Corrections to the scaling of the second-order structure function in isotropic turbulence

The approach of Obukhov assuming a constant skewness was used to obtain analytical corrections to the scaling of the second order structure function, starting from Kolmogorov＇s 4/5 law. These corrections can be used in model applications in which explicit expressions, rather than numerical solutions are needed. The comparison with an interpolation formula proposed by Batchelor, showed that the latter gives surprisingly precise results. The modification of the same method to obtain analytical corrections to the scaling law, taking into account the possible corrections induced by intermittency, is also proposed.

ANALYSIS OF CRITERIA PREDICTING THE TENDENCY OF PILOT INDUCED OSCILLATION FOR LINEAR NON-LINEAR SYSTEM

Some problems encountered in applying Smith's technique to predict the PIO tendency for non-linear pilot-vehicle loop, are thoroughly analyzed. Subsequently, modified PIO predictable criteria are developed, in addition, to make also a certain improvement on Smith's PIO definition and PIO types. These modified criteria are applied to predict PIO tendency of various different configurations on the variable stability aircraft NT-33 in case of supposed non-linearity, and predicted results are compared with the flight tests and analytical results in the case of linear hypothesis given in Ref. (4)

An Experimental Description of the Flow in a Centrifugal Compressor from Alternate Stall to Surge

The present paper gives the experimental results obtained in a centrifugal compressor stage designed and built by SAFRAN Helicopter Engines. The compressor is composed of inlet guide vanes, a backswept splittered un- shrouded impeller, a splittered vaned radial diffuser and axial outlet guide vanes. Previous numerical simulations revealed a particular S-shape pressure rise characteristic at partial rotation speed and predicted an alternate flow pattern in the vaned radial diffuser at low mass flow rate. This alternate flow pattern involves two adjacent vane passages. One passage exhibits very low momentum and a low pressure recovery, whereas the adjacent passage has very high momentum in the passage inlet and diffuses efficiently. Experimental measurements confirm the S-shape of the pressure rise characteristic even if the stability limit experimentally occurs at higher mass flow than numerically predicted. At low mass flow the alternate stall pattern is confirmed thanks to the data obtained by high-frequency pressure sensors. As the compressor is throttled the path to instability has been registered and a f＇wst scenario of the surge inception is given. The compressor first experiences a steady alternate stall in the dif- fuser. As the mass flow decreases, the alternate stall amplifies and triggers the mild surge in the vaned diffuser. An unsteady behavior results from the interaction of the alternate stall and the mild surge. Finally, when the pres- sure gradient becomes too strong, the alternate stall blows away and the compressor enters into deep surge.

Transient growth in Poiseuille-Rayleigh-Bénard flows of binary fluids with Soret effect

The transient growth due to non-normMity is investigated for the Poiseuille- Rayleigh-Benard problem of binary fluids with the Soret effect. For negative separation factors such as ψ = -0.1, it is found that a large transient growth can be obtained by the non-normal interaction of the two least-stable-modes, i.e., the upstream and downstream modes, which determine the linear critical boundary curves for small Reynolds numbers. The transient growth is so strong that the optimal energy amplification factor G（t） is up to 10^2 - 10^3. While for positive separation factors such as ψ = 0.1, the transient growth is weak with the order O（I） of the amplification factor, which can even be computed by the least-stable-mode. However, for both cases, the least-stable-mode can govern the long-term behavior of the amplification factor for large time. The results also show that large Reynolds numbers have stabilization effects for the maximum amplification within moderate wave number regions. Meanwhile, much small negative or large positive separation factors and large Rayleigh numbers can enlarge the maximum transient growth of the pure streamwise disturbance with the wavenumber α= 3.14. Moreover, the initial and evolutionary two-dimensional spatial patterns of the large transient growth for the pure streamwise disturbance are exhibited with a plot of the velocity vector, spanwise vorticity, temperature, and concentration field. The initial three-layer cell vorticity struc- ture is revealed. When the amplification factor reaches the maximum Gmax, it develops into one cell structure with large amplification for the vorticity strength.

Freshwater Purification by Vacuum Airlift Column Using Methyl Isobutyl Carbinol and Casein

Water purification by foaming in a bubble column is a major challenge for research. It leads to the development of innovative airlift column operated under depression. Sea water clarification by bubble column is well documented, but for freshwater remains insufficiently studied. Extraction of suspended clay particles in freshwater is carried out in an airlift column. The system used is under depression and operates in a closed circuit, thanks to a recirculation tank. Methyl isobutyl carbinol (MIBC) and soluble casein are used as surfactants to allow extraction. Clay used is fine and ultra-ventilated and a turbidimeter is used to measure turbidity. This study showed that the combined use of methyl isobutyl carbinol and casein in the airlift column makes it possible to completely clarify water loaded with clay particles. A turbidity of less than 1 NTU is obtained after 30 minutes of extraction.

Application of an Analytical Method to Locate a Mixing Plane in a Supersonic Compressor

In order to achieve greater pressure ratios, compressor designers have the opportunity to use transonic configurations. In the supersonic part of the incoming flow, shock waves appear in the front part of the blades and propagate in the upstream direction. In case of multiple blade rows, steady simulations have to impose an azimuthal averaging （mixing plane） which prevents these shock waves to extend upstream. In the present paper, several mixing plane locations are numerically tested and compared in a supersonic configuration. An analytical method is used to describe the shock pattern. It enables to take a critical look at the CFD （computational fluid dynamics） steady results. Based on this method, the shock losses are also evaluated. The good agreement between analytical and numerical values shows that this method can be useful to wisely forecast the mixing plane location and to evaluate the shift in performances due to the presence of the mixing plane.

Experimental Study of Corner Stall in a Linear Compressor Cascade

In order to gain a better knowledge of the mechanisms and to calibrate computational fluid dynamics （CFD） tools including both Reynolds-averaged Navier-Stokes （RANS） and large eddy simulation （LES）, a detailed and accurate experimental study of comer stall in a linear compressor cascade has been carried out. Data are taken at a Reynolds number of 382 000 based on blade chord and inlet velocity. At first, inlet flow boundary layer is surveyed using hot-wire anemometry. Then in order to investigate the effects of incidence, measurements are acquired at five incidences, including static pressures on both blade and endwall sur- faces measured by pressure taps and the total pressure losses of outlet flow measured by a five-hole pressure probe. The maxi- mum losses as well as the extent of losses of the comer stall are presented as a function of the investigated incidences.

Recent progress in augmenting turbulence models with physics-informed machine learning

In view of the long stagnation in traditional turbulence modeling,researchers have attempted using machine learning to augment turbulence models.This paper presents some of the recent progresses in our group on augmenting turbulence models with physics-informed machine learning.We also discuss our works on ensemble-based field inversion to provide training data for constructing machine learning models.Future and on-going research efforts are introduced.

Parameter study on numerical simulation of corner separation in LMFA-NACA65 linear compressor cascade

Large-eddy simulation（LES） is compared with experiment and Reynolds-averaged Navier-Stokes（RANS）, and LES is shown to be superior to RANS in reproducing corner separation in the LMFA-NACA65 linear compressor cascade, in terms of surface limiting streamlines,blade pressure coefficient, total pressure losses and blade suction side boundary layer profiles. However, LES is too expensive to conduct an influencing parameter study of the corner separation.RANS approach, despite over-predicting the corner separation, gives reasonable descriptions of the corner separated flow, and is thus selected to conduct a parametric study in this paper. Two kinds of influencing parameters on corner separation, numerical and physical parameters, are analyzed and discussed： second order spatial scheme is necessary for a RANS simulation; incidence angle and inflow boundary layer thickness are found to show the most significant influences on the corner separation among the parameters studied; unsteady RANS with the imposed inflow unsteadiness（inflow angle varying sinusoidally with fluctuating amplitude of 0.92°） does not show any non-linear effect on the corner separation.

Assessment of Linear and Non-Linear Two-Equation Turbulence Models for Aerothermal Turbomachinery Flows

Three linear two-equation turbulence models k- ε, k- ω and k- 1 and a non-linear k- 1 model are used for aerodynamic and thermal turbine flow prediction. The pressure profile in the wake and the heat transfer coefficient on the blade are compared with experimental data. Good agreement is obtained with the linear k-1 model. No significant modifications are observed with the non-linear model. The balance of transport equation terms in the blade wake is also presented. Linear and non-linear k - 1 models are evaluated to predict the threedimensional vortices characterising the turbine flows. The simulations show that the passage vortex is the main origin of the losses.

Experimental investigation of flow field in a laboratory-scale compressor

The inner flow environment of turbomachinery presents strong three-dimensional, rotational, and unsteady characteristics. Consequently, a deep understanding of these flow phenomena will be the prerequisite to establish a state-of-the-art design system of turbomachinery. Currently the development of more accurate turbulence models and CFD tools is in urgent need for a high-quality database for validation, especially the advanced CFD tools, such as large eddy simulation（LES）. Under this circumstance, this paper presents a detailed experimental investigation on the 3D unsteady flow field inside a laboratory-scale isolated-rotor with multiple advanced measurement techniques, including traditional aerodynamic probes, hotwire probes, unsteady endwall static pressure measurement, and stereo particle image velocimetry（SPIV）. The inlet boundary layer profile is measured with both hotwire probe and aerodynamic probe. The steady and unsteady flow fields at the outlet of the rotor are measured with a mini five-hole probe and a single-slanted hotwire probe. The instantaneous flow field in the rotor tip region inside the passage is captured with SPIV,and then a statistical analysis of the spatial distribution of the instantaneous tip leakage vortex/flow is performed to understand its dynamic characteristics. Besides these, the uncertainty analysis of each measurement technique is described. This database is quite sufficient to validate the advanced numerical simulation with LES. The identification process of the tip leakage vortex core in the instantaneous frames obtained from SPIV is performed deliberately. It is concluded that the ensemble-averaged flow field could not represent the tip leakage vortex strength and the trajectory trace. The development of the tip leakage vortex could be clearly cataloged into three phasesaccording to their statistical spatial distribution. The streamwise velocity loss induced by the tip leakage flow increases until the splitting process is weak and the turbulent mixing phase is dominant.

Laser Measurements in High Speed Compressors for Rotor-Stator Interaction Analysis

This paper deals with the experimental quantification of the unsteady effects of the interactions between rotor and stator rows in high speed compressors. Due to the fact that the levels of the periodic fluctuations arising from the unsteady interaction may be low compared with the random fluctuations arising from the measurement uncertainties, it is crucial to minimize the errors inherent to the used technique. The first part of the paper concentrates on technical details relative to the experimental process. The second part is devoted to the data post-processing. Two tools for analysing the rotor-stator interactions are presented. The first tool is based on a decomposition of the flow field which was initially introduced to solve numerical problems when attempting to calculate the flow field in a multi-row configuration. The second tool is based on a spectral analysis of the signal, that qualifies the interaction in a sense of circumferential spinning lobes. Experimental results obtained within both an axial and a centrifugal high speed compressors are used to illustrate the data processing. In both cases, the effects of the unsteady interaction are quantified.

Unsteady Rotor-Stator Interaction in High Speed Compressor and Turbine Stages

The blade row interaction can alter the time-mean flow and therefore be of interest for aerodynamic design analysis. Whereas results within low subsonic turbomachines are quite numerous in the literature, there have been far fewer works which give results of blade row interaction within high speed cases. Two cases are related in this paper. First, the effects of an incoming wake on the rotor flow field of a transonic compressor are analyzed. The blade row interaction proved to be positive regarding the total pressure ratio, but negative regarding the losses. The second case concerns a transonic turbine. Particular emphasis is placed on the assessment of the deterministic correlations included in the Averaged Passage Equation System.

Ship bow waves

The bow wave generated by a ship hull that advances at constant speed in calm water is considered. The bow wave only depends on the shape of the ship bow （not on the hull geometry aft of the bow wave）. This basic property makes it possible to de- termine the bow waves generated by a canonical family of ship bows defined in terms of relatively few parameters. Fast ships with fine bows generate overturning bow waves that consist of detached thin sheets of water, which are mostly steady until they hit the main free surface and undergo turbulent breaking up and diffusion. However, slow ships with blunt bows create highly unsteady and turbulent breaking bow waves. These two alternative flow regimes are due to a nonlinear constraint related to the Bernoulli relation at the free surface. Recent results about the ove^urning and breaking bow wave regimes, and the boundary that divides these two basic flow regimes, are reviewed. Questions and conjectures about the energy of breaking ship bow waves, and free-surface effects on flow circulation, are also noted.