Leakage Uncertainties in Compressors: The Case of Rotor 37 Pranay Seshadri ∗ and Geoffrey T. Parks † University of Cambridge, Cambridge, England CB2 1PZ, United Kingdom and Shahrokh Shahpar ‡ Rolls–Royce, plc., Derby, England DE24 8BJ, United Kingdom DOI: 10.2514/1.B35039 This paper revisits an old problem of validating computational fluid dynamics simulations with experiments in turbomachinery. The case considered here is NASA rotor 37. Prior computational fluid dynamics studies of this blade have been unable to predict a total pressure deficit at the hub as observed in the experiments. A possible explanation for this discrepancy is a small hub leakage flow emanating fore of the leading edge, between the forward stationary center body and the rotating disk. In this work, a large-scale high-fidelity uncertainty quantification study is carried out to investigate whether this indeed was the case. Computations are carried out on a 4.5-million-cell rotor 37 mesh with a small cavity fore of the leading edge. This cavity has an inlet with three boundary conditions: all assumed to be uncertain. A nonintrusive, orthogonal polynomial-based technique using sparse grids is used to propagate these three uncertainties, namely, leakage mass flow, leakage whirl velocity, and radial flow angle. A total of 158 sparse-grid- based design-of-experiment computations are carried out at two flow conditions. The results of the uncertainty quantification study show that a small amount of leakage flow can account for the hub pressure deficit at both on- and off-design conditions. For the uncertainty supports selected, the total pressure that best matched experiment was found to lie between the second and third standard deviations over the assumed uncertainties. I. Introduction I T HAS been over four decades since the first experiments on NASA rotor 37 were initiated. Over this period, it has been used extensively as a test case for turbomachinery computational fluid dynamics (CFD) validation [1–3], for testing optimization techniques and algorithms [4,5], for exploring tip leakage flows [6], for quantifying the effects of surface roughness [7], for investigating uncertainty quantification (UQ) approaches [8,9], and for pursuing robust design in compressors [10]. Experiments on rotor 37 and the subsequent wealth of numerical validations have been the subject of select review papers that have become a must read for every student of turbomachinery (see [11,12]). These papers highlight the effect of experimental and computational uncertainties in turbomachinery and how a lack of an accurate assessment of these uncertainties can affect design decisions. The primary motivation for this paper stems from one of the main conclusions of these reviews: the significance and origin of the discrepancy between the experiment and CFD. In this particular case, the error is attributed to an uncertainty in the rotor 37 experiments and not the subsequent CFD validations. The second motivation for this work arises from the recent growth of UQ methods and their increasing relevance to turbomachinery designers, practitioners, and students. These notions form the cornerstones of this paper on rotor 37. NASA rotor 37 is a rotor blade for an axial core compressor that was developed at the NASA Lewis Research Center. It was part of a broad program on axial flow fans and airbreathing compressors with the objective of attaining high-pressure ratios and efficiencies well within stall margins, in minimal stages. It has been extensively tested, both as an isolated component and in tandem with a stator [2,13]. It has a relatively high design speed pressure ratio of 2.1 with a tip speed of 454 m∕s, yielding a peak Mach number of approximately 1.4. It has been instrumental in shaping our understanding of both transonic fan flow physics and the application of CFD to compressors. CFD validations of rotor 37 include the results of the 1994 American Society of Mechanical Engineers/International Gas Turbine Institute blind test case study [1], studies by Denton [11], and, more recently, the work of Chima [3], Hah [2], and Ameri [14]. The main conclusions of the test case study, and of subsequent CFD studies, have been the following: 1) Most codes overpredicted the total pressure ratio (measured as the total pressure at the exit divided by the total pressure at the inlet) well beyond the experimental uncertainty (see [15] for error bars). Two-dimensional (2-D) profiles were well captured above 40% span and overpredicted below. 2) Total temperature ratios (total temperature at the exit divided by the total temperature at the inlet) were higher than those observed in the experiment. Specifically, toward the hub and tip, the total temperatures were far lower. 3) Depending on predictions of total temperature and total pressure ratios (PR), adiabatic efficiency η variations between numerous codes were quite large. However, in general, codes that obtained reasonable predictions of total pressure and temperature under- predicted the efficiency. The focus of this paper will be on conclusion 1, and a thus detailed inspection of the total temperature and efficiency profiles will not be undertaken. The intent is solely to investigate the origin of the hub pressure deficit. This is elaborated upon next. Figure 1 shows a schematic of rotor 37. It consists of three main components: an upstream stationary center body, a rotating disk, and a downstream stationary center body. There is a small clearance gap of 0.75 mm between the center bodies and the disk. In their work nearly two decades ago, Shabbir et al. [16] proposed that the pressure deficit was caused by a small hub leakage flow emanating from the gap fore of the leading edge. Through computational studies on rotor 37, and computational and experimental studies on rotor 35 (similar to 37 but with a lower peak Mach number and lower diffusion), they demonstrated that leakage could be the cause of the observed pressure deficit. For rotor 35, they introduced a small leakage flow through an external source just fore of the leading edge. They observed that, even with a leakage flow of 0.25–0.33% of the main Presented as Paper 2013-1815 at the 15th AIAA Non-Deterministic Approaches Conference, Boston, MA, 8–11 April 2013; received 14 May 2013; revision received 18 May 2014; accepted for publication 5 June 2014; published online 12 September 2014. Copyright © 2014 by Rolls–Royce plc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-3876/14 and $10.00 in correspondence with the CCC. *Ph.D. Candidate, Engineering Design Centre, Trumpington Street. Student Member AIAA. † Senior University Lecturer, Engineering Design Centre, Trumpington Street. ‡ Associate Engineering Fellow, CFD Methods, Design Systems Engineering, Moore Lane. Associate Fellow AIAA. AIAA Early Edition / 1 JOURNAL OF PROPULSION AND POWER Downloaded by UNIVERSITY OF CAMBRIDGE on September 14, 2014 | http://arc.aiaa.org | DOI: 10.2514/1.B35039