Effects of casing angle on the performance of parallel hub axial annular diffuser

: In this paper, the effects of non-swirling and swirling flow on the performance of parallel hub axial annular diffuser has been investigated. The study was conducted on a fully developed swirling flow and non-swirling flow to predict the separation of the flow from the wall. Three different annular diffusers were used with casing wall angles of 3 ° , 6 ° , and 9 ° . Furthermore, various swirl angles (0 – 25 ° ) at the inlet of diffusers have been investigated to analyze the performance across the length. It was found that parallel hub axial annular diffuser performance increases up to a certain length as the inlet swirl angle increases. However, the performance also improves as the diffuser area ratio (AR) increases. The performance is evaluated based on the static pressure recovery coef ﬁ cient (C p ) and the total pressure loss coef ﬁ cient (C TL ). The highest possible pressure recovery is achieved by the 12 ° swirl angle with a casing angle of 6 ° .


Introduction
Annular diffusers are extensively used in engineering applications such as outlet devices in case of the pump, turbines located in downstream turbomachinery, and in other numeral applications. In aircraft applications, an annular diffuser commonly operates at the downside of the compressor. The annular diffuser operates in the presence of swirl flow in turbomachinery. The swirl flow is generated by guide vanes located at the inlet and by some other components such as strut and by revolving of the central shaft passing through the diffuser and the compressor. The improvement in the overall performance of the system is due to a change in flow velocity caused by the swirl effect [1][2]. Swirling flow through diffuser was investigated by many researchers to analyze the behavior of the flow. Singh and Arora [3] carried out the work on annular diffuser having cone angle 20°, and AR varying between 2 and 4. The results show that maximum performance was achieved with swirl flow on the AR 2. Johnston [4] worked on annular diffusers having an AR of 3.2 and divergence angle varying from 6.5°to 15°. The performance of diffusers decreases as the divergence angle increases. Reneau et al. [5] performed the work on a series of two-dimensional diffusers and found that 6°≤ 2θ ≤ 8°gave the highest pressure recovery at a constant area ratio (AR). The efficiency of diffusers decreases as the divergence angle increases. Sovran and Klomp [6] studied more than one hundred geometries with conically central diverging center bodies having a radius ratio of 0.5-0.70. The test was conducted on the thin boundary layer fluid flow with free discharge and it was observed that the diffuser effectiveness decreases as the blockage increases for two dimensional flow. Stevens [7]; Adenubi [8] reported that there was a boost of 10-12% in the pressure recovery results when the turbulence intensity in annular diffuser increases from 4 to 10%. Critically distorted asymmetric inlet velocity profiles produce a severe drop in pressure recovery. Stevens and Fry [9] worked on two optimum straight-walled annular diffusers. One diffuser had a uniform diameter center body, the other had an expanding diameter center body (divergence angle 40°). Measurements of the pressure recovery, loss of total pressure, velocity profile in terms of boundary layer growth, and turbulence level were taken. Coladipietro et al. [10] reported that in the short diffusers, the variation of pressure recovery with blockage was similar to the channel and conical diffusers. The findings show that pressure recovery decreases with increasing blockage. Kumar and Kumar [11] concluded the swirling flow on the subsonic turbulence in the diverging equal hub and casing boundaries of annular diffusers. An inlet swirl reduces the flow separation that occurs at the casing of a stalled diffuser. Further, a large inlet swirl may result in the removal of the stall from the casing to the hub.
Singh et al. [12]; Singh et al. [13] showed the improvement in the performance of annular diffuser by using swirl flow in their experimental data. It is found that flow separation occurs on the hub wall and diminishes the performance beyond the swirl angle 30°. Mohan et al. [14] examined three annular diffusers with AR 3 and a half cone angles of 12.5°, 15°, and 17.5°. In each of the diffusers, the 6-8 level of swirl has been imparted at the inlet. It was deduced that the inlet swirls up to a particular level to improve the pressure recoveries but after that has a detrimental effect. Maximum pressure recoveries obtained were 72, 69, and 66% for the 12.5°, 15°, and 17.5°cases, respectively. Ubertini and Desideri [15]; Feldcamp and Birk [16] analyzed the performance of annular diffuser experimentally with and without strut. It was observed that performance improves with strut for the stalled diffuser. In the no swirl condition, there is a small effect of total pressure loss with the presence of strut. The pressure recovery assisted by the strut with an increase in swirl angle by 20°.
Literature shows that in addition to dynamic parameters such as velocity profile at inlet, inlet Reynolds number, and swirl flow at the inlet the performance of the axial annular diffuser also depends on the geometric parameters such as length L, AR, hub wall angle, and casing wall angle. The present analysis has been conducted for a constant axial length (L = 33.76 cm) with casing wall angles (3°, 6°, 9°) and (AR = 1.67, 2.48, 3.44) for the parallel hub axial annular diffuser. The performance characteristics of the diffuser have been evaluated based on non-swirling flow (0°) and swirl flow (7.5°, 12°, 17°, 25°) at the inlet. The computational study has been carried out on three different two-dimensional axisymmetric diffusers. The velocity profile obtained from the experiment was introduced in ANSYS Fluent with dynamic parameters in different turbulence models for swirling and non-swirling flow. The turbulence model, which is prognosticating the result more closely with the experimental results, was chosen for further investigation. The geometrical parameters of the annular diffuser are shown in Table 1 and Figure 1.

Experiment test rig
The experimental test rig consists of a centrifugal blower, a conical diverging section, a settling chamber, a swirl plate, an annulus cross-sectional area, and an annular diffuser as shown in Figure 2. The centrifugal blower delivers air at a flow rate of 1.5 m 3 /s and at a pressure equal to 0.1 bar. The air drawn from the ambiance is delivered to the conical diverging cross-sectional area which is then passed to the settling chamber having a honeycomb cross-section and very fine mesh screen. A flexible coupling of heavy fabric placed between the settling chamber and the blower avoids the vibration from reaching the blower to the settling chamber. The settling chamber consists of multiple folds of screen for decreasing the turbulence level, and for damping the flow fluctuations. The uniform flow enters into a constant area annular pipe from the smooth converging cross-section. A swirl plate with 12 vanes is installed at the entry of the annular passage to achieve the desired swirl level. The swirl plate is mounted at the upstream of the test diffuser to avoid the vane wake entry into the diffuser and also for the recovery of pressure, which is lost across the plate. The casing wall of the test diffuser is manufactured from Perspex. There are number of static pressure taps on the casing wall and hub wall along the length of the test diffuser for the measurement of static pressure using manometers. The longitudinal and swirl velocities are measured with a cobra probe. The null technique is used along the different axial locations in the test diffuser. The cobra probe yaw angle is set to zero by aligning with the incoming flow in this technique. The calibration range associated with the cobra probe is to measure the velocity within ±55°. The uncertainty of the manometer for measurement of the static pressure is ±1.5 mm of water, and the total pressure is ±1 mm of water.

Computational domain and boundary condition
The axisymmetric two-dimensional geometry of the annular diffuser has been modeled in the ANSYS workbench with proper dimensions, as shown in Figure 3. A mapped meshing scheme has been used on the computational domain with quadrilateral elements for all the cases. The mesh quality is controlled by maintaining the aspect ratio (less than 50) and skewness in the geometry. The distance of the first element fromthe wall is0.03 mm as per y + <1. Theboundary condition fed at the inlet in ANSYS Fluent is the velocity profile obtained from the experimental set up with a 3% turbulence level in the turbulence specification and the hydraulic diameter (h d ) value is as per the inlet geometry of diffuser. The boundary conditions are normal pressure, 3% level of turbulence, and hydraulic diameter (h d ) at the diffuser outlet. For better accuracy of the results, the 2nd order upwind scheme was used to control the solution for momentum, swirl velocity, turbulent kinetic energy (k), and turbulent dissipation rate (ω). The residuals convergence criterion of 10 −6 was employed to achieve convergence with an SIMPLE algorithm.

Governing equations
The continuity equation of 2D axisymmetric geometry is given by Here x, and r represent the axial and radial coordinate, respectively. υ x , and υ r represent the axial velocity and radial velocity, respectively. s m represents the mass added to the continuous phase from the dispersed phase.
The governing equation for steady axisymmetric nonswirling flow, and the conservation of axial and radial momentum equation is written as The swirling flow needs to be solved by tangential momentum equation which can be written as   Here υ z represents the swirl velocity

Diffuser performances
Static pressure recovery coefficient (C p ) The magnitude of the kinetic energy of flowing fluid transforms in to pressure energy due to the diffusing action at any cross-section along the length of the annular diffuser Dunn et al. [17].
Here -P out is the static pressure rise at the outlet; -P in is the static pressure at the inlet; u avg is the average velocity of the fluid.

Total pressure loss coefficient (C TL )
It is characterized by what quantity total pressure is lost to the average inlet dynamic pressure because of viscous forces and turbulent intermixing by Buice and Eaton [18]; Ibrahim et al. [19].
Where P tin and P tout represent the total pressure at the inlet and outlet section of the diffuser, respectively.

Diffuser effectiveness (ɳ)
It represents the ratio of real recovery of pressure diffusers to the ideal recovery of pressure diffusers for the same AR.

Grid independence test and validation of results
The test was performed to obtain the optimal mesh size after performing the convergence study. The mesh independence test was performed on the parallel hub axial annular diffuser with AR = 2.44, casing angle 6°, and axial length 33.77 and R e = 2.5 × 10 5 . Four types of mesh sizes have been tested with a turbulence model of RNG k-ε for swirl flow. Figure 4 shows the longitudinal velocity distribution profile at non-dimensional axial length (x/L) = 3 with four grid sizes having cell count (mesh 1 = 100,000 elements, mesh 2 = 160,000 elements, mesh 3 = 200,000 element, and mesh 4 = 250,000 elements). The longitudinal velocity profile for mesh 3 and mesh 4 at x/L = 0.3 are very close to each other. Hence, mesh 3 is used for the analysis of the results in the present study. The simulation was carried out using a system having i8 processor with 16 GB RAM. By using this configuration, the average time of 20 h is required for the simulation to converge. The computational results obtained from axial annular diffuser were validated with the experimental results as shown in Figure 5. The Figure presents the dimensionless velocity profile at x/L = 0.7 with different turbulence model (k-ε standard, k-ε RNG, k-ε realizable, k-ω standards, and k-ω sst) [20][21]. These models were tested against the velocity profile obtained experimentally from the axial annular diffuser at fully developed swirl flow. The k-ε RNG turbulence model shows very slight deviations from experimental results in comparison with k-ε realizable and k-ω sst. Hence RNG k-ε turbulence model is employed for further investigation for swirl flow in the axial annular diffuser with different casing angles.

Results and discussion
The flow behavior and performance of the three diffusers with different swirl flow conditions along the length have been presented and discussed in the form of the turbulence intensity, velocity vector, non-dimensional longitudinal velocity, swirl velocity, static pressure recovery coefficient (C p ), and total pressure loss coefficient (C TL ). The simulation was performed for five swirl conditions i.e. 0°, 7.5°, 12°, 17°, and 25°on the three diffusers. The detailed data of the analysis at 0°, 12°, and 25°inlet swirl angles are presented below.
Turbulence intensity Figure 6 shows the turbulence intensity at the entry of diffusers with different inlet swirl angle in the annulus passage. There is a significant variation observed in the turbulence intensity from the hub to the casing wall and a strong shear layer is observed close to the casing wall. The graph shows that swirl does not affect the magnitude of intensity and nature of the distribution. The nature of turbulence intensity for swirl and non-swirl flow at the inlet is similar to the studies by Coladipietro et al. [10] and Hoadley [22]. Figure 7(i-ix) shows the velocity vector in parallel hub axial annular axisymmetric diffuser at different inlet swirl angles 0°, 12°, and 25°. The direction of the vector clearly shows that flow is moving from the inlet to outlet of the diffuser passage with different inlet swirl angles. It is clear from Figure 7(i) that the flow is uniformly distributed between the hub and the casing wall from inlet to outlet of the diffuser passage. As the swirl angle increases up to 25°, the flow moves towards the casing wall from the hub due to less diffusion annular space, there is no turning of flow on the hub, and there exist less skin friction drag on the parallel hub as shown in Figure 7(iii). The reversal of flow occurs on the hub wall at the swirl angle 25°for B type diffuser due to the adverse pressure gradient on the wall. The reversal of flow occurs at 12°and 25°inlet swirl angles for C-type diffuser due to the high casing divergent angle and the escalation of centrifugal force take place toward the casing at high inlet swirl angle.

Velocity profile
All velocity profiles have been represented in the form of non-dimensional velocity at different diffuser passage, i.e., ratio of the local velocity to the local maximum velocity of the cross-section, as in Ref. [23]. The value y/Y m = 0 is designated as the hub wall position of the traverse, and nondimensional radial length (y/Y m ) = 1 is designated as the casing wall position. Figure 8, shows non-dimensional velocity profiles at x/L = 0.1, 0.3, 0.5, 0.7, and 0.9 of the diffuser passage for all ARs and inlet swirl angles. If the swirl is absent, the bulk flow is only between the hub and the casing wall. By introducing swirl at the inlet, the flow moves from the hub to the casing wall. There is no separation, and the reversal of flow occurs at any swirl angle for AR = 1.67 and for casing divergence angle 3°of A-type diffuser. The peak of the longitudinal velocity shift occurs towards the casing in the order of x/L = 0.9 with swirl angles 12°and 25°at y/Y m = 0.49 and 0.71 for A-type diffuser. The swirl velocity distribution corresponding to the inlet swirl angles 12°and 25°are shown in Figures 8(iii) and 9(ii) respectively. It can be seen that       beginning of the B-type diffuser. The maximum pressure recovery is observed on the 12°swirl angle and minimum loss coefficient in the B-type diffuser. There is a lower pressure recovery of the diffuser passage length beyond x/L = 0.50 and x/L = 0.25 at the swirl angles 17°and 25°. The reason is that the flow separation on the hub, is seen in longitudinal velocity distribution. In a C-type diffuser the magnitude of Cp of the swirl flow is lower than the 0°swirl curve at x/L = 0.56,0.48,0.15,0.12 at the different swirl angles i.e., 7.5°, 12°, 17°, and 25°. The marginal Cp increases with the swirling flow at the beginning of the diffuser passage and then decreases because of the high divergence angle of the casing; flow separation occurs on the hub and the casing wall for the swirling flow.
The C P varies with AR and Cp for the dimensionless length for the non-swirling flow as shown in Figure 17(i, ii) respectively. The obtained simulation result shows the meticulous agreement with the outcomes of Sovran and Klomp [6]; Coladipietro et al. [10] for the three tested diffusers (A, B, C). The diffuser B produces the highestpressure recovery in comparison to the other two type diffusers, as reflected by the curves in Figure 17(i, ii). The pressure recovery (C p ) in the A-type diffuser amongst others is very low due to the limited AR of 1.67. It has been found that 55%of pressure recovery is achieved in the C-type diffuser along the non-dimensional length. In C-type diffuser, having maximum pressure recovery up to the mid-length of the diffuser and after that pressure  recovery is falling between A and B-types diffusers due to separation of flow along the wall, as shown in Figure 17(ii).

Total pressure loss coefficient
The C TL of diffusers A, B, and C for AR 1.67, 2.48, and 3.67 are shown in Figures 14(ii), 15(ii), and ii16(ii).The minimum C TL is observed in swirl angle 7.5°in comparison to nonswirling flow and swirl flow in A-type diffuser. It is observed that there is no separation of fluid flow on the hub wall and casing wall. The maximum loss coefficient is equal to 40% and 23% at swirl angle of 25°in B and C-type diffusers, respectively, due to the separation of fluid flow on the casing wall.

Conclusion
The study of non-swirling and swirling flow of straight hub axial annular diffuser has been investigated and the following results were obtained. 1. In the case of swirling flow, the longitudinal velocity distribution profile shows an increment in the local velocity continuously downstream of the diffusers. 2. With the introduction of swirl flow, the fluid flow moves towards the casing wall due to which no stall is present on the casing wall. 3. Swirls improve the pressure recovery up to a certain length, however, after that it deteriorates the performance due to the flow separation from the hub wall. 4. The maximum pressure recovery coefficient and the minimum C TL are achieved in the B-type diffuser at the inlet swirl angle equal to 12°.
Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.