The aim of this paper is to investigate the design in similarity of a centrifugal compressor for micro gas turbine and the related scaling effects on performance using CFD investigations. This work is part of a research project carried out by the Department DIME of the University of Genova, with the purpose of investigating the performance of a micro gas turbine in the change from 100 kW electrical output to 250 kW, while maintaining the compressor pressure ratio and geometry in similarity. The first part of the work focuses on the comparison between the original and the scaled machine, while the second part of the study deeply investigates the tip gap effect in the new configuration. The aim is to provide information about the performance of the compressor designed in geometrical similarity and to evaluate the tip gap height impact. From the efficiency point of view, the scaled-up machine has higher efficiency (up to 1.4% increment in design conditions) keeping the same technological limit for impeller manufacturing. However, the variation of tip gap height in the range 0 ÷ 1 mm strongly affects this parameter, leading to 10% alteration in design conditions between the ideal and worst case. The results, both in terms of overall performance and flow fields, are widely discussed in order to obtain simple yet reliable correlation for preliminary design.
In recent years, MGT have been more and more used as cogeneration systems for distributed power generation; this is caused by their good performance, coupled with their compactness and low cost [
Scaling effects, which refer to the study of performance of turbomachinery designed in geometrical similarity, are another topic which has been widely discussed because of its practical application; indeed, this method allows designing machines of different power, maintaining the same components geometry and the same thermodynamic cycle. Head and Visser [
The compressor studied in this work has been developed by DIME in a research project related to the multidisciplinary optimization of several components of a MGT. The preliminary geometry, obtained by employing a classical one-dimensional and then two-dimensional design procedures [
α = p t 1 s p t 1 b β = R T t 1 s R T t 1 b λ = m ˙ s m ˙ b (1)
where p t 1 and T t 1 are the inlet total pressure and temperature, R is the gas constant and m ˙ is the mass flow rate. Since the inlet total conditions are the same for baseline and scaled machines ( α = β = 1 ) , while the mass flow rate scaling factor is equal to 2.5, the geometrical length scaling factor provided by [
D s D b = α − 1 2 β 1 4 λ 1 2 = 2.5 1 2 ≅ 1.58 (2)
The main parameters of these two machines are listed in
Quantity | Original (100 kWe) | Scaled up (250 kWe) |
---|---|---|
Number of impeller blades | 10 + 10 | 10 + 10 |
Number of diffuser blades | 19 | 19 |
Impeller exit radius [mm] | 64 | 101 |
Design efficiency [%] | 84 | 84 |
Total to total pressure ratio [-] | 4.6 | 4.6 |
Design mass flow rate [kg/s] | 0.74 | 1.85 |
Rotation speed [rpm] | 75,000 | 47,450 |
The tip gap was scaled, in this first analysis, using two different approaches: the first, maintaining the absolute value of the tip gap, equal to 0.2 mm, intended as a lower technological limit for impeller manufacturing; the second one, scaling the value of the tip gap itself, thus maintaining the same relative gap (intended as scaled percentage on the height of the blade), thus equal to 0.32 mm for this case. After this preliminary analysis, a detailed investigation about tip gap height effects on machine performance have been carried out. To achieve this result, different values of the tip gap height have been simulated. In this analysis, the geometry of the meridional channel and of the blades has not been modified with respect to the result of the scaling up process illustrated above. Therefore, the geometries investigated differ from each other only for the value of the tip gap height. In this second analysis, in addition to the ideal case, represented by a value equal to zero, five values of the tip gap height, with 0.2 mm pitch, were investigated, up to a maximum value of 1 mm, taken as the upper limit for the construction of the machine.
The computational mesh was generated in Autogrid [
In order to obtain the performance curve of the original and scaled up machines, several operating conditions were simulated, varying the mass flow rate. Using this outlet boundary condition, the solver adjusts the pressure ratio to satisfy continuity equation. Choking is detected when the inlet mass flow rate mismatches the outlet condition, so the flow rate is decreased in order to obtain a converged simulation. Stall is considered when the main machine parameters present unacceptable oscillations during simulations, leading to not converged calculations when the mass flow rate is strongly decreased. More precise considerations could be done using unsteady investigations near stall region, but this is out of the primary scope of this work, since it aims to provide simple yet useful indications in first guess design procedure.
In the following, the results obtained for scaled up machines are presented. In the first part, the Reynolds effect on scaling methods is presented, while in the second part, the effect of tip gap height on performance curves is presented, with a detailed investigation on flow field behavior. The first application concerned, as mentioned, the analysis of the scaling effects of the machine using absolute scaling and relative scaling of the tip gap height. These effects are first investigated by comparing the characteristic curves of the machines, in terms of efficiency and in terms of compression ratio. In
As expected, the scale effect leads to an increase in efficiency in all operating points of the curves of larger machines. In the case of absolute scaling, the efficiency curve shows a flatter behavior in the central zone, resulting in a high efficiency value in a wide range of flow rates, while the curve of the relative scaling machine has a shape very similar to that of the original one, simply translated upwards. From the extension of the operating range point of view, it is noted how the machine with relative scaling presents the point of surge moved to the right compared to that of the original machine, while the chocking point is roughly obtained for the same value of mass flow rate. In the case of the absolute scaled machine, instead, both extreme points of the curve are translated to the right, with amplitude of the operating range, in terms of variation in mass flow rate, almost equal to that of the original machine. For total to total pressure ratio β t t , shown in
This means that the effect of the Reynolds number appears to be for this second case, marginal as regards the value of the pressure ratio.
The effects of the tip gap height was investigated by simulating different values of this size, from the ideal case, with zero gap, up to a value of 1 mm, using a 0.2 mm pitch.
While the ideal case has a maximum efficiency of around 86.5%, the value is reduced of about 10 percentage points for 1 mm condition. Furthermore, there is a gradual decrease in both the value of the surge and chocking mass flow rates, and a strong reduction in the amplitude of the operating range. From
Investigating the full operating range, it was noticed that the choking mass flow rate varies linearly with tip gap height (
Finding a reliable correlation to predict the curve slope could be an important tool in preliminary design steps in order to understand the correct tip gap scaling; in particular, the upper limit beyond which the design mass flow cannot be processed which is strongly related to manufacture technologic requirements.
In order to better understand the effect of tip gap height on flow field main parameters and thus on overall performance of the machine, a detailed investigation of significant quantities and flow properties was performed. One of the most interesting section on which analyze these quantities is the impeller outlet section (corresponding also to diffuser inlet section), highlighted in cyan in
For this section, several color contour representations are reported in the following figures, representing two flow passages, each one constituted by a splitter blade and a main blade, in this order from left to right. In order to compare similar cases for each operating condition, the best efficiency point for each performance curve is considered. Thus, the mass flow rate changes for each represented condition, as reported in
In
Case | Tip gap height [mm] | Mass flow rate [kg/s] |
---|---|---|
a | 0.2 | 1.85 |
b | 0.6 | 1.75 |
c | 1.0 | 1.65 |
In
s c o r r = s − s 0 w 0 2 / 2 T 0 (3)
where w 0 is the inlet relative velocity and T 0 is the inlet temperature. From
On the contrary, as the tip gap increases, in addition to an increase of the value of the angle in the tip leakage area, characterized by an uncontrolled value of the absolute angle of the flow (approaching or exceeding 90˚), the value of the angle within the bladed channel undergoes a strong variation, with values that are reduced, near the hub region, at around 40˚ for the worst case (case c). To compensate the extensive flow blockage induced by the larger tip clearance, the fluid is deflected in the radial direction to preserve the assigned mass flow rate. These strong variations in the absolute flow angle from the design value entail an incorrect operation of the bladed diffuser located downstream of the rotor, with a consequent reduction in the effect of pressure recovery and consequently of the performance of the machine in terms of compression ratio and efficiency, as highlighted in
As can be seen from the trends of
In fact, in
The entropy increase at the inlet highlights the extension of the zone of flow recirculation. The losses are produced in the tip leakage region and are transferred back to the inlet section by the reverse flow.
A step forward is the prediction of performance variation with the tip gap height through simple one-dimensional equations, accordingly to what is discussed in literature [
Efficiency drop = Δ η η * = C τ Δ τ τ * − C s Δ s − Δ s * R (4)
where η is the efficiency, τ is the total temperature ratio and all the quantities with superscript * are referred to zero tip gap height. The coefficients C τ and C s are defined as:
C τ = 1 β t t * γ − 1 γ − 1 τ * − 1 (5)
C s = γ − 1 γ ( 1 + 1 β t t * γ − 1 γ − 1 ) (6)
where γ is the heat capacity ratio.
It is evident how the specific work reduction has a negligible effect on efficiency decrease with tip gap, while viscous losses are relevant. The linear pattern is conserved, but the correlation (sum of viscous and inviscid effects) underestimates the efficiency drop compared to CFD simulations. In similar manner, in
Pressure ratio drop = Δ β t t β t t * = γ γ − 1 Δ τ τ * − Δ s − Δ s * R (7)
In this case, the contributions to losses are equally important and the correlation well captures the results provided by numerical computations.
Numerical simulations were conducted in order to evaluate the centrifugal
compressor performance variation in scaling process. Global results (e.g. characteristic curves) were justified by detailed analysis on the flow field, with particular attention to the tip gap impact on flow structures. On the one hand, it is noticed that the classical scaling procedure leads to a machine in perfect similarity (velocity triangles, percentage operating range and total to total pressure ratio) with a little increment of efficiency due to the increase in Reynolds number with dimensions. On the other hand, keeping the same tip gap height (same technological limit for impeller manufacturing) has a strong impact on performance, leading to a different machine. Further investigations showed that the variation of tip gap height affects significantly the machine efficiency (up to 10% compared to the ideal case of zero leakage), pressure ratio and operative range extension. In particular, the design mass flow rate cannot be processed if the leakage flow structures are strong enough to obstruct the channel. The study suggests that the global tip gap effect can be determined using simple correlations which relate thermodynamic, aerodynamic and geometrical characteristics. The pattern of efficiency and pressure ratio variation follow the linear behaviour presented in literature, but there are large differences in curve slopes and mismatches in efficiency prediction.
The authors declare no conflicts of interest regarding the publication of this paper.
Barsi, D., Bottino, A., Perrone, A., Ratto, L. and Zunino, P. (2019) Design of a Centrifugal Compressor for Micro Gas Turbine: Investigation of Scaling and Tip Clearance Effects. Open Journal of Fluid Dynamics, 9, 49-62. https://doi.org/10.4236/ojfd.2019.91003