SCIENCE CHINA Technological Sciences • RESEARCH PAPER •
June 2013 Vol.56 No.6: 1361–1369 doi: 10.1007/s11431-013-5213-6
Effects of Reynolds number on the performance of a high pressure-ratio turbocharger compressor ZHENG XinQian1*, LIN Yun1, GAN BinLin2, ZHUGE WeiLin1 & ZHANG YangJun1 1
State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China; 2 Beijing Power Machinery Research Institute, Beijing 100074, China Received December 28, 2012; accepted March 22, 2013; published online April 29, 2013
The effects of Reynolds number on the performance of a high pressure-ratio turbocharger compressor were investigated by both experiments and numerical simulation. The experimental results show that the pressure ratio and the efficiency of the compressor respectively decrease by 7.9% and 6.9% when Reynolds number drops from 9.86×105 to 2.96×105. The numerical simulation predicts a similar trend as the experimental results although it underestimates the deterioration of the performance under low Reynolds number conditions. According to simulation results, the boundary layer thickness increases at the inducer, which decreases the throat area and leads to smaller choke mass flow rate. The increments of the boundary thickness are relatively small at the rear part of the impeller. The boundary layer separation flow is severe. The interaction between boundary layer separation flows and leakage flows causes the high loss region at the rear part of the impeller passage under low Reynolds number condition. Reynolds number, high pressure-ratio, turbocharger, centrifugal compressor, internal combustion engine Citation:
Zheng X Q, Lin Y, Gan B L, et al. Effects of Reynolds number on the performance of a high pressure-ratio turbocharger compressor. Sci China Tech Sci, 2013, 56: 13611369, doi: 10.1007/s11431-013-5213-6
Nomenclature Cp LE m M MP MS P PR Re S SP SS
specific heat at constant pressure (J/(kg K)) leading edge mass flow rate (kg s1) Mach number main blade pressure surface main blade suction surface pressure (Pa) pressure ratio Reynolds number entropy (J/(kg K)) splitter blade pressure surface splitter blade suction surface
*Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2013
S* T
entropy function temperature (K) increment or decrement isentropic efficiency specific heat ratio
Subscripts 1 2 a abs c ref t u
impeller inlet impeller outlet actual value absolute coordinate system corrected value reference value stagnation condition tangential component tech.scichina.com
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1 Introduction Atmospheric science missions for global climate change studies require the aircraft to cruise at a high altitude of about 30000 m [1]. In addition, the long endurance and low flying speed are desirable for sampling and monitoring the atmospheric conditions at a specified location. The turbocharged spark ignited engine is the best choice for the powerplant of this high altitude atmospheric science aircraft for [2]: (a) good adaptability for low operating speed; (b) low fuel consumption which allows longer endurance; (c) low manufacturing cost compared to other propulsion choices. One of the most important technological issues for the turbocharged spark ignited engine is the negative impact of the low Reynolds number flow conditions on the performance of the turbocharger centrifugal compressor. As the compressor working at high altitude, the Reynolds number of the inlet flow is much smaller than that on the ground mainly due to the much lower air density. The low Reynolds number inlet conditions help to develop the laminar boundary layer and extend the laminar/turbulence transition flow region, resulting in greater flow separation and higher flow blockage, thus deteriorating the compressor performance, which reduces the aircraft maximum cruising altitude as well as the endurance. Considerable attentions have been paid to the effect of low Reynolds number on the performance of compressors. The early studies suggested some empirical correction equations to predict the deterioration of compressor performance under low Reynolds number conditions [3, 4]. Most of these methods were based on the simplified models and statistical analysis of the available experimental data of that time, and thus lacks of universality. In order to set up better performance correction methods and improve the compressor performance under low Reynolds number conditions, the survey of the flow field and the aerodynamic loss mechanism at low Reynolds number is necessary. Both experiments and numerical simulations on this topic have been carried out. Some studies focused on the low Reynolds number flow in cascades. Schreiber et al. [5] researched the boundary lay transition in a compressor cascade through surface flow visualization, and revealed a clear laminar separation bubble structure on the suction surface at a relatively low Reynolds number. More attentions have been paid to the study of the low Reynolds number effect on the turbine cascades since the low pressure turbines are subjected to a low Reynolds number inlet flow when operating at high altitude. Treuren et al. [6] reported the detailed measurements of the flow under low Reynolds number conditions in a turbine cascade, and a large separation near the trail edge of the suction surface was identified. Matsunuma [7] studied the turbine cascade with tip clearance using both experiments and numerical simulation. The
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results showed that the leakage vortex spread toward the midpassage and enhanced the interaction with the passage vortex under low Reynolds number conditions, leading to the decrease of the mass-averaged exit flow angle. The methods for predicting separation and transitional flow were also developed based on the understanding of the turbine cascades flow at low Reynolds numbers [8, 9]. Meanwhile, some researches focusing on the whole stage were conducted. The effect of low Reynolds number on loss characteristics in a subsonic axial compressor was studied by Choi et al. using the three-dimensional CFD, and the results showed that the performance deterioration at low Reynolds number condition was caused by the full-span separation on the suction surface and the boundary layer on the hub [10]. Sonoda et al. [11] reported that larger corner stalls in the hub and tip regions caused the dramatically increasing loss in the outlet guide vane of a turbofan engine under low Reynolds number conditions. Du et al. [12] conducted the numerical simulation of the low Reynolds number flow in a transonic axial compressor. The results showed that the low momentum fluid due to the surface boundary layer separation was the dominant factor affecting the flow field of tip section as well as the stability of the compressor. Based on the gained insights about the effects of low Reynolds number, different approaches were investigated to improve the performance under low Reynolds number conditions. The design methods of compressor blades adapted to low Reynolds number applications were developed [13, 14]. Vortex generator jets were applied to low-pressure turbine airfoils for separation control under low Reynolds number conditions [15, 16]. Zhou et al. [17] even applied a slotted compressor airfoil to blow off the boundary layer separation flow, in order to reduce the loss under low Reynolds number conditions. With increasing cruising altitude, the pressure ratio of the centrifugal compressor has to be going up to maintain the engine power, and it is shown that the individual stage pressure ratio of approximately 4.0 for a three-stage turbocharger is necessary in order to fly at an altitude at 26000 m [18]. At this stage pressure ratio, the flow field of the compressor inducer is expected to be transonic with complicated interaction of shock wave, clearance flow and boundary layer on blades and endwalls [19, 20]. Although extensive studies have been done on the effect of low Reynolds number on the performance of turbomachinery, most of them focused on the axial compressors or the turbines with subsonic inlet flow. Knowledge about how low Reynolds numbers affect a transonic centrifugal compressor is rare. In this work, the influence of low Reynolds number on a high pressure-ratio centrifugal compressor was investigated using both experiments and numerical simulation.
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2 Experiments 2.1
Table 1
Experiment facilities
The performance of the high pressure-ratio centrifugal compressor with variable inlet Reynolds number flow conditions was tested on an experimental rig developed by Tsinghua University, as shown in Figure 1. The flow in the rig went in a closed loop, with a large air chamber simulating the high altitude environment. An air pump was connected to the chamber and worked before the test to create a certain vacuum in the air chamber. During the test, the air pump may work to pump away the air leakage from external environment due to the not enough pressure tightness of the chamber. The total pressure of the inlet flow could be set from 10 to 100 kPa, and accordingly the inlet Reynolds number could vary over a wide range. The centrifugal compressor was propelled by a turbine. The rotational speed of the compressor was controlled by two valves in front of the turbine to allow for control of the flow rate in the turbine. The flow rate in the compressor was controlled by two valves at its outlet with a sensitivity of 0.002 kg s1. An air cooler was assembled at the outlet of the compressor to cool the outflow. By adjusting the cooling rate, the total temperature of the inlet flow could be controlled to vary within a small range of about ±3°C. The major parameters measured during performance testing included total/static pressure and temperature at the inlet/outlet of the compressor, mass flow rate, rotational speed, ambient pressure and temperature in the air chamber. The temperature was measured by thermocouple with an error of less than ±1.75°C; pressure was measured by diaphragm pressure sensors with an error of less than ±0.25 kPa; mass flow rate was measured using a vortex flow meter with a relative error within ±0.5%; rotating speed was measured by an electromagnetic transducer with a relative error within ±0.25%. A relative error of total pressure-ratio is evaluated to be less than ±0.4% and an absolute error of efficiency to be less than ±0.5% at design conditions. The key geometries and operational characteristics of the investigated centrifugal compressor are listed in Table 1. The design rotational speed and the design mass flow rate in the table are the corrected values based on the referenced atmosphere condition (Pref=100 kPa, Tref=298 K).
2.2
Main parameters of the compressor Parameter Design pressure ratio Design rotating speed Design mass flow rate Blade number Impeller inlet diameter Impeller outlet diameter
Value 4.0 170000 (r min1) 0.23 (kg s1) 6/6 main/splitter 44.8 (mm) 61.0 (mm)
Experimental results
The tested Reynolds number based on the impeller inlet tip speed at the designed status (namely at the designed rotating speed and designed mass flow rate), impeller inlet tip diameter and inlet airflow conditions varied from 2.96×105 to 9.86×105. The following Reynolds numbers all refer to the values calculated at design status, except as otherwise noted. Figure 2 shows the compressor performance characteristic at Reynolds number of 2.96×105 (marked as Low Re No Exp) and 9.86×105 (marked as High Re No Exp), respectively. The performance was characterized by the total pressure ratio and corrected mass flow rate. The latter is defined as mc
ma Pref Tt1 Pt1 Tref
.
(1)
Five lines are represented corresponding to the inlet absolute Mach number (Mu1) of 0.93, 1.00, 1.07, 1.13 (design status), and 1.20, respectively. Both the mass flow and the total-to-total pressure ratio (PR) were normalized values in the figure. As shown in Figure 2, the characteristic map moved down to the left as the Reynolds number decreased. Figure 3 shows the normalized total-to-total PR and the normalized isentropic efficiency at design status under different Reynolds number conditions. It is shown that the total-to-total PR and the isentropic efficiency of the compressor decreased approximately linearly as the Reynolds number decreased. The total-to-total PR at Reynolds number of 2.96×105 dropped by about 7.9%, and the isentropic efficiency dropped by about 6.9% in comparison with that at Reynolds number of 9.86×105. The isentropic efficiency is defined as
Figure 1 Schematic diagram of the test rig (the arrows represent the flow direction).
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Tt1 [( Pt 2 / Pt1 )( 1) / 1] . Tt 2 Tt1
(2)
Under low Reynolds number conditions, the actual mass flow rate of the compressor was much lower and the heat leakage to the external environment became considerably severe. It was difficult to capture the accurate temperature of the outflow of the compressor (Tt2) in the test. In the calculation of the isentropic efficiency () for all the three Reynolds number conditions in Figure 3, the values of Tt2
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were obtained from the numerical simulation results. Early studies [3, 4] suggested some empirical equations for efficiency correction under low Reynolds number conditions. The basic form of these equations is n
1 Re a (1 a) ref , 1 ref Re
(3)
in which a represents the Reynolds independent loss fraction; n is the Reynolds ratio exponent; Reref is the referenced Reynolds number, and equals to 9.86×105 in this work; ref is the referenced efficiency and usually set as the compressor efficiency at zero altitude. Although mass work had aimed at finding a universal value or model of the parameters a and n, it seems that these parameters varied for different compressors, as summarized in ref. [3]. For this work, when a=0 and n=0.1 the prediction given by the empirical equations fits the experimental results well, as shown in Figure 3. As the trend of the pressure-ratio distribution is similar to that of the efficiency, as shown in Figure 3, the above equation can also be applied to the correction of pressure ratio under low Reynolds number conditions.
3 Numerical simulation 3.1 Numerical method The simulation was performed using NUMECA EURANUS
Figure 2
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solver, which is based on a three-dimensional steady compressible, finite volume scheme to solve Reynolds-averaged Navier-Stokes equations in conservative formulation. The Spalart-Allmarsa (S-A) one equation model was chosen for turbulence closure [21]. The criterion of Abu-Ghannam/ Shaw [22] was adopted to predict boundary layer transition. Central scheme was applied to spatial discretization and a fourth-order Runge-Kutta scheme was used for temporal discretization. One passage of the impeller was modeled for the simulation. The computational domains in both upstream and downstream of the impeller were extended, as shown in Figure 4. Spatial discretization error was closely related to the grid number. The grid independency assessment was carried out and a final grid of the model consisted of 18 blocks with about one million nodes in order to attain a higher resolution of flow quantities. The passage consists of 151 nodes in the streamwise direction, 86 nodes in the pitchwise direction, and 65 nodes in the spanwise direction. A constant tip clearance of 0.25 mm was assumed, and modeled using the C-type grid, which included 145 nodes around pressure and suction surface of the blade from the leading edge to the trailing edge, 17 nodes from the blade top to the casing, and 17 nodes across the blade thickness. The grids exhibited a minimal grid quality as defined by measures of orthogonality (especially at the block boundaries; minimum about 20°), relative grid spacing in boundary layer (expansion ratio
