Where β B2 = 0 for radial vane Weisner equation[10] Stanitz equation:[10,14] Impeller blade hub thickness (t bh ) can be determined from exit flow area correlation based on blade thickness consideration as, Where, b 2t = 1.1b 2 9) Step 9: Impeller geometry for Centrifugal Compressor Vanes [11] Wallace (1975) represented impeller geometry by means of Lame Ovals equation of general form: Where, x is radius (r) for hub or shroud lines for radial blade impeller. The coefficients a, b, c and d are obtained from the end conditions (x 1, z 1 ) and (x 2, z 2 ) for shroud and hub curve with assumption and axial inlet and radial exit blade. p and q are indices and can be varied to get series of analytic curves. From an aerodynamic standpoint, Birdi [5] has suggested correlation for optimal axial length- tip diameter ratio. Fig. 2.4: Impeller meridional geometry REFERENCES [1] Duccio Bonaiuti, Andrea Arnone and Mirco Ermini Analysis and Optimization of Transonic Centrifugal Compressor Impellers Using the Design of Experiments Technique ASME Vol. 128, OCTOBER 2006. [2] Hua Chen and Vai-Man Lei Casing Treatment and Inlet Swirl of Centrifugal Compressors ASME Vol. 135 JULY 2013. [3] Abraham engeda and yunbae kim The inlet flow structure of centrifugal compressor stage and its influence on the performance ASME journal of engineering for power, 2003. [4] Barend w. botha and andriaan moolman Determining the impact of the different losses on Centrifugal compressor R&D journal,2005. [5] Pekka R oytt a, Aki Gr onman, Ahti Jaatinen, Teemu Turunen-Saaresti, and Jari Backman Effects of Different Blade Angle Distributions on Centrifugal Compressor Performance Hindawi Publishing Corporation International Journal of Rotating Machinery Volume 2009 23 November 2009. [6] Milesh coopinger Aerodynamic performance of an industrial centrifugal compressor variable inlet guide vane system Lough borough university,1999, [7] Nilesh paul murray Effect of impeller diffuser interaction on centrifugal compressor performance Massachusetts institute of technology, 2000. [8] James M. Sorokes, Cyril J. Borer ans Jay M. Koch Investigation of the Circumferential Static Pressure Non-Uniformity Caused by a Centrifugal Compressor Discharge Volute Dresser-Rand, Olean, USA All rights reserved by www.ijsrd.com 842
[9] Adnan Hamza Zahed and Nazih Noaman Bayomi Design Procedure of Centrifugal Compressors ISESCO JOURNAL of Science and Technology Volume 10 - Number 17 - May 2014 (77-91) [10] C. Xu and R. S. Amano Meridional Considerations of the Centrifugal Compressor Development Hindawi Publishing Corporation International Journal of Rotating Machinery Volume 2012,4 september 2012. [11] Flore Crevel,Nicolas Gourdain and Xavier Ottavy Numerical Simulation of Aerodynamic Instabilities in a Multistage High-Speed High- Pressure Compressor on Its Test Rig Part II: Deep Surge ASME OCTOBER 2014, Vol. 136 [12] Flore Crevel,Nicolas Gourdain and St_ephane Moreau Numerical Simulation of Aerodynamic Instabilities in a Multistage High-Speed High- Pressure Compressor on Its Test-Rig Part I: Rotating Stall ASME OCTOBER 2014, Vol. 136. [13] D pan and A whitefield Design consideration for the volutes of centrifugal fan and compressor Journal of Mechanical engineering science, Vol.213, 1999. [14] I Bennett and R L Elder The Design and analysis of pipe diffuser for centrifugal compressor Journal of power and energy, Vol.214,2000. [15] G. Naga Malleshwar Rao, Dr. S.L.V. Prasad and Dr. S. Sudhakarbabu A COMPUTER PROGRAMMED DESIGN OPTIMISATION AND ANALYSIS OF COMPRESSOR IMPELLER Volume 2, Issue 1, January 2014 International Journal of Research in Advent Technology. BOOKS: [16] Whitefiled and N.C.Basines Design of radial turbomachines Longman scientific and technical publication. [17] David Japikse Centrifugal compressor Design and performance ETI. Non-Dimensional Aerodynamic Design of Centrifugal Compressor for Small Scale All rights reserved by www.ijsrd.com 843