Yi-Chih Chow

Experimental Investigation of Unsteady Flow Field Within a Two Stage Axial Turbomachine Using Particle Image Velocimetry

Detailed measurements of the flow field within the entire 2 nd stage of a two stage axial turbomachine are performed using Particle Image Velocimetry. The experiments are performed in a facility that allows unobstructed view on the entire flow field, facilitated using transparent rotor and stator and a fluid that has the same optical index of refraction as the blades. The entire flow field is composed of a “lattice of wakes”, and the resulting wakewake and wake-blade interactions cause major flow and turbulence non-uniformities. The paper presents data on the phase averaged velocity and turbulent kinetic energy distributions, as well as the average-passage velocity and deterministic stresses. The phase-dependent turbulence parameters are determined from the difference between instantaneous and the phase-averaged data. The distributions of average-passage flow field over the entire stage in both the stator and rotor frames of reference are calculated by averaging the phase-averaged data. The deterministic stresses are calculated from the difference between the phase-averaged and average-passage velocity distributions. Clearly, wake-wake and wake-blade interactions are the dominant contributors to generation of high deterministic stresses and tangential non-uniformities, in the rotor-stator gap, near the blades and in the wakes behind them. The turbulent kinetic energy levels are generally higher than the deterministic kinetic energy levels, whereas the shear stress levels are comparable, both in the rotor and stator frames of references. At certain locations the deterministic shear stresses are substantially higher than the turbulent shear stresses, such as close to the stator blade in the rotor frame of reference. The non-uniformities in the lateral velocity component due to the interaction of the rotor blade with the 1 st stage rotor-stator wakes, result in 13% variations in the specific work input of the rotor. Thus, in spite of the relatively large blade row spacings in the present turbomachine, the nonuniformities in flow structure have significant effects on the overall performance of the system. NOMENCLATURE k Turbulent kinetic energy kdet Deterministic kinetic energy Ls Stage length starting from the rotor leading edge N Total number of instantaneous samples NaI Sodium Iodide t Time T Blade passing period u Instantaneous axial velocity Utip Velocity of rotor blade tip v Instantaneous lateral velocity

Flow Nonuniformities and Turbulent “Hot Spots” Due to Wake-Blade and Wake-Wake Interactions in a Multi-Stage Turbomachine

This experimental study provides striking examples of the complex flow and turbulence structure resulting from blade-wake and wake-wake interactions in a multi-stage turbomachine. Particle image velocimetry (PIV) measurements are performed within the entire 2 nd stage of a two-stage turbomachine. The experiments are performed in a facility that allows unobstructed view of the entire flow field, facilitated using transparent rotor and stator and a fluid that has the same optical index of refraction as the blades. This paper contains data on the phase-averaged flow structure including velocity, vorticity and strain-rate, as well as the turbulent kinetic energy and shear stress, at mid span, for several orientation of the rotor relative to the stator. Two different test setups with different blade geometries are used in order to highlight and elucidate complex phenomena involved, as well as to demonstrate that some of the interactions are characteristic to turbomachines and can be found in a variety of geometries. The first part of the paper deals with the interaction of a 2 nd -stage rotor with the wakes of both the rotor and the stator of the 1 st stage. Even before interacting with the blade, localized regions with concentrated mean vorticity and elevated turbulence levels form at the intersection of the rotor and stator wakes of the 1 st stage. These phenomena persist even after being ingested by the rotor blade of the 2 nd stage. As the wake segment of the 1 st -stage rotor blade arrives to the 2 nd stage, the rotor blades become submerged in its elevated turbulence levels, and separate the region with negative vorticity that travels along the pressure side of the blade, from the region with positive vorticity that remains on the suction side. The 1 st -stage stator wake is chopped-off by the blades. Due to difference in mean lateral velocity, the stator wake segment on the pressure side is advected faster than the segment on the suction side (in the absolute frame of reference), creating discontinuities in the stator wake trajectory. The nonuniformities in phase-averaged velocity distributions generated by the wakes of the 1 st stage persist while passing through the 2 nd -stage rotor. The combined effects of the 1 st -stage blade rows cause 10-12 deg variations of flow angle along the pressure side of the blade. Thus, in spite of the large gap between the 1 st and 2 nd rotors (compared to typical rotor-stator spacings in axial compressors), 6.5 rotor axial chords, the wake-blade interactions are substantial. The second part focuses on the flow structure at the intersection of the wakes generated by a rotor and a stator located upstream of it. In both test setups the rotor wake is sheared by the nonuniformities in the axial velocity distributions, which are a direct result of the discontinuities in the trajectories of the stator wake. This shearing creates a kink in the trajectory of the rotor wake, a quadruple structure in the distribution of strain, regions with concentrated vorticity, high turbulence levels and high shear stresses, the latter with a complex structure that resembles the mean strain. Although the hot spots diffuse as they are advected downstream, they still have elevated turbulence levels compared to the local levels around them. In fact, every region of wake intersection has an elevated turbulence level.

The Effect of Inlet Guide Vanes Wake Impingement on the Flow Structure and Turbulence Around a Rotor Blade

The flow structure and turbulence around the leading and trailing edges of a rotor blade operating downstream of a row of inlet guide vanes (IGV) are investigated experimentally. Particle image velocimetry (PIV) measurements are performed in a refractive index matched facility that provides unobstructed view of the entire flow field. Data obtained at several rotor blade phases focus on modification to the flow structure and turbulence in the IGV wake as it propagates along the blade. The phase-averaged velocity distributions demonstrate that wake impingement significantly modifies the wall-parallel velocity component and its gradients along the blade. Due to spatially non-uniform velocity distribution, especially on the suction side, the wake deforms while propagating along the blade, expanding near the leading edge and shrinking near the trailing edge. While being exposed to the nonuniform strain field within the rotor passage, the turbulence within the IGV wake becomes spatially nonuniform and highly anisotropic. Several mechanisms, which are consistent with rapid distortion theory (RDT) and distribution of turbulence production rate, contribute to the observed trends. For example, streamwise (in rotor frame reference) diffusion in the aft part of the rotor passage enhances the streamwise fluctuations. Compression also enhances the turbulence production very near the leading edge. However, along the suction side, rapid changes to the direction of compression and extension cause negative production. The so-called wall blockage effect reduces the wall-normal component.

Experimental Investigation of Unsteady Flow Field Within a Two-Stage Axial Turbomachine Using Particle Image Velocimetry

Detailed measurements of the flow field within the entire 2nd stage of a two-stage axial turbomachine are performed using particle image velocimetry. The experiments are performed in a facility that allows unobstructed view on the entire flow field, facilitated using transparent rotor and stator and a fluid that has the same optical index of refraction as the blades. The entire flow field is composed of a lattice of wakes, and the resulting wake-wake and wake-blade interactions cause major flow and turbulence nonuniformities. The paper presents data on the phase averaged velocity and turbulent kinetic energy distributions, as well as the average-passage velocity and deterministic stresses. The phase-dependent turbulence parameters are determined from the difference between instantaneous and the phase-averaged data. The distributions of average passage flow field over the entire stage in both the stator and rotor frames of reference are calculated by averaging the phase-averaged data. The deterministic stresses are calculated from the difference between the phase-averaged and average-passage velocity distributions. Clearly, wake-wake and wake-blade interactions are the dominant contributors to generation of high deterministic stresses and tangential nonuniformities, in the rotor-stator gap, near the blades and in the wakes behind them. The turbulent kinetic energy levels are generally higher than the deterministic kinetic energy levels, whereas the shear stress levels are comparable, both in the rotor and stator frames of references. At certain locations the deterministic shear stresses are substantially higher than the turbulent shear stresses, such as close to the stator blade in the rotor frame of reference. The nonuniformities in the lateral velocity component due to the interaction of the rotor blade with the 1st-stage rotor-stator wakes, result in 13 percent variations in the specific work input of the rotor. Thus, in spite of the relatively large blade row spacings in the present turbomachine, the nonuniformities in flow structure have significant effects on the overall performance of the system.

Average Passage Flow Field and Deterministic Stresses in the Tip and Hub Regions of a Multistage Turbomachine

This paper continues our effort to study the dynamics of deterministic stresses in a multistage turbomachine using experimental data. Here we focus on the tip and hub regions and compare them to mid span data obtained in previous studies. The analysis is based on data obtained in PIV measurements performed in the second stage of a two-stage turbomachine. A complete data set is obtained using blades and fluid with matched optical index of refraction. Previous measurements at mid span have shown that at mid span and close to design conditions, the deterministic kinetic energy is smaller than the turbulent kinetic energy. The primary contributor to the deterministic stresses at mid span is the interaction of a blade with the upstream wakes. Conversely, we find that the tip vortex is the dominant source of phasedependent unsteadiness and deterministic stresses in the tip region. Along the trajectory of the tip vortex, the deterministic kinetic energy levels are more than one order of magnitude higher than the levels measured in the hub and mid-span, and are of the same order of magnitude as the turbulent kinetic energy levels. Reasons for this trend are explained using a sample distribution of phase-averaged flow variables. Outside of the region affected by tip vortex transport, within the rotorstator gap and within the stator passages, the turbulent kinetic energy is still 3-4 times higher than the deterministic kinetic energy. The deterministic and turbulent shear stress levels are comparable in all spanwise locations, except for the wakes of the stator blades, where the turbulent stresses are higher. However, along the direction of tip vortex transport, the deterministic shear stresses are about an order of magnitude higher than the turbulent shear stresses. The decay rates of deterministic kinetic energy in the hub and mid-span regions are comparable to each other, whereas at the tip, the decay rate is higher. The decay rates of turbulent kinetic energy are much smaller than those of the deterministic kinetic energy. The paper also examines terms in the deterministic kinetic energy transport equation. The data indicate that “Deterministic Production” and a new term, called here “Dissipation due to Turbulence” are the dominant source/sink terms. Regions with alternating signs of Deterministic Production indicate that the energy transfer between the phase-averaged and average-passage flow fields can occur in both directions. The divergence of the PressureVelocity correlation, obtained from a balance of all the other terms, is dominant and appears to be much larger than the deterministic production (source/sink) term. This trend indicates that there are substantial deterministic pressure fluctuations in the flow field, especially within the rotor-stator gap and within the stator passage.

Decomposition of the spatially filtered and ensemble averaged kinetic energy, the associated fluxes and scaling trends in a rotor wake

Particle image velocimetry data obtained in the rotor wake of a turbomachine are used for examining elements of the ensemble averaged and spatially filtered kinetic energy. These two distinct averaging processes decompose the kinetic energy into four parts, consisting of the mean-flow resolved, mean-flow subgrid, fluctuating resolved, and fluctuating subgrid parts. Their evolution equations include energy flux terms among these parts. The results elucidate the fundamental difference between the filtered turbulence (Reynolds) production and the ensemble averaged subgrid scale (SGS) dissipation rates. Each of these terms consist of three energy fluxes, but only one of them is common to both, the flux from the mean-flow resolved to the fluctuating subgrid kinetic energy parts. The other two elements of the SGS dissipation are the fluxes from the mean-flow resolved to the mean-flow subgrid parts and the fluctuating resolved to the fluctuating subgrid parts. Likewise, the other two contributions to the turbule...

Numerical study of turbulent flow over two-dimensional surface-mounted ribs in a channel

This study accurately predicts the cases of turbulent flow around a surface-mounted two-dimensional rib with varying lengths. The numerical method employs a differencing scheme for integrating the elliptic Reynolds-averaged Navier-Stokes equations and the continuity equation. A two-equation κ-e turbulence model is employed to simulate the turbulent transport quantities and close the solving problem. The near-wall regions of the separated sides of the rib are resolved by a near-wall model of a two-layer approach instead of the wall function approximation. Computations for flow over a surface-mounted rectangular rib are conducted for the variations in the rib lengths. Results indicate that upstream of the obstacle, the length of the recirculating region remains unchanged with varying rib lengths; while the downstream length of the recirculating region is a strong function of rib length and changes nearly linearly for the varying lengths of B/H = 0.1 to B/H = 4.0. Reattachment on top of the rib, owing to its increasing length, affects the downstream boundary layer development

A database of PIV measurements within a turbomachinery stage and sample comparisons with unsteady RANS

This paper describes an experimental database obtained using two-dimensional Particle Image Velocimetry (PIV) measurements within an axial turbomachinery stage, and presents sample unsteady Reynolds Averaged Navier–Stokes (RANS) simulations to illustrate its applicability for turbomachinery model validation. The experiments are performed in a refractive-index-matched facility that provides unobstructed view, and cover the entire second stage of a two-stage axial pump. The data were obtained at ten different rotor phases covering one rotor blade-passing period, and at mid-span. Several features of the data at selected phases have already been presented and discussed in prior publications. Here we present the complete database together with sample CFD results. Two-dimensional unsteady RANS simulations are performed using the commercial flow solver FLUENT™, with two standard turbulence models, i.e. Renormalization Group (RNG) k-ϵ and Reynolds Stress Transport Model (RSM). The spatially non-uniform inlet velo...

EXPERIMENTAL STUDY OF THE STRUCTURE OF A ROTOR WAKE IN A COMPLEX TURBOMACHINERY FLOW

Unobstructed PIV measurements within complex turbomachinery flow fields are performed in an opticalrefractive-index-matched facility consisting of a 2-stage axial turbomachine. Two different test setups are utilized to demonstrate wake-wake, wake-blade interactions and the associated flow non-uniformities and turbulence. The flow consists of a lattice of interacting wake segments, which are being chopped by the rotor and stator blades. The wake fragments become discontinuous due to the velocity differences across the rotor blades. Striking flow phenomena that occur as a result of this non-uniform flow field, such as turbulent “hot spots” and kinking of the rotor wake are presented at high magnification and samples that are large enough to obtain converged statistics. In this paper we focus on the flow field and turbulence within the rotor wake. One thousand instantaneous realizations at the same phase are used for determining the phase averaged flow and turbulence statistics including Reynolds stresses, turbulence spectra, production, dissipation, and mean strains. Three methodologies are adopted to investigate the details of the rotor wake structure: 1. Local maximization of 2-D shear strain and Reynolds shear stress; 2. 1-D energy spectral analysis; and 3. Subgrid-Scale (SGS) energy budget. Alignment of the local coordinates with direction that maximizes the local shear strain shows that except for the hot spot regions the rotor wake consists of two parallel layers exposed to planar shear strain. The normal strains in this system are significantly lower, indicating that out-of-plane normal straining is much weaker than the in-plane shear (except near the hot spot and close to the trailing edge of the rotor). Significant differences exist in several regions between the orientation of a coordinate system that maximizes the shear strain, and the system that maximizes the Reynolds shear stress, particularly around the hot spot, near the trailing edge, and within the stator wake segments on both sides of the rotor wake. 1-D spectral analysis reveals that the turbulence near the trailing edge is anisotropic and highly dissipative. The dissipation decreases and turbulence becomes more isotropic further away from the trailing edge, but becomes anisotropic again near the hot spot. Spatial filtering of data and measurement of the resulting SGS stresses enable us to examine and compare energy fluxes from the mean flow to the resolved and subgrid scales, as well as from the resolved to the subgrid scales. Due to the limitation in resolution, the present filter scale is 50% of the integral scale (~wake width). Consequently, the energy flux from the mean flow to the subgrid scales is much higher than flux from the resolved turbulence to the subgrid scales. The production term, representing the energy flux from the mean flow to the resolved scales is typically higher than the flux from the resolved to the subgrid scales. Thus, build-up of large-scale energy occurs in substantial part of the near wake. The dissipation rates estimated from the spectra are everywhere (including the hot spot) of the same order as the overall SGS dissipation rate.

The Effects of Inlet Guide Vane-Wake Impingement on the Boundary Layer and the Near-Wake of a Rotor Blade

This paper examines the response of a rotor blade boundary layer and a rotor near-wake to an impinging wake of an inlet guide vane (IGV) located upstream of the rotor blade. Two-dimensional particle image velocimetry (PIV) measurements are performed in a refractive index matched turbomachinery facility that provides unobstructed view of the entire flow field. Data obtained at several rotor phases enable us to examine the IGV-wake-induced changes to the structure of the boundary layer and how these changes affect the flow and turbulence within the rotor near-wake. We focus on the suction surface boundary layer, near the blade trailing edge, but analyze the evolution of both the pressure and suction sides of the near-wake. During the IGV-wake impingement, the boundary layer becomes significantly thinner, with lower momentum thickness and more stable profile compared with other phases at the same location. Analysis of available terms in the integral momentum equation indicates that the phase-averaged unsteady term is the main contributor to the decrease in momentum thickness within the impinging wake. Thinning of the boundary/shear layer extends into the rotor near-wake, making it narrower and increasing the phase-averaged shear velocity gradients and associated turbulent kinetic energy (TKE) production rate. Consequently, the TKE increases during wake thinning, with as much as 75% phase-dependent variations in its peak magnitude. This paper introduces a new way of looking at the PIV data by defining a wake-oriented coordinate system, which enables to study the structure of turbulence around the trailing edge in great detail.