The presented research demonstrates the results of a series of numerical simulations of gas flow through a singlestage centrifugal compressor with a vaneless diffuser. Numerical results were validated with experiments consisting of eight regimes with different mass flow rates. The steadystate and unsteady simulations were done in ANSYS FLUENT 13.0 and NUMECA FINE/TURBO 8.9.1 for oneperiod geometry due to periodicity of the problem. Firstorder discretization is insufficient due to strong dissipation effects. Results obtained with secondorder discretization agree with the experiments for the steadystate case in the region of high mass flow rates. In the area of low mass flow rates, nonstationary effects significantly influence the flow leading stationary model to poor prediction. Therefore, the unsteady simulations were performed in the region of low mass flow rates. Results of calculation were compared with experimental data. The numerical simulation method in this paper can be used to predict compressor performance.
Detailed experimental and numerical research of flow structures in centrifugal compressors began in the last century. Nonstationary effects were experimentally observed and described in detail in [
Eckardt (1976) [
Compressor Design Department of Saint Petersburg Polytechnical University has a special test stand for gas compressors. This stand allows the measurement of different instantaneous and mean parameters, such as pressure, velocity, and temperature. The basic characteristic of gas compressors is the pressure characteristic that shows the dependence of the gas pressure ratio from mass flow rate for a given rotational speed.
The compressor under research is a laboratory lowpressure centrifugal compressor with a vaneless diffuser. It was designed for very low total pressure ratios (
Up to now, there were a small number of papers, known to authors, devoted to numerical simulation of the centrifugal compressor [
The objective of this work is a numerical simulation of the gas flow in the centrifugal compressor and validation of the obtained results against the physical experiment.
Experimental data and the geometry of a singlestage centrifugal compressor with a vaneless diffuser were provided by Compressor Design Department of Saint Petersburg State Polytechnical University. The experiments were carried out for eight regimes with different mass flow rates. Three different crosssections of the compressor duct were examined during the experiments. These crosssections are the inlet, diffuser inlet, and diffuser outlet (see Figure
Geometry of the centrifugal compressor.
Tables
Experimental data for regimes 1–4.
Regimes  1  2  3  4 


294.6  294.8  294.8  294.9 

0.629  0.553  0.495  0.434 

101791  101778  101778  101778 

1.047  1.053  1.060  1.066 

1.045  1.051  1.056  1.061 
Experimental data for regimes 5–8.
Regimes  5  6  7  8 


295.0  295.0  295.1  295.2 

0.312  0.266  0.116  0.105 

101911  101765  101765  101765 

1.073  1.076  1.076  1.075 

1.068  1.069  1.068  1.067 
The compressor contains 16 rotational blades. The rotating speed of the impeller is 6944 rpm. The diameter of the impeller is 275 mm (Figures
Geometry of the impeller.
Geometry of the blade.
Periodic boundary conditions are used when the flows across two opposite planes in a computational model are identical [
Wall boundaries can be either stationary or moving. The stationary boundary condition specifies a fixed wall, whereas the moving boundary condition (e.g., using a moving reference frame) can be used to specify the translational or rotational velocity of the wall or the velocity components [
The boundary conditions for the studied model are shown in Figure
Boundary conditions.
Steadystate simulations were done in NUMECA FINE/TURBO 8.9.1 using different available turbulence models and discretization schemes. The calculations were carried out on a single structured mesh with 700 000 control volumes. The mesh was constructed to fit the wall
Figures
Pressure characteristic at the diffuser inlet for different turbulence models using firstorder upwind discretization.
Pressure characteristic at the diffuser outlet for different turbulence models using firstorder upwind discretization.
The firstorder turbulence models give out similar results of pressure characteristic. As could be noticed from the figure, the calculated pressure characteristics are plain even where nonstationary effects are strong (below 0.3 kg/s). Moreover, the obtained total pressure ratio is within predicted values in the region of high mass flows. It could result in high pressure losses due to dissipation effect of firstorder schemes. Therefore, the firstorder approximation is insufficient to reproduce the stationary characteristic of the lowpressure ratio compressor.
Figures
Pressure characteristic at the diffuser inlet for the SpalartAllmaras turbulence model using secondorder central discretization.
Pressure characteristic at the diffuser outlet for the SpalartAllmaras turbulence model using secondorder central discretization.
The conclusion could be that the secondorder central discretization scheme conforms to the pressure characteristic shape much better than firstorder upwind schemes. In addition, the pressure ratio does not conform to the experimental results in the region of high mass flows. Due to ignoring of hub and shroud leakages, the observed deviation of the pressure ratio was to be expected. In the region of low mass flow rates, nonstationary effects are dominant and steadystate simulations are not capable of capturing them.
Figures
Flows paths at mass flow 0.4 kg/s, firstorder upwind and secondorder central discretization.
Flows paths at mass flow 0.3 kg/s, firstorder upwind and secondorder central discretization.
Flows paths at mass flow 0.2 kg/s, firstorder upwind and secondorder central discretization.
Flows paths at mass flow 0.175 kg/s, firstorder upwind and secondorder central discretization.
The large vortex structure starts to form when the flow rate falls below 0.4 kg/s only if the secondorder scheme is used. Firstorder schemes do not predict any vortex structures until the flow rate falls below 0.2 kg/s, but even then predicted structures are not very large. This could be attributed to strong numerical dissipation effects that are present when using firstorder schemes. The stalling regime is very strong when using secondorder central schemes. Due to strong influence of unsteady effects on mean flow parameters, unsteady simulations are needed to be carried out for accurate capturing of these effects.
Steadystate and unsteady simulations were done in ANSYS FLUENT 13.0 using the realizable
Figures
Pressure characteristic at the diffuser inlet for the stationary case in the diffuser inlet.
Pressure characteristic at the diffuser outlet for the stationary case in the diffuser outlet.
It is clear from the pressure characteristic that computed pressure ratio values are slightly over experimental curve. This could be attributed to neglecting the influence of hub and shroud leakages. The shape of the numerical characteristic is in a good agreement with the shape of the experimental characteristic.
All nonstationary effects were observed in the experiments in the regimes with small mass flow rates. Therefore, only the first three regimes in the unsteady simulations were omitted.
Unsteady calculations were done in a transient formulation with firstorder time discretization. 20 and 100 time steps for one period for the coarse and refined mesh were chosen, respectively. Thus, the time step for the coarse mesh was equal to
The pressure characteristics for the unsteady case are shown in Figures
Pressure characteristic at the diffuser inlet for the unsteady case in the diffuser inlet.
Pressure characteristic at the diffuser outlet for the unsteady case in the diffuser outlet.
As can be clearly seen from the figures, the unsteady pressure characteristics are very similar to stationary pressure characteristics.
To provide accurate results, the dependence of mass flow rate in the inlet on the mesh size was investigated (Figure
Mesh sensitivity analysis.
Table
Results of mass flow rate in the inlet for unsteady simulations.


Err_{CM} 

Err_{RM} 

0.4338  0.4678  7.32  0.4434  3.15 
0.3123  0.3443  9.29  0.3264  4.32 
0.2661  0.3169  16.03  0.2983  10.79 
0.1158  0.2618  55.57  0.2248  48.49 
Unfortunately, no vortex structures are present and no rotating stall is reproduced for this case. The possible meaning is that the unsteady calculations do not cover nonstationary effects. It could be attributed to oneperiod geometry or the turbulence model. Further study of this phenomenon is necessary.
Numerical results of executed calculations show strong dependence on the order of discretization. Firstorder discretization schemes are unacceptable because they do not reproduce large scale vortex structures due to numerical dissipation effects. Secondorder schemes are capable of reproducing these structures.
Numerical results agree with the experiments for regimes with high mass flow rates. In the regimes with low mass flow rates, formation of large nonstationary vortex structure (rotating stall) leads to the inability of stationary models to accurately reproduce flow physics. However, these effects have not been reproduced in unsteady simulations in ANSYS FLUENT 13.0. A possible reason for this is that oneperiod geometry is incapable of reproducing these nonstationary effects.
Steadystate calculations of a oneperiod model are required to be done for different turbulence models with secondorder discretization schemes and on more refined meshes. Also, unsteady flow simulations for 360degree geometry should be carried out.
Since the experimental measurements exist for the modelled compressors, it was possible to carry out the verification and validation of user software. The agreement between the results obtained by numerical modelling and by experiments is satisfactory, which enables complete replacement of the timeconsuming experimental investigations by much rapid numerical simulations.
The represented numerical modelling of flow in centrifugal compressor makes it possible to carry out the optimisation of basic part of compressor (e.g., impeller) with the aim of improving the efficiency of machinery.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The work has been carried out at the Department of Mathematics and Physics, Lappeenranta University of Technology, and Department of Applied Mathematics, Saint Petersburg State Polytechnical University. The experimental results have been obtained by the test stand for gas compressors at the Compressor Design Department, Saint Petersburg State Polytechnical University.