Mean flow field measurements in an axisymmetric conical diffuser with and without inlet flow distortion

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 16, August 2009, pp Mean flow field measurements in an axisymmetric conical diffuser with and without inlet flow distortion E Karunakaran & V Ganesan* Internal Combustion Engines Laboratory, Department of Mechanical Engineering Indian Institute of Technology, Chennai , India Received 5 September 2008; accepted 12 June 2009 The prime objective of this paper is to present the details of the experimental investigation and measurements made in an axisymmetric 5 conical diffuser model. The flow through a diffuser is studied with and without the inlet flow distortion. A simple cylindrical bluff body placed at the inlet of the diffuser creates the inlet flow distortion. A 5 mm diameter five-hole pitot sphere of cobra type has been used along with electronic digital manometers for the measurements. The velocity at the near wall regions and wake regions are well captured with the five-hole probe. The measurements along the entire length of the model at different stations, allow the determination of axial mean velocity component and pressure field parameters, which provide comprehensive information to aid and understand such complex flows. Performance and flow characteristics along the centerline of diffuser are presented. Diffusers are often used in conjunction with turbo machines to increase the static pressure and reduce the velocity of the discharge flow. In many instances the flow entering these diffusers are distorted because of the incomplete straightening of the flow behind the shafts and mechanical structures placed in the upstream of the flow field. A good example of the aforesaid case is the diffusers used in conjunction with gas turbine combustors. Improvements in technology of the compressor and combustor components of the aircraft gas turbine engine have in recent years placed a greater emphasis upon the requirement for an efficient diffuser between these components Diffuser is a duct where the flow velocity decreases and the static pressure increases as the fluid moves from inlet to outlet. Aircraft engines and jet engines contain diffusers for a variety of purposes. In all cases, maximum recovery of static pressure without substantial loss of integrated total pressure must be achieved in order to obtain good performance. Diffuser performance and flow characteristics are strongly coupled so that the knowledge of flow conditions is absolutely necessary in the interpretation of performance parameters. Pressure recovery performance depends on inlet wall boundary layer conditions as well as diffuser geometry. Hence, for a fixed geometry, the inlet boundary layer or the inlet *For correspondence ( vganesan@iitm.ac.in turbulence level sets the performance level. The results available in the literature include only a few qualitative studies of effect of variation of the inlet conditions. Since an adequate investigation is lacking, availability of systematic experimental results is particularly important for design and to improve understanding. The present study has two objectives: (i) Provision of systematic and detailed results on the effect of inlet conditions on diffuser flows to allow a more comprehensive study of the underlying flow phenomena and energy distributions in adverse pressure gradient system; and (ii) Evaluation of the diffuser performance parameters with and without inlet distortion. Flow through an axisymmetric diffuser involves the consideration of many complex flow phenomena. A voluminous literature on flow through axisymmetric diverging passages is available. Although a great deal of investigation on flows in diverging passages has been done, very little of it has been found for flow with inlet distortion. This led us to make detailed experimental investigations on aerodynamics involved. Dean and Senoo 1 investigated the influence of temporal variations in the inlet velocity profiles to a vaneless diffuser. A theory based on a simplified model was developed for this axially symmetric unsteady flow and it predicted a significant reversible work transfer between parts of the flow with different

2 212 INDIAN J. ENG. MATER. SCI., AUGUST 2009 velocities. It was concluded that the total pressures in the diffuser might be less for distorted inlet flow than for undistorted inlet flow. According to Cockrell and Markland 2, the roughness of the inlet duct and the Reynolds number based on the inlet diameter are important in determining the probable performance of a conical diffuser. Tyler and Williamson 3 conducted tests on a series of conical and annular diffusers under nonuniform inlet velocity distributions. It was concluded that the area ratio for maximum pressure recovery at a specified non-dimensional length decreases rapidly with an increases of the inlet distortion factor beyond about1.1. Rao 4 studied the effect of radial splitters in the large area ratio, wide-angle conical diffusers. It is found that the splitter apex provided with a circular disc whose area and location influence the maximum pressure recovery. The effective expansion angle of the diffuser is reduced by the provision of radial splitter vanes. Welsh 5 studied flow control in wide angled conical diffusers. This is a comprehensive study of a passive device with eight radial spokes called as stars. Each star, including the central boss was supported on a rod which was held central by mechanical means at two locations within the tail pipe. Two stars with large arm thicknesses were used in this study. The star produces a moderate wake near the center line of the diffuser and therefore, by continuity, the velocity near the outer wall is increased. The outcome is reduction in losses associated with flow unsteadiness near the outer wall and a more uniform exit velocity profile which leads to reduced exit kinetic energy losses. Provided the total reduction in the above losses is greater than the losses due to the star, there is a gain in the overall diffuser pressure recovery. The geometry of star flow control device necessary to improve the performance and flow stability was sensitive to the diffuser inlet conditions. It was concluded that the optimum performance of diffuser is dependent upon star arm (spokes) thickness, star location and diffuser inlet conditions. Shimizu et al. 6 studied the effect of different types of inlet velocity profiles on the performance of straight conical diffusers. Provision of various pipe bends in front of the diffuser created different kinds of velocity profiles. It was found that improved pressure recovery was obtained in the case of flow with a symmetrical axial velocity profile along with one directional swirling component or with a distorted axial velocity profile along with double spiral swirling components at inlet. Jeyachandran and Ganesan 7 have studied numerical prediction of performance and effectiveness of conical diffusers with velocity distortions at the inlet. Performance and effectiveness of the diffuser at various down stream stations have been computed from the predicted velocity profiles. It is seen that the pressure gradient increases with increase in half cone angle. Also it is observed that the inlet velocity distortion increases the pressure gradient. An experimental study of turbulent characteristics of incompressible flow in a two dimensional diffuser with inlet velocity distortion was reported by Chidambaram et al 8. The velocity distortion at the inlet of the diffuser was produced by NACA0009 aerofoil ahead of the diffuser. It is seen from the results that the entry flow distortion has a significant effect on the turbulent characteristics. Hoffman and Gonzalel 9 found that increasing the inlet turbulence intensity increased the pressure recovery of the diffuser. They conducted experiments in a two dimensional diffusers of total included angles of 9 and 20 for the conditions with and without upstream rods. With the high intensity turbulence, the pressure recovery coefficient of the diffuser was improved by 10% in 9 diffuser and by 22% in 20 diffuser. The improvement in the pressure recovery coefficient was a result of the improved velocity profiles with reduced distortion and delayed separation. Jeyachandran et al. 10 have numerically studied flow through 4.5 and 6 conical diffusers with uniform and wake type velocity profiles at the inlet. The prandtl mixing length hypothesis is used to model the turbulence. The experimental results already available in literature are used for comparison. They found that the model is able to predict the flow through diffusers satisfactorily for a uniform velocity profile at inlet. Mahalakshmi et al. 11 have studied numerical predictions of wake type distortions at the inlet of conical diffusers. A central body is placed at the entrance of the diffuser to create the distortion. It is seen that the Cebeci-Smith model with the addition of wake model is able to predict the wake flows under adverse pressure gradient quite satisfactorily. Yongsen et al. 15 have carried out theoretical investigation on a 8 0 core angle diffuser with 4:1 area ratio. They have predicted the mean flow velocity and turbulence energy successfully using boundary fit

3 KARUNAKARAN & GANESAN: AXISYMMETRIC CONICAL DIFFUSER 213 coordinates approach. Singh et al. 16 have studied the effect of inlet swirl on the performance of wide-angles diffusers. Further, interesting studies have been carried out by Klein 17, Shuja and Habib 18, Ubertini and Desideri 19,20 on various forms of diffusers. Jain et al. 21 have carried out flow analysis of a can type combustor with diffusers. They have reported that when diffusers are attached to combustors the convection and radiate hear transfer plays a part in flow development and pressure recovery. Recently, Ko and Anand 22 have carried out convective radiative heat transfer analysis over a horizontal backward facing step a finite volume method. Further, Kumar and Eswaran 23 have studied the effect of radiation on flow in a conical diffuser. Thus, it is seen that there is considerable effect of the inlet conditions on the diffuser performance. Hence, this work is concerned with the experimental study of flow through diffuser with two types of inlet conditions. Experimental Procedure Experiments have been carried out in a low speed wind tunnel test facility. It consists of a settling chamber of 1 m 1 m 2 m size with six filters and a bell mouthed nozzle giving a low turbulence (1 % at 35 m/s) flow. Figure 1 shows the details of experimental set-up with diffuser model, which shows the inlet pipe of length 600 mm, diffuser section with inlet and exit diameter of 107 mm and 195 mm respectively with a wall thickness of 3 mm. The set-up also consists of an exit tail pipe of 500 mm length connecting the down stream section of the diffuser. Based on the axial velocity profile at the inlet of the test section the bulk mean velocity is found to be 31.5 m/s and 35 m/s respectively for the flow with and without distortion. On the surface of the diffuser 10 numbers of 8 mm diameter holes are drilled at the planes shown where the velocity and pressure measurements were to be made. Figure 2 shows clearly the various measuring stations for inserting the probe at the inlet, diffuser and exit tail pipe sections. Table 1 gives the nondimensional position (X/L) of the measuring locations with respect to the axial length of the diffuser section (L), taking the inlet of the diffuser as the reference location to measure the positive X values. Mean velocity measurement The measuring instrument used for measuring velocities at various stations is the five-hole probe with a spherical diameter of 5 mm. The spherical pressure probe employed in the present study is model type f / 2, Swiss made from Schiltknecht. The details of the probe are shown in Fig. 3. The sensing head is Table 1 Measurement point locations Station X/L A B C D E F G H I J Fig. 1 Photograph of the experimental set-up Fig. 2 Details of measuring stations in the geometry Fig. 3 Details of five-hole probe

4 214 INDIAN J. ENG. MATER. SCI., AUGUST 2009 cobra shaped to allow probe shaft rotation without altering the probe tip rotation. The data reduction includes a calibration chart (shown in Fig. 4), which was obtained from single calibration velocity. The spherical head is turned in its guide about its axis until the pressures on the apertures 4 and 5 are equal and the torsional angle β can be read off the dial on the fixed marker. The readings in the pressure transmitters p 1, p 2, p 3 and p 4 are noted down. The calibration curve is used to get the remaining properties such as the angle of flow α and speed of flow U, with all the components of velocity (Eqs (1) - (4)) with the pressure values measured from the above. The instrumentation system, in addition to five-hole probe, consists of five digital micro-manometers (Furness controls Ltd., U.K.) and a traversing mechanism (Dantec Dynamics, Denmark) with an ability to traverse in all the three directions. Measurements of axial, radial and azimuthal components of velocities are obtained at 10 axial locations. U 2 ( p p ) 2 4 = (1) ρ k 24 U = U cos β cosα (2) V = U sinα (3) W = U cosα sin β (4) where U, V and W are the axial, radial and tangential components of velocity U, k 24 is the constant obtained from calibration curve, p 1, p 2, p 3 and p 4 are the static pressures at respective holes and ρ is the density of air. Uncertainty analysis According to Chue 12, the five-hole spherical probe can be used in the fixed system over a pitch and yaw range of ± 60º with an accuracy upto ± 0.3 % for pitch angle, ± 1 % for velocity pressure and ± 1 % for stream static pressure. Uncertainties associated with the pressure probe measurements are based on data presented by Rhode et al. 13. The velocity measurements are affected typically by less than 5 % for Re p 400, corresponding to a local velocity greater than 2 m/s, where Re p is the Reynolds number based on probe tip diameter. Around 5% inaccuracy is expected for most of the measurements, increasing upto 10% in regions of low velocity below approximately 2 m/s because of the probe insensitivity to low dynamic pressure. Geometric details The perspex model consists of a 5-degree cone angle conical diffuser of length 500 mm followed by a cylindrical pipe of 500 mm length. The diffuser section is connected to the outlet of the wind tunnel via an inlet pipe of 600 mm length. The cylindrical bluff body with three numbers of struts is placed at 110 mm in front of the diffuser entrance section. The bluff body and struts are also made out of the same perspex material ensuring smooth surface without any roughness and indentation. Figure 5 shows the details of the bluff body, which is placed in the upstream section. Fig. 4 Calibration curves for five-hole pitot probe Fig. 5 Details of dimensions of bluff body

5 KARUNAKARAN & GANESAN: AXISYMMETRIC CONICAL DIFFUSER 215 Results and Discussion Flow regime The present study provides a complete set of information in the upstream, diffuser section and downstream of the 5 cone angle diffuser model. Experiments have been carried out with a Reynolds number of and respectively for flow with and without distortion. It is found from the measurements that the axial velocity profile is axisymmetric from wall to wall. Therefore, measurements are taken only from center to wall for the measuring stations in order to save time. Also it is observed that the value of the other two velocity components is considerably of lower in magnitude, hence, not presented here. Figure 6 shows the radial profiles of the mean velocities in the centerline of the diffuser. Station number A is located at an X/L distance of 0.82, where L is the axial length of the diffuser. It represents the velocity profile in the inlet pipe measured in front of the bluff body. The symbols (circular rings and dark dots) indicate the experimental results obtained for the case of flow with and without distortion. Figure 6 shows the flow fields plotted for nine stations, i.e., for 1 to 9 along the diffuser axis. As there is no significant change in the velocity profile at the last position (station-j), it is not presented and included in the discussion. The mean axial velocity profiles provide information about the distribution of fluid velocity in any given crosssection of the diffuser. In the region near the diffuser wall, the mean velocity is influenced by the presence of the wall and a boundary layer type velocity distortion develops. In the central region of the cross section, the presence of wake, shed by a central body ahead of the diffuser inlet will produce a velocity distribution, which is similar to that in a wake. If wake is not present, the development of the wall boundary layer alone will be reflected in the mean velocity profile. In order to know the type of mean velocity distribution in the flow approaching the diffuser inlet, measurements have been made just upstream of the diffuser inlet when no central body is present and at a location downstream of the central bodies when they are present. It is seen that in both the cases the profiles have a flat central portion combined with the typical turbulent wall boundary layer velocity distribution. Compared to the fully developed turbulent velocity profile in a smooth pipe, the approach velocity profile show in Fig. 6 (at station-a) has a large region of constant velocity combined with relatively a thin boundary layer due to wall. The ratio of the sectional average velocity to the maximum velocity for the profiles shown is of the order of 0.95, whereas for the one-seventh-power law velocity distribution in a smooth pipe, the corresponding value of the ratio works out to be In the same figure, typical mean velocity distributions measured at a station down stream of the diffuser entry, at station (B) at X/L = 0.076, are also shown for the flow configurations in the diffuser with the central bluff body and without any central body. The velocity profile without central body is more or less similar to the approach velocity profile at the station (A), having flat central region combined with the wall boundary layer distribution. In the case of the flow with central bluff body, the body wake has already traversed some distance in the approach duct and decayed to some extent before it reaches the station (B). Hence, the velocity profile for the flow with bluff body has a shallow wake type distribution in the central region together with the turbulent wall boundary layer distribution. The velocity profiles in the further down stream sections of diffuser are also shown in Fig. 6 from station (C to H). The general features seen in these stations are the non-uniform nature of the velocity distributions in the initial part of the diffusers and the progressively decreasing wake velocity defect as the flow traverses through the diffuser as observed by Chidambaram et al. 8 and Lakshminarasimhan 14. A region of nearly constant mean velocity in almost all the cross-sections distinctly separates the wall boundary layer region and the wake region. At station H and I, there is a sudden dip in the velocity profile for inlet distortion, which is unexpected. Repeated measurements were carried out to ascertain the accuracy and it is found that there is a dip. Probably it may be due to not so perfect joining of the diffuser exit with tail. Pipe. Hence, velocity values at these points may be taken with a caution in these two stations. It is noted that the wall boundary layer thickness at the exit section increases substantially to nearly twice the inlet value with the central body. These profiles are to be compared with the relatively flat profiles obtained for the plain conical diffusers without central body at these stations. The central wake almost decays beyond the section X/L= thus showing scarcely any different from the velocity

6 216 INDIAN J. ENG. MATER. SCI., AUGUST 2009 profiles without central body. The distance traversed by the wake of bluff body is about 4.4 times the radius of the diffuser inlet section. Performance characteristics of diffuser Fig. 6 Velocity profiles at different station with and without distortion

7 KARUNAKARAN & GANESAN: AXISYMMETRIC CONICAL DIFFUSER 217 The performance evaluation parameters considered in the present study includes the pressure recovery coefficient, effectiveness, head loss coefficient and the blockage factor. Figures 7 and 8 show the plot of variation of these performance parameters along the non-dimensional geometric dimension area ratio. Pressure recovery coefficient (C p ) The performance of any diffuser is dependent on its ability to recover the kinetic flow energy in the form of static pressure rise. The performance is normally Px Pi defined as, Cp =, where U is the mean 2 0.5ρU velocity at the diffuser inlet section and Pi,Px is the static pressure at the inlet and x location downstream of the diffuser inlet and ρ is density. The measured pressure recovery coefficient for the different stations is shown in Fig. 7a for the flow with and without distortion. The ideal flow pressure recovery coefficient (CPRI) is also represented in Fig.7a in order to give an idea as to what extent the actual pressure recovery is got affected by the flow fields in the adverse pressure gradient The measurement shows the well-established trend of pressure recovery in diffusers, initially rapid increase in the Cp values for relatively small area ratio (AR) followed by a more gradual rate of increase as the flow approaches the outlet. It shows clearly that the effect of inlet distortion is felt in the pressure recovery up to an area ratio value of In other words the effect of inlet distortion is carried away by the fluid for an X/L value of and further down stream in the flow the wake is decayed completely. Also it reveals the interesting feature that there is a slight improvement in the pressure recovery at an X/L of for the flow with inlet distortion. The improvement in the recovery may be attributed to better mixing because of the increased turbulence level in the central region of the diffuser as explained elsewhere 5-7. However, the recovery coefficient found to be in line with the case of flow without inlet distortion at the outlet of the diffuser. The decay of Fig. 7 Plots show the effect of inlet distortion on (a) recovery and (b) effectiveness Fig. 8 Effect of inlet distortion on (a) head loss coefficient and (b) blockage factor

8 218 INDIAN J. ENG. MATER. SCI., AUGUST 2009 the wake in the extreme down stream section of the diffuser could be the reason for the decline of improvement of the recovery. When bluff body is placed at the entrance of the diffuser the wake effect is felt throughout the diffuser section and there was considerable improvement in the recovery as found in the experiments of Lakshminarasimhan 14. This shows that there is no loss in the total pressure for a distorted velocity inlet in contradiction to the results as expected by the predictions of Dean and Senoo 1. Effectiveness (η) The effectiveness of the diffuser is given by the expression η = C PRI /C p. The ideal pressure recovery coefficient can be calculated by the equation, C PRI = 1- (1/A R ) 2, where A R is A x /A i. The diffuser effectiveness is plotted in relation to the area ratio for both the flow with and without inlet distortion as show in Fig. 7b. The measurements indicate that the η decrease with increasing area ratio approaching a constant value at higher values of A R. It also points out the slight fall in effectiveness of the diffuser in the station just down stream of the inlet distortion. The presence of wake in the core region has affected the actual pressure recovery in the station just down stream of the bluff body as show in Fig. 7a. This could be the reason attributed for decline in the effectiveness at that station. Head loss coefficient (ε) The loss coefficient is shown in Fig. 8a in relation to the area ratio for the different measuring stations for the flow through diffuser with and without distortion. The head loss coefficient is the difference in ideal static pressure recovery coefficient and the actual static pressure recovery coefficient (C PRI -C p ). The value of the loss coefficient first increases steeply in the initial part of the diffuser and the levels off to constant values as can be seen from the measurements shown in Fig. 8a. Blockage factor (B) As the measurements of mean velocity distribution have been carried out at various cross-sections of the diffusers, it is possible to calculate the blockage factor in relation to the area ratio and study its growth under the different flow situations. The blockage factor is calculated from the velocity distribution in any cross - section from the expression, B = 1-U av /U max, where U av, U max are the mass weighted average and maximum velocity at the station. Figure 8b shows the growth of the blockage factor for the flow with and without central body. In both the cases, starting from the inlet value of about 0.05, the value of B grows steadily in the diffuser as the thickness of the wall boundary layer increases along the length. The blockage factor starts to grow beyond A R value of 2. This is due to significant reduction in the average velocity because of the spreading of wake near the axis of the diffuser caused by the inlet distortion and the adverse pressure gradient. As explained earlier, the accelerating flow between the body and the inlet duct enters the diffuser and the wake of the body is formed under these conditions at the diffuser entry. The wake, after its formation, rapidly expands thus its contribution to the blockage factor decreases rapidly. This is shown by the slight fall of the blockage factor within short distance from the entry (A R = 2) due probably to the influence of the accelerating flow entering the diffuser. This effect continues for some distance before it is encountered by the diffuser pressure gradient. But the growth of the blockage factor with the central bluff body in the diffuser reveals a slightly different trend at area ratio, 3 to 3.5. The blockage factor starts to grow due high turbulent flow crossing over the axis and proceeding to the tail pipe as noted in Fig. 6 at station - H and I. Conclusions Detailed experimental investigations have been carried out in a model conical diffuser with and without inlet flow distortion. The following conclusions can be drawn from this study: The measurements reveal the growth and development of boundary layer as the flow moves downstream of the flow domain. Also the deceleration of the near wall flow and the core flow field acceleration is well measured. The wake region behind the bluff body and the effect of the inlet flow distortion on the flow field is well represented by the measurements. The diffuser performance parameters like pressure recovery and effectiveness are found to be influenced by the inlet distortion. References 1 Dean R C & SenooY, Trans ASME, J Basic Eng, 82 (1960) Cockrell D J & Markland E, J Royal Aeronaut Soc, 66 (1962) Tyler R A & Williamson R G, Proc Inst Mech Eng, 182 (1968) Rao D M, J Royal Aeronaut Soc, 75 (1971) Welsh M C, J Fluids Eng, 98 (1976)

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