Diffuser Radius Ratio Research Articles

Dynamics of global instabilities in the vaneless diffuser: A numerical approach and its applications

The effect of inviscid main flow and backflow boundary layer at diffuser walls both contribute to the instability of vaneless diffuser. This study is carried out to investigate the instability induced by the inviscid main flow. The biglobal instability analysis adopted here is focused on the large time scale growth of perturbations imposed on a base flow. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. In order to access the given state is stable or not, a linearized Euler’s equations for compressible base flow is used with a small-amplitude perturbation assumption. The eigenvalue problem is established through the spectral collocation discretization. Compared with experimental data, the stability model proposed in this paper is verified. Based on this numerical approach, the influence of inflow condition and geometric parameters, especially the compressibility effect on the stability of diffuser are investigated. And based on the results from some experiment measurement, the reliability of the stability analysis is verified through comparison. It is showed that diffuser instability increases rapidly and the stall rotation speed decreases quickly with the increase of diffuser radius ratio. The largest critical inflow angle can be obtained when the wave number m is around 3–5 for the radius ratio between 1.5 and 2.2. The present biglobal stability method has the capability to predict the onset of rotating stall, especially for wide diffusers.

A numerical approach to predict the rotating stall in the vaneless diffuser of a centrifugal compressor using eigenvalue method

A two-dimensional incompressible flow model is presented to study the occurrence of rotating stall in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. The linearized 2D Euler equations for an incompressible flow in a fixed frame of the coordinate system are considered. After discretization by a spectral collocation method based on Chebyshev-Gauss-Lobatto points, the generalized eigenvalue problem is solved through the QZ algorithm. The compressor stability is judged by the imaginary part of the eigenvalue obtained. Based on the 2D stability analysis, the influence of inflow angle, radius ratio and wave number are studied. The results from the present stability analysis are compared with some experimental measurement and Shen’s model. It is showed that diffuser instability increases rapidly and the stall rotational speed decreases quickly with an increase in the diffuser radius ratio. The largest critical inflow angle can be obtained when the wave number is around 3 ∼ 5 for the radius ratio between 1.5 to 2.2. It is also verified that the stability model proposed in this paper agrees well with experimental data and has the capability to predict the onset of rotating stall, especially for wide diffusers.

A three-dimensional compressible flow model for rotating waves in vaneless diffusers with unparallel walls

A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in unparallel wall vaneless diffusers in centrifugal compressors. The model extends the three-dimensional compressible flow model for parallel wall diffusers recently developed by present authors. Linearised three-dimensional compressible Euler equations casted on a rotating frame of reference travelling at the same speeds as the waves are employed and the viscous effects are ignored. Complex functions of the solutions to the linearised Euler equations are then obtained by a second-order finite difference method and the singular value decomposition technique. Undisturbed flow is assumed potential and first solved by numerical method of strongly implicit procedure. Critical inlet flow rate and rotating wave speed of diffusers of three different shroud wall shapes, namely, convergent, convergent then divergent and constant area tapered, are studied for three different diffuser outlet-to-inlet radius ratios and for different inlet Mach numbers, and results compared with those from diffusers with parallel walls. The results show suppression effects on rotating stall by the contracting walls and the suppression effects vary with wall contraction rate, wall shape, inlet Mach number and the diffuser radius ratio. Further, the effects of diffuser inlet contraction are studied and prediction of the model is compared with experimental result.

A 3D Compressible Flow Model for Weak Rotating Waves in Vaneless Diffusers—Part I: The Model and Mach Number Effects

A three-dimensional compressible flow model is presented to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. The diffuser considered has two parallel walls, and the undisturbed flow is assumed to be circumferentially uniform, isentropic, and to have no axial velocity. Linearized 3D compressible Euler equations were casted on a rotating coordinate system traveling at the same angular speed as the wave cells. A uniform static pressure at the outlet of the diffuser was imposed. Complex functions of the solutions to the equations were obtained by a second-order finite difference method and the singular value decomposition technique. The influences of the inlet Mach number of undisturbed flow, inlet spanwise distribution of undisturbed radial velocity, and diffuser radius ratio on the rotating waves were studied and results show that (1) the critical flow angle and rotating wave speed are both affected by the Mach number. However, the angle only increases slightly with the Mach number while the wave speed increases rapidly with the Mach number; (2) inlet distribution has minor influences on diffuser instability but the wave speed increases with the inlet distortion; (3) diffuser instability increases rapidly and the wave speed decreases quickly with the diffuser radius ratio; and (4) backward traveling rotating wave may occur if diffuser is sufficiently long and the inlet Mach number is sufficiently small.

A 3D Compressible Flow Model for Weak Rotating Waves in Vaneless Diffusers—Part II: Detailed Results

A 3D compressible flow model was presented in Part I of the paper to study the occurrence of weak rotating waves in vaneless diffusers of centrifugal compressors. In this paper, detailed results on the influences of flow and diffuser geometry parameters, including inlet Mach number, inlet distortion, wave number, diffuser outlet-to-inlet radius ratio, diffuser width to inlet radius ratio, and impeller backswept angle, on the rotating waves are presented. It was found that inlet spanwise distortion of radial velocity has little effects on diffuser stability, but rotating wave speed increases with the distortion. The speed also increases with inlet Mach number, so does diffuser instability. Impeller backswept improves diffuser stability and this effect increases with diffuser radius ratio. Multiple resonances were found when impeller backswept is coupled to inlet distortion of radial velocity. These resonances may have similar stabilities but with different wave speeds, suggesting that two rotating waves with different rotating speeds may occur at the same time. Diffuser width was found to have little effects on stability and on wave speed if the same maximum and same minimum values of inlet distortion of radial velocity are kept, but have some effects if the values are not kept. A comparison was also made between the present model predictions and results in open literatures, and good agreement with the experimental results than previous 2D models was achieved.

An experimental investigation of the flow field between two radial plates

The flow field in a radial diffuser downstream of a radial impeller is highly complex, as the flow is turbulent, unsteady, viscous, and three-dimensional. Depending on the initial conditions at the diffuser inlet, the flow may separate from one or both walls of the diffuser. The objective of this experimental investigation of flow characteristics in a radial vaneless diffuser of a centrifugal blower is to enhance the performance of centrifugal compressors over a wide operating range. Numerical and experimental investigations of rotating stall effects on compressors and blowers have been conducted over the past four decades to achieve this objective. The flow characteristics in a radial diffuser were measured while changing the impeller speed and keeping other parameters such as diffuser radius and width ratio constant. The velocity and pressure distributions in the diffuser were measured along a radial path using a miniature X-wire probe and dynamic as well as static pressure transducers. The axisymmetrical radial and tangential mean velocity distributions and their statistics, as well as pressure distributions, are reported. Some of the results presented in this paper agree with those from earlier work on this subject. For example, the flow angle α (measured at half the diffuser width and from the diffuser inlet to its outlet) did not exceed 65°. This means that α < αc, although a recirculation region was present on the diffuser shroud wall. The critical flow angle αc required to initiate self-excited flow oscillations has been generally reported to be about 78°. Current data also indicate that the flow exiting the impeller is skewed, as revealed by the triple velocity product correlations. The current data are valuable for vaneless diffuser numerical model developers, since there are very limited similar data available in the open literature. The current data support the opinion that the flow separation is not enough to trigger or initiate stall at the diffuser.

Analysis of Geometries' Effects on Rotating Stall in Vaneless Diffuser with Wavelet Neural Networks

Wavelet neural network (WNN), which combines the capability of neural network in learning from process and that of wavelet decomposition, was used to study geometry factors on rotating stall in vaneless diffusers. A new error function called cross entropy squared (CSE) function was derived and put forward for the purpose of convergence acceleration. WNN was trained and validated with experimental data from literature. Comparison results showed the reliability. With the trained WNN, detailed investigation was carried out mainly to understand the effects of impeller blade number, blade-exit angle, impeller rotating speed, diffuser radius ratio, and width ratio on stall inception and cell speed of vaneless diffuser. Network results clearly show the existence of distinct stall mechanisms for narrow and wide diffusers, which also make different responses to variation of the above- mentioned parameters.

An Experimental Study on the Development of a Reverse Flow Zone in a Vaneless Diffuser.

This study presents the measured rotating stall signal patterns in a vaneless diffuser in a centrifugal compressor with a radial bladed impeller. Unsteady flow and totating stall in the vaneless diffuser were investigated by measuring unsteady velocity fluctuations at several different diffuser radius ratios and axial distances using a hot wire anemometer. The flow characteristics in terms of the radial and tangential velocity compenents and the flow angle distribution in the vaneless diffuser during rotating stall were investigated using phase-locked averaging techniques. The results clearly indentified abrupt rotating stall at several different impeller rotational speeds. According to the experimental results, two different mechanisms exist for the development of the reverse flow zone in a vaneless diffuser. One is dominated by the extension of the reentering flow from the diffuser exit, and the other is dominated by the growth of the local flow separation zone on the hub and shroud side. The fluctuation in the flow direction increases a the diffuser radius ratio increases and is dominated by the strength of the reverse flow. At the onset of rotating stall, the radial velocity for one period of the rotating stall slowly increased to a maximum value and then decreased quickly to a minimum value with an intermediate peak. However, at lower flow rates, this intermediate peak did not occur.

Study of Vaneless Diffuser Rotating Stall Based on Two-Dimensional Inviscid Flow Analysis

Rotating stalls in vaneless diffusers are studied from the viewpoint that they are basically two-dimensional inviscid flow instability under the boundary conditions of vanishing velocity disturbance at the diffuser inlet and of vanishing pressure disturbance at the diffuser outlet. The linear analysis in the present report shows that the critical flow angle and the propagation velocity are functions of only the diffuser radius ratio. It is shown that the present analysis can reproduce most of the general characteristics observed in experiments: critical flow angle, propagation velocity, velocity, and pressure disturbance fields. It is shown that the vanishing velocity disturbance at the diffuser inlet is caused by the nature of impellers as a “resistance” and an “inertial resistance,” which is generally strong enough to suppress the velocity disturbance at the diffuser inlet. This explains the general experimental observations that vaneless diffuser rotating stalls are not largely affected by the impeller.

Vaneless Diffuser Rotating Stall Based on Two-Dimensional Inviscid Flow Analysis. 1st Report, Linear Analysis.

Rotating stalls in vaneless diffusers are studied from the viewpoint that they are basically two-dimensional inviscid flow instability under the boundary conditions of vanishing velocity disturbance at the diffuser inlet and of vanishing pressure disturbance at the diffuser outlet. The linear analysis in the present report shows that the critical flow angle and the propagation velocity are functions of only the diffuser radius ratio. It is shown that the present analysis can reproduce most of the general characteristics observed in experiments : critical flow angle, propagation velocity, velocity and pressure disturbance field. It is shown that the venishing velocity disturbance at the diffuser inlet is caused by the nature of impellers as a resistance and an inertial resistance, with is generally strong enough to suppress the velocity disturbance at the diffuser inlet. This explains the general experimental observations that veneless diffuser rotating stalls are not largely affected by the impeller.

Effects of Diffuser Geometry on Rotating Stall in Vaneless Diffusers.

This paper deals with the effects of the diffuser radius ratio and diffuser width ratio on rotating stall in parallel walled vaneless diffusers. Equations for predicting initiation flow rate and rotational speed of cells presented in previous studies are examined using experimental data. The ratio of the radial length to the width of a diffuser affects the occurrence of rotating stall. Weak rotating stall occurs when this ratio is small. The reasons for this are discussed based on the results of previous studies. Predicted values of the rotational speed of cells agree well with measured values for the diffuser with a relatively large radius ratio. However, a small correction is required in the case of a small radius ratio.

A study on the rotating stall in vaneless diffusers of centrifugal fans. 3rd report. Effect of diffuser radius ratio.

This paper dials with the effect of a diffuser radius ratio (exit radius/inlet radius) on the predicting equations, that is, the equations of a critical inlet flow angle for the onset of a diffuser rotating stall and of rotational speeds of stall cells. The main results in this study are as follows : A measured critical inlet flow angle for the diffuser with the largest radius ratio is the largest in this experiment and it is close to a predicted value. A non-dimensional form of a rotational speed of cells used in this paper proves to be valid for the diffusers with radius ratio smaller than 2.35. The predicting equations of rotational speeds of cells are available over wide ranges of a non-dimensional width and of a diffuser radius ratio. The predicting method of rotational speeds of cells presented in this paper is very simple ; nevertheless, predicted values agree well with measured values.

Studies on Performance and Internal Flow of Twisted S-Shaped Bend Diffuser—The So-Called Coiled Bend Diffuser: 1st Report

This paper is the result of our research into the twisted S-shaped bend diffuser—the so-called coiled bend diffuser. It is a diffuser with a centerline in the shape of a twisted “S.” Our studies show that the performance characteristics of this bend diffuser are greatly improved when interaction by the bend elements generates an adequate secondary flow inside the diffuser. Full consideration was given to the influence of the divergent angle of the bend elements, consisting of the diffuser or curvature radius ratio of the bend, on these performance characteristics. The relation between diffuser performance and internal flow also was studied. Some guidelines for designing such a high performance diffuser is given.