This work describes the development and the application of a quasi3D method for the simulation of turbochargers for automotive applications under unsteady flow conditions. The quasi3D approach is based on the solution of conservation equations for mass, momentum, and energy for unsteady flows and applied to zero-dimensional (0D) and one-dimensional (1D) elements arbitrarily oriented in the space. The compressor is divided into different regions, each one treated numerically in a different way. For the impeller region, a relative reference system has been used, and the presence of a centrifugal force field has been introduced both in the momentum and energy conservation equations. The direction of the ports at the inlet and outlet of the impeller are used to determine the design flow angles and therefore the deviation during off-design conditions. Conversely in the vaneless diffuser, the conservation of the angular momentum of the flow stream has been imposed in the tangential direction and then combined with the solution of the momentum equation in the radial direction. The model has been validated against measurements carried out on the test bench of the University of Genoa both in diabatic and adiabatic conditions.

A centrifugal compressor requires a wide operating range as well as a high efficiency. At high pressure ratios, the impeller discharge velocity becomes transonic and effective pressure recovery in a vaned or vaneless diffuser is necessary. At high pressure ratios, a vaned diffuser is used as it has high pressure recovery, but may have a narrow operating range. At low flow, diffuser stall may trigger surge. At high flow, choking in the throat of the vanes may limit the maximum flow rate. A low solidity diffuser allows a good pressure recovery because it has vanes to guide the flow and a wide operating range as there is no geometrical throat to limit the maximum flow. In experimental studies at a pressure ratio around 4:1, the author has replaced vaned diffusers with a range of low solidity diffusers to try to broaden the operating range. The test results showed that the low solidity diffuser also chokes. In this paper, a virtual throat is defined and its existence is confirmed by flow visualization and pressure measurements. A method to select low solidity diffusers is proposed based on test data and the fundamental nature of the flow. The extension of the proposed method to the selection of a vaneless diffuser is examined and a design approach for a vaneless diffuser system to minimize surge flow rate without limiting the attainable maximum flow rate is proposed.

A simplified one-dimensional model for the performance estimation of vaneless radial diffusers is presented. The starting point of such a model is that angular momentum losses occurring in vaneless diffusers are usually neglected in the most common turbomachinery textbooks: It is assumed that the angular momentum is conserved inside a vaneless diffuser, although a nonisentropic pressure transformation is considered at the same time. This means that fluid-dynamic losses are taken into account only for what concerns pressure recovery, whereas the evaluation of the outlet tangential velocity incoherently follows an ideal behavior. Several attempts were presented in the past in order to consider the loss of angular momentum, mainly solving a full set of differential equations based on the various developments of the initial work by Stanitz (1952, “One-Dimensional Compressible Flow in Vaneless Diffusers of Radial or Mixed-Flow Centrifugal Compressors, Including Effects of Friction, Heat Transfer and Area Change,” Report No. NACA TN 2610). However, such formulations are significantly more complex and are based on two empirical or calibration coefficients (skin friction coefficient and dissipation or turbulent mixing loss coefficient) which need to be properly assessed. In the present paper, a 1D model for diffuser losses computation is derived considering a single loss coefficient, and without the need of solving a set of differential equations. The model has been validated against massive industrial experimental campaigns, in which several diffuser geometries and operating conditions have been considered. The obtained results confirm the reliability of the proposed approach, able to predict the diffuser performance with negligible drop of accuracy in comparison with more sophisticated techniques. Both preliminary industrial designs and experimental evaluations of the diffusers may benefit from the proposed model.

One of the main challenges of the present industrial research on centrifugal compressors is the need for extending the left margin of the operating range of the machines. As a result, interest is being paid to accurately evaluating the amplitude of the pressure fluctuations caused by rotating stall, which usually occurs prior to surge. The related aerodynamic force acting on the rotor can produce subsynchronous vibrations, which can prevent the machine's further operation, in case their amplitude is too high. These vibrations are often contained due to the stiffness of the oil journals. Centrifugal compressor design is, however, going towards alternative journal solutions having lower stiffness levels (e.g., active magnetic bearings or squeeze film dampers), which will be more sensitive to this kind of excitation: consequently, a more accurate estimation of the expected forces in the presence of dynamic external forces such as those connected to an aerodynamically unstable condition is needed to predict the vibration level and the compressor operability in similar conditions. Within this scenario, experimental tests were carried out on industrial impellers operating at high peripheral Mach numbers. The dedicated test rig was equipped with several dynamic pressure probes that were inserted in the gas flow path; moreover, the rotor vibrations were constantly monitored with typical vibration probes located near the journal bearings. The pressure field induced by the rotating stall in the vaneless diffuser was reconstructed by means of an ensemble average approach, thus defining the amplitude and frequency of the external force acting on the impeller. The calculated force value was then included in the rotordynamic model of the test rig: the predicted vibrations on the bearings were compared with the measurements, showing satisfactory agreement. Moreover, the procedure was applied to two real multistage compressors, showing notable prediction capabilities in the description of rotating stall effects on the machine rotordynamics. Finally, the prospects of the proposed approach are discussed by investigating the response of a real machine in high-pressure functioning when different choices of journal bearings are made.

Radial loads and direction of a centrifugal gas compressor containing a high specific speed mixed flow impeller and a single tongue volute were determined both experimentally and computationally at both design and off-design conditions. The experimental methodology was developed in conjunction with a traditional ASME PTC-10 closed-loop test to determine radial load and direction. The experimental study is detailed in Part 1 of this paper (Moore and Flathers, 1998). The computational method employs a commercially available, fully three-dimensional viscous code to analyze the impeller and the volute interaction. An uncoupled scheme was initially used where the impeller and volute were analyzed as separate models using a common vaneless diffuser geometry. The two calculations were then repeated until the boundary conditions at a chosen location in the common vaneless diffuser were nearly the same. Subsequently, a coupled scheme was used where the entire stage geometry was analyzed in one calculation, thus eliminating the need for manual iteration of the two independent calculations. In addition to radial load and direction information, this computational procedure also provided aerodynamic stage performance. The effect of impeller front face and rear face cavities was also quantified. The paper will discuss computational procedures, including grid generation and boundary conditions, as well as comparisons of the various computational schemes to experiment. The results of this study will show the limitations and benefits of Computational Fluid Dynamics (CFD) for determination of radial load, direction, and aerodynamic stage performance.

An analytical model is proposed to calculate the three-dimensional axisymmetric turbulent flowfield in a radial vaneless diffuser. The model assumes that the radial and tangential boundary layer profiles can be approximated by power-law profiles. Then, using the integrated radial and tangential momentum and continuity equations for the boundary layer and corresponding inviscid equations for the core flow, there result six ordinary differential equations in six unknowns which can easily be solved using a Runge-Kutta technique. A model is also proposed for fully developed flow. The results using this technique have been compared with the results from a three-dimensional viscous, axisymmetric duct code and with experimental data and good quantitative agreement was obtained.

The flow at the stall line of a centrifugal compressor with vaneless diffuser was investigated at different speeds. A distinction between three kinds of stall phenomena could be made. One type of stall with regurgitation of fluid at the impeller inlet was of a nonperiodic character, whereas two different types of periodic stall appeared at higher speeds. The rotating nature of these two types of stall was verified from a comparison of signals of peripherally spaced pressure transducers. The low-frequency rotating stall exhibited features of diffuser generated stall and a lobe number of three was measured. From a detailed investigation of the high-frequency rotating stall, which included unsteady probe measurements upstream and downstream of the impeller, it can be shown that this type of rotating stall is generated in the impeller by a periodic breakdown of energy transfer from the rotor to the flow. This conclusion is supported by the distribution of shroud static pressures.

A theoretical model for rotating stall in the vaneless diffuser of a centrifugal compressor is presented. It consists of a time-evolutive calculation of the strong interaction between the inviscid flow core and the unsteady boundary layers along the walls. It is shown that, depending on the diffuser geometry and the diffuser inlet flow angle, a transient perturbation of the outlet static pressure will generate a rotating flow pattern, if the periodicity of this perturbation corresponds to the experimentally observed number of cells. The relative rotational speed and the phase relation between the velocity and the flow angle variations are also in agreement with experimental data.

The limit of rotating stall was experimentally determined for three very small specific speed centrifugal blowers. The impellers were specially designed for stall-free at very small flow rates, so that the cause of rotating stall could be attributed to the vaneless diffusers. Experimental results demonstrated that the blowers did not stall until the flow coefficient was reduced to very small values, which had never been reported in the literature. The critical flow coefficient for rotating stall agreed very well with the prediction based on a flow analysis and a criterion for rotating stall in vaneless diffusers developed by the authors.

This paper describes the results of an experimental investigation of the sub-synchronous rotating flow patterns in a centrifugal compressor with vaneless diffuser. Several compressor configurations have been examined by means of hot wire anemometry, Fourier analysis allowed one to distinguish between the different modes of unstable operation. For both impeller and diffuser rotating stall, comparison is made between the amplitude, frequency, and periodicity of the induced velocity fluctuations. The results are further cross-checked with other experimental data.

The flow discharged from centrifugal impellers is highly distorted and its behavior in the diffuser could be expected to have a determining effect on the performance of the compressor. The present work sets out to investigate this. The experimental work reported in this paper was designed to investigate the interaction between the vaned diffuser and the impeller. Unsteady measurements of velocity and wall static pressure were made at numerous positions in a vaned diffuser using an on-line data logging system. Experiments were carried out at a range of flow coefficients for three diffusers with 10, 20, and 30 vanes set at each of three different radius ratios, 1.04, 1.1, and 1.2. A limited number of experiments were also carried out with restaggered diffuser vanes and as a reference case extensive measurements were made in a vaneless diffuser build. The impeller, which was designed for a pressure ratio of 4.6, was run at low speed (3000 rpm) after modification to make its overall diffusion equivalent to that at the high speed for which it was designed. The circumferential distortion from the impeller was attenuated very rapidly in the entrance region of the diffuser vanes and suprisingly had only minor effects on the flow inside the vaned diffuser passage. The effect of the diffuser vanes on the flow discharged from the impeller was evident and reversal of flow back into the impeller was detected when the diffuser vanes were close to the impeller and the flow rate was not very high. The time-mean total and static pressure at impeller outlet were found to vary over the pitch of a diffuser vane, and a variation in the strength of the impeller wake was also observed.

Shop performance tests were conducted on a four-stage industrial centrifugal compressor. The first stage consisted of a radial plenum inlet, an open inducer type impeller with high hub/tip ratio and radial exit blades, a short vaneless diffuser, and a scroll including a conical diffuser. These stages with high flow coefficients and high tip speed Mach numbers are sometimes used as a first stage with multistage process compressors to increase the volumetric capacity of the given casing and reduce the number of stages. We have four versions of the vaneless diffuser with a radius ratio of 1.46: wide parallel walled, narrow parallel walled, constant area tapered, and reduced area tapered. The influence of these modifications was tested within a tip speed Mach number range of 0.94 to 1.07. Improvement of turn-down was obtained by narrowing and tapering. But the two extremely narrow diffusers reduced the rated point efficiencies beyond acceptable limits. The wide parallel walled diffuser has the highest efficiency and the most unfavorable surge, whereas the constant area diffuser achieved 10 percent better surge without practically any detrimental effects on efficiency.

Centrifugal compressors for gas compression applications usually employ low-pressure ratio, backward-swept impellers with vaneless diffusers. To increase the compressor flow range and speed, impeller blades are occasionally trimmed, resulting in an extended shroud configuration. The effect of extended front and back impeller shrouds on the performance of centrifugal compressors with vaneless diffusers, and the variation of this effect as a function of specific speed, is thus of concern and is the subject of this paper. An investigation was carried out on two backward-swept shrouded impellers of common blade tip and inducer hub diameters, but different inducer tip diameters (corresponding to low and high specific speeds), with the front and back shrouds extending 20 percent above the blade’s outside diameter.

The flow field development within a centrifugal compressor stage was analyzed using an advanced laser velocimetry [4]. A splitter blade impeller coupled with a vaned and vaneless diffuser has been found to have similar internal flow patterns for both the vaneless and vaned diffuser design. Different velocity profiles have been analyzed for adjacent channels behind the splitter blade leading edge. A considerable wake flow was observed near the impeller exit. Detailed optical measurements within the vaned diffuser entrance region gave evidence of a periodically fluctuating, highly distorted diffuser inlet flow. Unsteady flow angle deviations of 13 degrees have been discovered within the diffuser throat. Maximum flow angle differences up to 27 degrees occurred from hub to shroud.

An important task in the design of turbo machinery is the determination of the aerothermodynamic parameters necessary to assure optimum matching of the individual compressor components. With centrifugal compressors, the problem is to design impeller and diffuser such that a maximum overall efficiency is achieved for the desired design point. For this purpose, a mathematical model is developed coupling the individual component efficiencies. In the first part of this paper, the aerothermodynamic bases are derived and the coupling equation is illustrated. In the second part, a solution is displayed for the complex problem of matching the impeller and the vaneless diffuser of a centrifugal compressor. The solution is obtained by means of a stochastic-mathematical optimization procedure based on the biological evolution strategy.

Test results pertaining to the stalling characteristics of centrifugal compressor impellers with parallel wall vaneless diffusers are presented and studied to correlate the coincidence of stall with a limiting impeller diffusion capability. It is suggested that a modified diffusion factor, to include the effects of meridional curvature, provides improved stall correlation for a wide specific speed range of backswept impeller types. The possibility of applying this diffusion factor to high loading radially bladed impellers is discussed as dependent upon blockage and windage plus recirculation effects. Use of the diffusion factor limit in the preliminary design of most common turbomachinery types, incompressible and compressible, to assess impeller (or rotor) stall is conceivable.

The behavior of the distorted flow discharged from a centrifugal impeller within a vaneless diffuser is examined theoretically by assuming small disturbances to a main flow. The inlet static pressure distribution is found in the calculation and allowance is made for circumferential nonuniformity in the relative flow angle. The flow is treated as incompressible and inviscid. The analysis shows that the decay of irrotational disturbances is more rapid with increasing disturbance wave number (e.g. more impeller blades) and the effect of the main flow condition on this behavior is very small. With rotational disturbances, however, the decay is slower than in the irrotational case and the effect of wave number is less. However, the phase angle between radial and tangential velocity fluctuations is found to have a strong influence on the decay processes for rotational disturbances. The present small perturbation theory is compared with the well-known Dean and Senoo theory which assumes that the relative flow angle is circum ferentially uniform. The comparison shows that the present theory predicts results very similar to the Dean and Senoo theory for impellers with large blade numbers (>20). For small numbers of blades the large circumferential nonuniformity in relative flow angle, appears at smaller radii and the inaccuracy of the Dean and Senoo theory becomes pronounced.