A Three-Dimensional Unsteady CFD Model of Compressor Stability

ABSTRACTA three-dimensional unsteady CFD code called CSTALL has beendeveloped and used to investigate compressor stability. The codesolved the Euler equations through the entire annulus and all bladerows. Blade row turning, losses, and deviation were modeled usingbody force terms which required input data at stations between bladerows. The input data was calculated using a separate Navier-Stokesturbomachinery analysis code run at one operating point near stall,and was scaled to other operating points using overall characteristicmaps. No information about the stalled characteristic was used.CSTALL was run in a 2-D throughflow mode for very fast calcula-tions of operating maps and estimation of stall points. Calculated pres-sure ratio characteristics for NASA stage 35 agreed well withexperimental data, and results with inlet radial distortion showed theexpected loss of range. CSTALL was also run in a 3-D mode to inves-tigate inlet circumferential distortion. Calculated operating maps forstage 35 with 120 degree distortion screens showed a loss in range andpressure rise. Unsteady calculations showed rotating stall with twopart-span stall cells. The paper describes the body force formulation indetail, examines the computed results, and concludes with observa-tions about the code.NOMENCLATUREb blockageinviscid fluxese total energyF body force for turningf body force for lossh, p, T, s enthalpy, pressure, temperature, entropyCentrifugal, Coriolis, and blockage source termsm meridional directionalcorrected mass flowq vector of conserved variablest timeV velocitycylindrical coordinatescylindrical velocity componentsrelative flow, blade, and deviation anglesdifferencestreamwise grid directiondensitythroughflow time scalebody force vectorbody force scaling functionturning function for deviationblade row angular velocityloss coefficientSubscripts0 stagnation state1,2 upstream, downstreamLE, TE leading edge, trailing edgeturning, entropy, deviation, reference pointgrid exit, downstream of throttleSuperscriptsrelative velocityss steady stateINTRODUCTIONCompressor stall and surge can have catastrophic consequences inaircraft, yet prediction of these phenomena remains as one of themajor unsolved problems in turbomachinery. Many models of stallthat give some insight into the phenomena have been developed butfew models are capable of predicting stall onset, except perhaps forfull computational fluid dynamic (CFD) analysis of the entire com-pressor which is beyond the scope of this paper. Existing modelsrange from analytic models of rotating stall or compression systemstability to 2-Dor 3-DCFD models of compression systems. All mod-els require input of some information about compressor performance,E,G,HKm˙