Performance Evaluation of an Air-Conditioning Compressor Part II : Volute Flow Predictions *

A numerical method that solves the Reynolds-averaged Navier-Stokes equations is used to study an inefficient component of a shipboard air-conditioning HCFC-124 compressor system. This high-loss component of the centrifugal compressor was identified as the volute through a series of measurements given in Part of the paper. The predictions were made using three grid topologies. The first grid closes the connection between the cutwater and the discharge diffuser. The other two grids connect the cutwater area with the discharge diffuser. Experiments were performed to simulate both the cutwater conditions used in the predictions. Surface pressures along the outer wall and near the inlet of the volute were surveyed for comparisons with the predictions. Good agreements between the predicted results and the measurements validate the calculations. Total pressure distributions and flow stream traces from the prediction results support the loss distribution through the volute. A modified volute configuration is examined numerically for further loss comparison.

INTRODUCTION U.S. Navy shipboard centrifugal chilled water airconditioning systems currently utilize refrigerant CFC-114. In response to the world community decision to eliminate the use of CFC refrigerants, the U.S. Navy has begun a program to convert the air conditioning plants to an environmentally acceptable refrigerant. HCFC-124 was identified as a potential candidate to replace the CFC-114.
contains the largest area of loss in the compressor. Thus, a computational analysis was made to investigate the loss in the volute.
Limited studies (Iversen et al., 1960;Stiefel, 1972;Brownell and Flack, 1985; Van Den Braembussche and Hande, 1990;Elholm et al., 1992;Ayder et al., 1993;Ayder and Van Den Braembussche, 1991;1994) were performed for the volute flow and its interaction with other rotating and non-rotating components of centrifugal compressors. Most of these works concentrated on the experimental studies. A recent study by Ayder and Van Den Braembussche (1994) used an Euler solver to examine the volute flow. They implemented a loss model in the code to account for the friction losses. The current numerical model solves Reynoldsaveraged Navier-Stokes equations. In the following sections, the experimental facility used to record the volute flow characteristics and the measured quantities are first introduced. A brief review of the current numerical method follows. For the numerical results, three different gridding approaches are examined and the predicted pressure distributions are compared with the experimental data. The flow region with a high loss is identified from total pressure distributions. A modified volute configuration is studied based on the present numerical model to evaluate the effect of flow recirculation downstream of the cutwater region. EXPERIMENTAL SETUP l.n order to provide detailed information for understanding the compressor performance shown in Fig. 1 The flow coefficient is 0.0654 and the head coefficient is 1.2324. The specific speed is 0.0903 (which is calculated using rpm, cfs, and enthalpy difference). A total of 40 static pressure taps were installed along the front plate and the back plate of the compressor in the vaneless diffuser and the volute sections. They are distributed along the complete volute flow passage with a concentration of pressure taps at the cutwater. In addition, five total pressure probes were installed to measure velocities at the exit of the vaneless diffuser, inside the volute immediately downstream of the cutwater, in the middle of the volute, and at the exit of the discharge diffuser. Three dynamic pressure transducers were installed in the vaneless diffuser and one in the volute to measure the dynamic pressure response. The estimated error for the static AIR-CONDITIONED COMPRESSOR: PART II 243 pressure measurements is 2%. The details of the measurement setup are shown in Bein and Lee (1998a,b).
For evaluating the effect of the flow through the volute, the measurements were carried out in two steps. A flush mounted movable cutwater plug was installed near the cutwater. This plug, when pushed out from outside of the back plate, was designed to block the fluid flowing back to the cutwater from the discharge diffuser. The experimental condition was adjusted to the compressor design condition.
Three sets of pressure data were taken from each pressure probe. The steady static pressures, referred to as the data of the open cutwater, were obtained by averaging these three data sets. Under the same conditions, a second set of measurements was performed for the closed cutwater. The second series is referred to as the data of the closed cutwater. The measured isentropic efficiency of the closed cutwater condition drops 0.5% when compared with the open cutwater condition as shown in Bein and Lee (1998a,b). Finite-difference approximations are used to discretize the transport equations on non-staggered grid mesh systems. A second-order upwind scheme is used to model the convective terms and secondorder central difference schemes are used for the viscous and source terms of Eqs. (1) and (2). For turbulence quantities, the convection process is modeled by a first-order upwind scheme. A pressure based predictor/corrector solution procedure shown in Chen (1989) is employed to achieve velocitypressure coupling. The discretized systems are solved by an implicit Euler time-marching scheme.

PREDICTION FOR CLOSED CUTWATER
For the flow past the vaneless diffuser and the elbow, both calculations and the experimental data indicated that flow past the vaneless diffuser is completely mixed out before reaching the 90-degree elbow. Thus, the inflow condition for the present calculations to the volute after the elbow was assumed to be uniform initially along the meridional direction. The swirl component of the inlet velocity was taken from the measured value. As the time-marching scheme proceeded the total mass flow through the volute inlet was maintained at the design condition. It is worth noting that the uniform-flow assumption was used in the conventional volute design theory described by Traupel (1977) and by Eckert and Schnell (1980). The measured static pressure at exit plane of the discharge diffuser was used as the exit boundary condition. In order to account for the real gas properties (HCFC-124) the computation was performed using the perfect gas law with an isentropic exponent for the real gas.
An O-grid topology, shown in Fig. 3, at each volute cross section was first used to study the flow pattern. The grid contains 151 meridional nodes and 75 x 25 nodes at each cross plane. This grid system has a singular line at the center of the volute cross section. This singular line prevents the generalization of the grid transition in the cutwater region for connecting with the discharge diffuser.
The predicted pressure distributions at the volute inlet and at the wall of mid-radius are compared in Fig. 4 with the measured distributions for the closed cutwater case. The labeled "EXP (INLET)" pressure is the measured pressure at the vaneless diffuser exit. The cutwater region starts at 0= 22.5 where the measured minimum pressure occurs. The computational grid starts at 0 25 Since the cutwater was not connected, the pressure recovery at smaller volute angles was not predicted. The predictions agree well with the measurements at the inlet and the wall locations. Both the prediction and the measurement, however, show differences between the inlet and the wall pressures.  volute pass. The pressure distribution is uniformly distributed on the left side of the figure, i.e. larger radius wall. There is a pressure gradient between the inlet and the bottom wall as it is shown in Fig. 4. In addition, the results indicated that the sharp suction pressure near the cutwater was not produced by the returning flow from the discharge diffuser through the cutwater. This result also confirms the small measured difference in efficiency between the closed and open cutwater cases.

PREDICTION FOR OPEN CUTWATER
In order to connect the cutwater with the discharge diffuser, the O-grid topology was changed to an Hgrid. In Fig. 6, the H-grid is a one block structured grid and has 162 nodes in the meridional direction, 8 x 14 nodes on each cross plane of the volute pass. Since the inlet portion of the grid is relatively finer than the other parts, the gridlines are very skew near the inlet. The overall grid distribution is coarse because of the restriction of the grid skewness. Similar boundary conditions were applied except an interface boundary was used at the connecting plane of the cutwater between the volute and the discharge diffuser. The predicted inlet and wall pressures shown in Fig. 7 show that the variation A two-block grid structure was generated to reduce the grid skewness of the one-block approach. Figure 8 shows the 2-block grid structure.
The first block contains the inlet portion and consists of l9 x 21 47 nodes and the second block has 201 x 35 47 nodes. The grid nodes at each cross-section are more than quadrupled. The predicted pressure is compared with the measurement in Fig. 9. The agreement between the calculation and the measurement is better than the one-block approach due to the grid resolution and grid distribution. Figure 10 shows the predicted pressure contours for the open cutwater condition at the same section as Fig. 5 shows. The general feature is similar between Figs. 5 and 10 except the overall pressure levels. Due to the opening of the cutwater, the inlet pressure and its gradient between the inlet and the wall are lower than the closed cutwater case. Both cases from the experiment and the calculation, however, show that the low pressure occurs near the cutwater. Figure 11 shows a combined plot for the open and the closed cutwater conditions from both measurements and predictions. Unfilled symbols used in Fig. 11 are for the open cutwater and filled symbols are for the closed cutwater. It is shown clearly from calculations and measurements that the inlet pressure is consistently lower for the open case than for the closed case. The wall pressure, however, remains similar. The measured data shows that the pressure for the open cutwater condition is about 2-4% lower than that for the closed cutwater condition at the inlet and the difference is less than 2% at the wall. Although both the measurement and the prediction show lower peak pressures for the open cutwater case at the design condition, the peak low pressure near the cutwater is independent of whether the cutwater is AIR-CONDITIONED COMPRESSOR: PART II 247 open or closed. This matches with the efficiency measured results between the two conditions. Figure 12 shows the predicted total pressure contours at six cross-sections. The total pressure contours shown indicate that a large loss occurs the inflow at the cutwater as shown in Fig. 12. This flow mixing and the recirculation cause the loss and low pressure which is independent of the cutwater conditions for the returning flow from the discharge diffuser.

A MODIFIED SHAPE IN THE MIXING AREA
Since the flow recirculation region occupied the bottom portion of the cross section downstream of the cutwater, a modified volute shape from 0 27 to 0= 125 was examined. Figure 13 shows the difference between the original and the modified shapes at 0 56. Transition of the cross-sectional shape was smoothly changed. Figure 14 shows the difference in calculated pressures along the volute wall. The peak suction pressure at the cutwater increases slightly, but the pressure recovery through the rest of the volute increases.  pressure, however, was not changed due to prescribing the same exit pressure during the calculation. Figure 1.5 shows the mass-averaged total pressure on each cross section along the volute pass for both the original and the modified cross sections. The modified shape produces slightly larger loss at the cutwater. The loss that occurs in the other part of the volute decreases, although it remains the same at the exit due to the prescribed boundary condition.

CONCLUSIONS NOMENCLATURE
A numerical method that solves the Reynoldsaveraged Navier-Stokes equations was used to study the volute flow of a shipboard air conditioning compressor system. The predictions were made using three grid topologies. The first grid closes the connection of the cutwatef region with the discharge diffuser. The other two grids connect the cutwater area with the discharge diffuser. Experiments were performed to simulate both the cutwater conditions used in the predictions. Good agreements between the predicted results and the measurements validate the calculations. The comparison between the prediction results and measurements indicates that (i) the low pressure and the large loss at the cutwater are not related to the volute returning flow through the cutwater and are related to the inlet flow at the cutwater from the vaneless diffuser and the cutwater's specific geometry; (ii) the loss occurs downstream of the cutwater due to flow mixing and recirculation and is improved by reshaping the cross section; (iii) when the cutwater is closed, the pressure gradient that existed between the inlet and the wall is larger than the open cutwater case, and so is the secondary loss; (iv) the conventional cutwater design at the operating condition has an adverse contribution in pressure recovery due to the low-pressure peak produced at the cutwater.

Acknowledgments
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