Numerical study of internal flow field and flow passage improvement of an inlet particle separator

Abstract

By performing gas flow field numerical simulations for several inlet Reynolds numbers Re (from 2 × 10⁵ to 9 × 10⁵) and byflow ratios x (from 10% to 20%), the present study has proposed to improve the flow passage of an inlet particle separator. An adjacent objective of the study is to lower pressure losses of the inlet particle separator (IPS). No particle has been included in the gas flow for a k-epsilon turbulence model. The velocity distribution in different sections and the pressure coefficient C_p along the duct have been analyzed, which indicates that there exist important low-velocity regions and vortices in the separation area. Therefore, the profile of streamlines along the original passage has been considered. This profile illustrated a vacuum region in the same area. All investigations suggest that the separation area is the most critical one for fulfilling the objective on pressure losses limitation. Then the flow passage improvement method has focused on the separation area. An improved shape has been designed in order to suit smoothly to the streamlines in this region. Similar numerical studies as those for the original shape have been conducted on this improved shape, confirming some considerable enhancements compared with the original shape. The significant vortices which appear in the original shape reduce in amount and size. Besides, pressure losses are greatly decreased in both outlets (up to 30% for high Reynolds number) and the flow is uniform at the main outlet. Subsequent engineering surveys could rely on expressions obtained for C_p in both outlets which extend the pressure losses for a wide range of inlet Reynolds numbers. As a result, the numerical calculations demonstrate that the flow passage improvement method applied in this study has succeeded in designing a shape which enhances the flow behavior.

Keywords

streamlines / pressure losses / flow passage improvement / inlet particle separator (IPS)

Introduction

Ingestion of particles is a great problem facing the aeronautics industry. The intake of particles occurs usually during flights in dusty environments, e.g. when flying above deserts or when taking off and landings in various fields areas [1,2], and especially when flying through volcanic ash clouds.

The will to fix particle ingestion is comprehensible for technical and economical reasons. Particles ingested provoked problems about performances and life expectancy of engines such as surface erosion, and corrosion [3,4], or cooling system failures [5,6]. The most exploited devices to deal with this problem are inertial type inlet particle separators (IPS), which are often considered as the best applicable systems, and have proved their efficiency for reducing the amount of particles ingested. Being widely used in the aero propulsion engines industry, the IPSs are often placed upstream of the engine inlet. The major kind of IPS to deal with air-intake to gas turbine engines in the aeronautics are particle deflectors. The IPS models chosen in this study is a particle deflector device initially designed for helicopters [7-10], but it is assumed that this device can also be adapted and implemented in other aircrafts engines.

Several studies [11-14] have been conducted for establishing a computational fluid dynamics (CFD) method which will lead to an optimized and proper shape of an IPS under constraints representing diverse flight conditions. Commonly those constraints have a sufficient high efficiency value and geometrical dimensions. Besides, those methods have an adjacent objective to restrict pressure losses between the inlet and the exit of the IPS. The implementation of those procedures is complicated and demands considerable computer resources, computation time and competent personals. Given those requirements, this study proposes to focus on a simplest process called flow passage improvement method for improving the shape of an IPS. The method is based on the profile of the streamlines along the passage of the duct and the numerical study of the internal flow field. The main objective of the method is to lower pressure losses of the IPS. Objectively this method will not lead to the optimal shape of the IPS, but it allows fixing a sketch of the final shape.

In later studies, particles with diameters between 5 µm and 100 µm are investigated. For this range of particles, it is assumed that the mass of the particles are insignificant. Also the volume fraction of the particles is particularly small given that they are extremely dilute in the flow. Considering the large particle-to-air density ratio, the virtual mass and Basset force can be omitted, too. Therefore inertial effects are supposed to be negligible. Numerical simulations with particles injected in the flow have proved this assumption (see Section 3.1). In another word, the main flow path (so the streamlines) can be presumed not to be perturbed by particles evolving in the flow [15-17]. Then the gas flow field is simulated numerically for the IPS.

Shape design and computational methodology

Even though this study just focuses on streamlines of the gas flow in the IPS without paying attention to particles effects, the original three-dimensional duct used for modeling the shape has been designed following the main considerations detailed previously in some US Patents documents about IPS [18,19]. Those patents are all based on the same technical principles but have shown some improvements throughout the year. In those references [18,19], an annular shaped model was composed of one inlet, and two outlets. There is one inner passage where the flow mainly goes through, and one outer passage to bypass particles. Wall shapes were defined such that particles will mainly be forced to go in the outer passage by deflections on inner and outer walls. The inner wall form is generally composed of concave parabolic curves [20] whereas the outer wall form is composed of convex parabolic curves [21] such that they led to a throat. The aim of this throat is to accelerate the flow in the passageway between the inner and outer walls in a specific axial direction in order to facilitate deflections.

The original shape model defined for the study have smoother wall curves than the IPS models presented above. It is explained by the will to lower pressure losses. The less the flow bounced on the walls, the less losses occurred in the passage. The position of the splitter also differs since its location is higher than the inner part of the throat. Therefore the flow should stream more smoothly and then losses should be limited. Moreover in order to simplify the future manufacturing of the model defined in this study, features set up for its design are a combination of straight lines and circles. The shape of this model is described in Fig. 1 and names of boundaries used in this paper are drawn.

In Fig. 1 the inlet area is located at l/L = -0.20, and the throat area (the narrowest area at the intersection of convergent and divergent parts of the IPS) at l/L = 0.25. The valuable part of the IPS is from positions l/L = 0 to l/L = 1 for the main outlet and from l/L = 0 to l/L = 0.50 for the bypass outlet. The part of the duct from positions [-0.20, 0], and the part in the bypass outlet after position l/L = 0.50 are implemented to improve the results obtained by CFD simulations. The angle which concerns the “opening” of the IPS has restricted the design of the duct. It has to be taken under 10° and as near as possible to 8°. The value of the zone ratio Z defined in Eq. (1) for position l/L = 0.50 is equal to 90%.

(1)z={\displaystyle \frac{A_{\mathrm{b}\mathrm{y}\mathrm{p}\mathrm{a}\mathrm{s}\mathrm{s},\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{t}}}{A_{\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n},\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{t}}}}.

Numerical calculations are done with the CFD commercial code CFX<FootNote>

ANSYS, Inc., ANSYS CFX Release 11.0, 2006, (ANSYS Inc.: New Hampshire)

</FootNote> under the following specifications. The flow is defined as compressible, in steady-state, and set up as an air ideal gas as in Musgrove et al. [22]. Advection schemes are second order accurate. The reference pressure is fixed to p = 101.325 kPa, and the environment temperature to T = 293.15 K. The turbulence model choice is turned to the k-ϵ model [23] with scalable functions for turbulence on the walls that improve robustness and accuracy when the near-wall mesh is fine. In CFX, the wall-function approach is an extension of the method of Launder and Spalding [24] (logarithmic laws). The boundary conditions at the inlet and both outlet boundaries are defined as constant mass flow rates \dot{m} (kg/s) on the sections. To study the influence of the inlet velocity on the flow, the inlet mass flow rate simulated four Reynolds number Re values is as shown in Eq. (2): values: 202667, 506667, 770133, and 912000.

(2)\mathit{R}{\mathit{e}}_{\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}={\displaystyle \frac{V_{\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}{D}_{\mathrm{H},\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}}{\nu }}.

This study focuses on proportional relations between mass flow rates of both outlets. Therefore the byflow ratio x is set: it represents the percentage of the mass flow rate of the bypass outlet compared to the mass flow rate of the main outlet (see Eq. (3) for its definition). Five values of x are implemented for the simulations: 10%, 14%, 16%, 17%, and 20%. Walls are all classified as smooth and no-slip walls.

(3)z={\displaystyle \frac{{\stackrel{.}{m}}_{\mathrm{b}\mathrm{y}\mathrm{p}\mathrm{a}\mathrm{s}\mathrm{s},\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{t}}}{{\stackrel{.}{m}}_{\mathrm{m}\mathrm{a}\mathrm{i}\mathrm{n},\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{l}\mathrm{e}\mathrm{t}}}}.

The mesh is composed of tetrahedral mesh elements, with some pyramidal and wedge elements. A boundary layer is set with a first layer thickness of 0.1 mm and a total of 13 layers near the boundary intersection of the grid and every wall. This mesh number is 2.5 × 10⁶. For all computed cases, the convergence history of calculations indicates small residuals-the residuals decrease by nearly five orders of magnitude. Moreover the convergence criteria are reached, every calculation respects the limitation on y⁺ provided by the turbulence model<FootNote>

ANSYS CFX User’s Guide, ANSYS, Inc., Version 11.0, 2006, (ANSYS, Inc.: New Hampshire)

</FootNote>.

Several figures are drawn and discussed for making the comparison between the two shapes models. Total pressure values are analyzed in different sections in order to get pressure losses Δp_t and pressure coefficient C_p. This last coefficient is calculated along the duct by Eq. (4), and its evolution modeled by expressions depending on the Reynolds number Re.

(4)C_p=|{\displaystyle \frac{p_{\mathrm{t},\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}-p_{\mathrm{t},\mathrm{s}ec\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}}}{p_{\mathrm{t},\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}}}|.

In Eq. (4), p_t,inlet and p_t,section are respectively the total pressure values at the inlet and the section considered. Total pressures have to be used since the entropy rise depends on total pressure loss between the inlet and the outlet, which itself affects the efficiency of the IPS.

Results and interpretation of the original shape model of the IPS

Validity of the model

Experiments are made to confirm the quality of the numerical calculations. Particles of cornstarch are injected in an IPS at a corresponding inlet Reynolds number between Re = 250000 and Re = 400000, and for several byflow ratios x. The average diameter of these particles is 20µm, and the density is approximately 670 kg/m³. The volume fraction of the particles is slightly below 0.001 and the equivalent Stokes number St (see definition in Eq. (5)) of the particles ranges from 0.17 to 0.27.

(5)St={\displaystyle \frac{{\rho }_p{d}_p^{\mathrm{2}}{V}_{\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}}{\mathrm{18}\mu D_{\mathrm{H},\mathrm{i}\mathrm{n}\mathrm{l}\mathrm{e}\mathrm{t}}}}.

Tang et al. [25], Yang et al. [26], and Aggarwal et al. [27] have reported that for such a value of St lower than unity, particles adjust to the flow field rapidly and will follow it. Therefore they affect lightly the flow itself, and their influence on the gas flow can be assumed to be negligible. Thus particles can be used as trackers to visualize the streamlines, and then to compare the experimental and simulation results. Particles are tracked using a high-speed CCD camera (FASTCAM-APX 120 KC, Photron) with a shutter speed of 1/2000 s. The shape of this experimental IPS are designed and meshed with the same process for the shape models used in this report. Then a numerical simulation is set with the same boundary conditions for the experimental case of the byflow ratio x = 14.5%, and the inlet Reynolds number Re = 250000. Figure 2(a) represents the normalized vectors of the dimensionless velocity in a longitudinal section of the IPS, near the splitter at an angle θ = 270° (defined in Fig. 3(a)). Zooms of pictures in the splitter area extracted from the experiments cited above are illustrated in Fig. 2(b) to Fig. 2(e), showing great similarity. Particularly, the location of the vortex above the splitter at the entry of the bypass outlet is almost identical. For the simulation, the dimensionless velocity V/V_inlet at the exterior of the vortex amounts to V/V_inlet = 0.35; whereas the dimensionless width of the vortex is equal to w/L = 0.040 and its dimensionless height to h/L = 0.018. For the equivalent experiment, these values are respectively equal to V/V_inlet = 0.31, w/L = 0.036, and h/L = 0.016. Same conclusions can be made for the other experiments. Other pictures extracted from the experiments show similar vortices in the separation area. Vortices always appear at the same location whatever the inlet Reynolds number Re and the byflow ratio x at stake. Therefore the previous figures are nearly of the same order of magnitude for the calculation and experiments results; and the presence of vortices is verified continuously through the experiments. Thus, it is possible to deduce the validity of the computation models used in this report compared with the experiments which have been analyzed.

Reynolds number characterization

The preponderant factor in the expression of Re is the hydraulic diameter D_H shown by comparing orders of magnitude of terms which composed Re. The evolutions of Re and D_H along the duct are due to similar reason. To analyze the flow, a better method is to consider in terms of velocity. The evolution of the velocity mean values in transverse sections along the duct is investigated. In the first part of the IPS [-0.20, 0], the velocity can be approximated as a constant. In the convergent part of the duct, the velocity increases up to the throat at l/L = 0.25. Finally, depending on the outlet where the flow goes through, the velocity increases (main outlet) or decreases (bypass outlet).

Then the dimensionless velocity (V/V_inlet) is analyzed in different sections in the bypass outlet of the IPS to verify the quality of its distribution. The magnitude of this dimensionless velocity in transverse sections in the region [0.38, 0.50] is plotted as well as normalized vectors of the dimensionless velocity in those sections.

A representation of the transverse section of the bypass outlet at l/L = 0.50 is demonstrated in Fig. 3(a). There are two low-velocity regions as illustrated in Fig. 3(a) for θ = 90° and θ = 270°. The two low-velocity regions gradually increase and develop from the splitter at l/L = 0.38-where they are insignificant, to the outlet at l/L = 0.50-where they cannot be neglected. Also the dimensionless velocity vectors are plotted for different angles θ in the longitudinal direction of the IPS (see Fig. 3(b) to Fig. 3(d)) at the entry of the bypass outlet. The plots of Fig. 3 are relevant to each other and give complementary information. There are two low-velocity regions where vortices appeared: around θ = 90°, and especially around θ = 270° where an important vortex is observed. The flow could almost be considered as an unfavorable reverse flow for θ = 270°. For the other angle θ, vortices exist but are substantially smaller (as proved by θ = 0° plot) than those encountered for the two previous angle values. Whatever the byflow ratio x value, vortices are always present for the same angles θ = 90° and θ = 270°. Besides, the higher the inlet Reynolds number Re is, the more vortices are there near those locations. And the higher the byflow ratio x is, the better the circular symmetry of velocity is in transverse sections and the more the number of vortices decreases. Given the size of bigger vortices, those vortices should influence greatly the amount of pressure losses and potentially the separation rate of particles contained in the fluid.

Here the flow cannot be studied only with one two-dimensional representation, even though the duct is axisymmetric, since the distribution of the velocity depends on θ, which explains the choice of several angles of θ as shown in Fig. 3. The reverse flow could be interpreted as the consequence of a flow separation behavior near the splitter. This separation can be caused by low occupation of the whole section by the gas in the bypass outlet. Compared with the height of the bypass outlet, the height of the low velocity zones in longitudinal sections is sizeable (as proved by Fig. 3). In addition, partitions of the flow happen in a short distance. Then conditions could be fulfilled to undergo stalls phenomena. Those stalls happen around the horizontal longitudinal section of the duct, and are accompanied with big scale vortices which led to the reverse flow. Such a reverse flow for some angles of θ in the separation area has to be avoided. It implies some problems for turbo-machinery. For instance it can lead to mechanical destructions of the engine and deteriorate the gas flow properties.

Pressure coefficient

After the study of macroscopic parameters, the microscopic scale parameter C_p is set up to discuss the evolution of pressure losses Δp_t. Since C_p and Δp_t are proportional, their evolutions are similar. Non-dimensional parameter C_p is chosen to represent pressure losses. Figure 4 displays the pressure coefficient C_p in the main outlet at position l/L = 0.50. All inlet Reynolds numbers and byflow ratios x cases are plotted. Those figures prove that x = 16% is of great importance. First, this value is widely accepted in the industry. Secondly as curve of x = 16% is the nearest from the fitted curve representing the evolution of the mean values of C_p (and then Δp_t) for each byflow ratio cases, x = 16% characterizes well the mean microscopic behavior in the main outlet of all cases for Reynolds number Re in the range [2 × 10⁵; 9 × 10⁵]. The more the byflow ratio x increases, the more the C_p decreases. It can be put in relation to the improvement on the velocity distribution in the bypass outlet discussed above following x.

The same conclusions can be drawn for C_p in the bypass outlet (see Fig. 5) about the behavior following the byflow ratio x. The C_p value in this outlet is important in order to proportion the power of devices as fans and collectors used for recovering the particles.

The evolution of C_p along the duct, from the inlet position (l/L = -0.20) to the final position (l/L = 0.50), was considered. The location where the main amount of pressure losses takes place can then be deduced. This critical place is situated between the throat (l/L = 0.25) and the separation area (l/L = 0.38). This location is independent of the values taken by x and Re. The evolution of C_p can be divided into three parts. The first part starts from positions l/L = -0.20 to l/L = 0.34, and can be considered as a linear relation between parameters. The second part is from positions l/L = 0.34 to l/L = 0.38. The biggest growth occurs in this part: approximately 50% of the overall increase takes effect there. This is definitely the critical area in terms of pressure losses as explained previously. Finally the third and last part, from positions l/L = 0.38 to l/L = 0.50, represents the two outlets. C_p keeps on increasing slightly in the bypass outlet and sharply in the main one.

Figure 6 shows the intersection of the curves for C_p in the main and bypass outlets for x = 16% respectively. This intersection is realized for an inlet Reynolds number of Re = 641729 and for C_p = 6.22 × 10^-3. This point can be named inversion point I₁ because there is an inversion of the outlet which has the biggest value of the parameter considered. That is to say that before Re = 641729, C_p (and pressure losses Δp_t) is lower in the main outlet than in the bypass outlet; and inversely after Re = 641729. This means, therefore, that the two parameters increase faster with the inlet Reynolds number in the main outlet than in the bypass outlet. Considering all values of x, inversion points are comprised in a small interval (between Re = 640000 and Re = 650000), and C_p (and Δp_t) values keep decreasing with an increase in x.

Modification of the shape of the IPS: improved shape model

The results of the original shape model show something critical in the flow behavior. The amount of pressure losses could be improved because existence of vortices in the bypass outlet is proved. As the objective is to lower pressure losses it seems to be important to design a shape which will lower the number and the size of vortices. The less the number of vortices, the less the losses of pressure. The method implemented consists in holding modifications on the original shape model of the IPS by analyzing streamlines along the duct, and by interpreting the results of the original shape model calculations. The plots of streamlines in longitudinal section for all inlet Reynolds number and byflow ratios are used. Figures 7(a)–(b) show a combination of plots of those streamlines on the same value (by superposing all plots via a transparency method).

It is then evident, by observing Fig. 6(a), that there is a vacuum in the bypass outlet near the upper wall in the separation area. For all the cases taken into account, no streamline goes through this location. Moreover this vacuum corresponds to the location of small vortices seen previously. It seems highly likely to reduce the phenomena of vortices appearanced in this area, if the design of the upper line of the duct in this region is changed. Minimizing the vortices influence in the bypass outlet is of great importance for the IPS because the movement of micro-particles inside the duct is determined by the behavior of the flow. Since the initial function of an IPS is to isolate particles from the flow, the particle separation efficiency of the IPS is affected by the vortices. The shape has to be adjusted such that it suits the outermost line of the whole streamlines. Then it should be better in term of pressure losses. The pressure losses mainly occur after the throat (l/L = 0.25) and before the splitter (l/L = 0.38). Furthermore, the outermost line of the IPS has to be modified smoothly from the position l/L = 0.25-which coincides with the throat position-up to the end of the bypass outlet (at position l/L = 0.50).

The modifications are designed with the help of several circles tangent to each other, and tangent to the lines at both extremities. Comparatively with the original shape model in this region, the radiuses of curvatures of those circles are smaller for concave curve lines, and bigger for convex curve lines. Changes have been implemented gradually on the outermost line of the original shape model until reach the present improved shape model. The shape model fulfilled the expectations when the streamlines fit perfectly to the outermost line of the IPS. The new shape model then has a smaller area in the bypass outlet. Figure 7(b) presents the streamlines of the improved shape model. No more stall of these streamlines are now observed on the outermost line of the IPS, and the streamlines match with the outermost line. The more visible changes with the original shape model occur where the vacuum region is located (see Fig. 7(b) for comparing the two shape models). As anywhere else on the walls of the original shape model streamlines fitted with the walls, no other modifications are done. Therefore all the main dimensions of the duct are the same as those for the original shape model excepted for the line of the exterior wall in positions [0.25, 0.50] near the separation area.

Results of the improved shape model of the IPS

The same analysis is conducted for the improved shape model. By applying for this improved shape model the same specifications for the original shape model, the convergence history and curves of y⁺ lead to the pertinence of the calculations. For this improved shape model, the convergence history occurs faster than for the original shape model (the convergence even appears four times more quickly), and the upper limit of y⁺ is still respected. This part focuses on the improvements obtained by the improved shape model of the IPS compared with the original shape model to prove the benefits of the improved shape model. Generally each parameter and behavior described in this paper indicates progress for the improved shape model.

Reynolds number characterization

As the shape of the IPS is slightly modified, the evolution of the Reynolds number along the duct is similar to that of the original shape model. Nevertheless the values are lower for the improved shape model. For instance, the dimensionless maximum value is approximately V/V_inlet = 1.78, whereas for the original shape model it is approximately V/V_inlet = 1.91. The same conclusions for the original shape model can be drawn on the velocity evolution.

An observation of Figs. 8(a)–(b) leads to the conclusion that the two low-velocity main regions where vortices appear in the original shape model (around θ = 90°, and θ = 270°) almost completely disappear. For this model, the velocity is much better distributed over each section considered, particularly in the bypass outlet since practically no vortex is visible. Also, whatever the angle θ considered, the behavior of the flow can be judged as identical in the whole longitudinal and transverse sections. The velocity increases gradually in the radial direction. However, some small vortices are still located in the bypass outlet near the wall exterior, but they are insignificant compared to the vortices which appeare in the original shape model. In addition, no reverse flow is observed this time. The new shape show great improvement, and should then lead to a drop in pressure losses, which is the aim of this work. This is related to the disappearance of the most important vortices in the bypass outlet. This effect is also preponderant for improvements in the main outlet because it affects the flow upstream and so have repercussions on pressure and velocity before the separation area. The height of transverse sections in the bypass outlet has been reduced. Therefore the distribution of the velocity in these sections has been improved (since the heights of low velocity regions are smaller than those for the original shape model), and then no more stall happens.

Figure 9 is a contour figure of the Mach number (Ma) field of the improved shape model. Its maximum value indicates that the flow in this case is clearly compressible because Ma>0.3 once the flow enters the main outlet. By definition, the high Mach number areas are equivalent to the high velocity areas. Those areas are located at the innermost side of the splitter and at the middle of the divergent nozzle of the main outlet. This phenomenon is caused by the confluence of the flows situated at the outermost and innermost of the duct in the splitter area. Then convergent flows mixed together and contracted on the splitter surface. Figure 9 allows affirming the flow uniformity at the main outlet. It has been addressed thanks to the design of the most downstream part of interior and separator walls (see Fig. 1). As far as the separator wall is concerned, it has been designed following small and soft variations of its curvature such that the boundary layer of the flow field will not separate from it. The condition on the interior wall is to avoid causing too much turbulence at the joining of the main flow. Therefore the wall at this location should not provoke sharp stalls of the boundary layer before the joining. This means that the slope of the “interior cone” should not stay constant along the symmetric axis of the IPS, but needs to tend smoothly and asymptotically to this axis in the case that the chord of the interior wall keeps going.

The improvements on the flow and particularly on the reverse flow behavior are essential. They enhances the gas flow behavior (compared to the original shape model) before it enters the engine, and decreases the risk of stalls.

Pressure coefficient

The C_p values in the two outlets (at l/L = 0.50) confirm the drop in pressure losses supposed above. The values are lower for the improved shape model than for the original shape model as plotted in Figs. 10-11. Figures 10-11 also illustrate the importance of byflow ratio value x = 16% for the same reasons as those for the original shape model. The byflow ratio value x = 16% describes well the mean comportment of all cases for inlet Reynolds number in the range [2 × 10⁵, 9 × 10⁵]. This value is then used as well for presenting the results. Variation of those parameters following x and Re are unchanged.

An estimate expression which approximates the value of C_p coefficient in the main outlet is proposed for the byflow ratio x = 16%. This expression is based on the polynomials of degree 2 in the Reynolds number Re obtained by the least square method. It is given by Eq. (6) for a correlation coefficient of 0.948.

(6)C_{p,main}=\mathrm{3.053}\times {\mathrm{10}}^{-\mathrm{14}}\mathit{R}{\mathit{e}}^{\mathrm{2}}-\mathrm{1.553}\times {\mathrm{10}}^{-\mathrm{8}}\mathit{R}\mathit{e}+\mathrm{22.717}\times {\mathrm{10}}^{-\mathrm{4}}.

For the bypass outlet, the least square method provides the expression noted in Eq. (7). Since the evolution of the C_p in this outlet seems to be almost linear, the correlation coefficient is better than in the main outlet and equals 0.998. The modeling of those expressions could be helpful for further engineering applications. The power necessary for sucking the particles is lower than that for the original shape model and thus the dimension of the devices conceived for too. This equipment will then be more compact and more convenient to install.

(7)C_{p,bypass}=\mathrm{1.972}\times {\mathrm{10}}^{-\mathrm{15}}\mathit{R}{\mathit{e}}^{\mathrm{2}}+\mathrm{8.616}\times {\mathrm{10}}^{-\mathrm{9}}\mathit{R}\mathit{e}-\mathrm{11.442}\times {\mathrm{10}}^{-\mathrm{4}}.

Table 1 resumes the progress made in term of C_p. For instance for x = 16% and Re = 770 133, the parameters of the improved shape model are reduced by approximately 25%. The critical place for the C_p evolution along the IPS is as before situated just after the throat and before the splitter. This evolution can be partitioned into the same three different parts as for the original shape model.

The more the inlet Reynolds number increases the more significant the improvement is. For example for the case Re = 912000 and x = 16%, pressure loss value at the end of the main outlet passes from C_p = 2.41 × 10^-2 (C_p = 1.22 × 10^-2 in the bypass outlet) for the original shape model to C_p = 1.37 × 10^-2 (C_p = 8.26 × 10^-3 in the bypass outlet) for the improved shape model.

Table 2 confirms in term of vorticity (defined as the curl of the velocity) decrease in the amount of vortices. For the minimum and the maximum values of the vorticity in the separation area, where the vortices appear, a non negligible reduction of vorticity exists. As for C_p, the bigger the inlet Reynolds number, the bigger this diminution.

For a byflow ratio x = 16%, inversion point I₂ (visible on Fig. 6) occurs for a bigger Reynolds number (velocity) and for a smaller value of C_p (or Δp_t) than for I₁. It appears for an inlet Reynolds number of Re = 664 463 and respectively for C_p = 5.47 × 10^-3 (and Δp_t = 603 Pa). Conclusion of the original shape model is always verified: both parameters increase faster with the inlet velocity in the main outlet than in the bypass outlet. The interval which contains inversion points is larger than that for the original shape model (between Re = 610000 and Re = 670000). But values of C_p and Δp_t are less dispersed and for every case smaller. It proves a general improvement for the behavior of the IPS.

The improved shape model objective to lower pressure losses compared with the original shape model has been realized. The method employed in this study proves its success, and could then be applied successively up to get a shape which satisfies all criterions.

Conclusion

The method illustrated in this paper for reducing pressure losses in an IPS has been successful. The first part of the study leads to an examination of the internal flow field of the original shape model for suggesting the way to enhance the flow passage by the flow passage improvement method. The analysis of the profile of streamlines, the velocity distribution and the pressure losses along the duct for the original passage have given the design modifications to apply in the flow passage improvement method by CFD calculations for several inlet Reynolds numbers Re and byflow ratios x. Then the flow passage improvement method has been implemented and similar numerical study conducted for the improved shape model compared with the original shape model.

The flow passage improvement method makes some considerable enhancements on the improved shape model compared with the original shape model. The improved shape has been designed such that it fits smoothly to its streamlines. Those enhancements are clear about the pressure losses which have sharply decreased with the improved shape model in both outlets (diminution up to 30% for high Reynolds number). Additionally, the velocity distribution in the bypass outlet of the IPS has been improved by reducing the amount and size of vortices. Those vortices can be considered as insignificant in the separation area for the improved shape model. Expressions on C_p have been obtained. They allow extending the pressure losses results obtained by the calculations for a wide range of inlet Reynolds numbers which can be useful for subsequent engineering surveys. It appears that the behavior of the IPS is opposite depending on the evolution of x or Re.

During the development of this study, some general rules about the design of an IPS have been underlined, and are written as guidance for further studies. The splitter should normally be located such that particles cannot directly enter the main outlet in a way the compressor blades are more efficiently protected (hidden by the throat). However simulations show that it implies great flow losses and this design should then be avoided. It could be replaced by an upper location of this splitter as for the IPS designed in this study. Besides, the shape of the bypass outlet in the separation area should be slightly convergent-divergent as proved its efficiency for decreasing flow loss and vortex appearance compared with the simpler shape of the original shape model. The improved shape model seems to offer good flow conditions such that micro-particles mixed in a gas flow are well separated by this IPS. Since micro-particles mass are considered as negligible, it is then possible to assume that these particles do not modify the behavior of the flow inside the duct. Nevertheless, a further study is to analyze the efficiency of the separation of particles by using the original and improved shape models of the IPS designed in this work.

Notation

References

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