# Computational Investigation of Flow Control Methods in the Impeller Rear Cavity

Authors: Guang Liu; Qiang Du; Jun Liu; Pei Wang; RuoNan Wang; ZengYan Lian
Journal: International Journal of Aerospace Engineering
 (2020)

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## Abstract

In typical median and small aeroengines, the air used to realize the functions such as cooling of turbine blades and disks, sealing of turbine cavities and bearing chambers, adjusting of rotating assembly axial load is normally drawn through the rear cavity of centrifugal impeller, so the thorough understanding of flow characteristics and pressure distribution and the proposal of the corresponding control methods in the cavity are the key to design the rational secondary air system. With an impeller rear cavity in a small turbofan engine as an object, the current study was dedicated to the investigation of flow control methods in the cavity. Two methods, namely, baffle and swirl-controlled orifice, were proposed to regulate the pressure loss and distribution in the cavity. Furthermore, the influence of geometry parameters of the two methods such as the length of baffle, the space between the baffle and rotating disk wall, the orientation, and radial position of swirl-controlled orifice was investigated. The CFD results show that the swirl-controlled orifice which could deswirl the flow is more effective in regulating the pressure loss and its distribution in cavity than baffle. The variation of the radial position of the swirl-controlled orifice had little influence on pressure loss but obvious influence on pressure distribution; therefore, decreasing the radial position could reduce the axial load on the rotating disk without changing the outlet pressure.


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## Body

## 1. Introduction

During the aeroengine design process, the impeller rear cavity differs broadly in the parameters of inlet/outlet conditions because of the different centrifugal compressor and turbine aerodynamic designs and the different demands to ensure adequate cooling of turbine blades and disks, sealing of turbine cavities and bearing chambers, and adjusting of rotating assembly axial load. Furthermore, in the aeroengine test process, the deviation between the true matching point of the whole machine and the design matching point will lead to the deviation of pressure distribution in the impeller rear cavity and thus causes the failure of the functions. Hence, the accurate prediction of the pressure distribution and the proposal of the corresponding control methods in the impeller rear cavity have great significance in the optimization of the secondary air system of aeroengines.A considerable amount of work about the flow characteristics in the rotor-stator cavity with a centripetal inflow has been carried out by a number of workers [1–6]. The results show that for a rotor-stator cavity with centripetal flow, the internal flow conforms to the Batchelor type which consisted of an inviscid core and two Ekman type boundary layers. In the core region, the axial velocity and radial velocity are negligibly small, so the equation of the tangential velocity in the NS equation is simplified to the balance of the centrifugal force and the radial pressure gradient. Thus, the radial distribution law of the pressure in the cavity is determined by the tangential velocity distribution in the core region. EI-Oun et al. [7] used the pitot tube measurement to obtain the velocity distribution in the rotor-stator cavity with a centripetal flow. Pincombe [8] used the LDV flow field visualization method to measure the velocity profiles in the cavity under different inlet swirl ratio β0 and different rotational Reynolds number Reφ. It is found that the value of β0 has a significant influence on the distribution of the swirl ratio β in the central core region. Hart and Turner [9, 10] used numerical and experimental methods to obtain the pressure and swirl ratio in the impeller rear cavities with different geometries and air bleed flow. The aim of their researches was to obtain a series of curves that can help predict velocity and pressure distribution quickly and accurately without the need for costly CFD work or rig testing during the initial engine design phase. Through the above researches, it is found that the regulation of the pressure distribution in the impeller rear cavity is to regulate the tangential velocity distribution.Three types of flow control methods used to regulate the tangential velocity distribution in the rotating cavity are investigated in previous papers: fin [11], deswirl nozzle [12, 13], and tube [14] vortex reducers. For fin vortex reducer, the flow with high tangential velocity gets through the diversion passage between rectangular fins that are axial-symmetrically mounted and extended radially on the disks. For deswirl nozzle vortex reducer, the flow gets through the angled nozzles that are installed on the rotating disks. Because the nozzles are angled, the direction of the air from the outlet of nozzles could be varied from 0 to 180° theoretically by altering the angle. For tube vortex reducer, the flow gets through the axial-symmetrically installed radial tubes from the compressor blade platforms to the disk bores with constant swirl ratio.However, because of the structure limitation, all the above three vortex reducers are not suitable for the rotor-stator cavity. Therefore, in the present paper, two methods, namely, baffle and swirl-controlled orifice, were proposed to regulate the pressure loss and distribution in the rotor-stator cavity: (1) a baffle, shown in Figure1(a), is installed between the rotating and stationary walls. More detailed introduction about baffle can be seen in the author’s previous paper [15]. (2) Swirl-controlled orifice is shown in Figure 1(b). The stationary wall in the cavity can be provided with a plurality of orifices through which the impeller rear cavity is in fluid communication with the combustion section such that the pressurized air around the combustor is directed into the impeller rear cavity. The orifices extend axially and tangentially in a direction substantially the same or opposite to the tangential velocity of the pressurized air flow to direct the air flow from the combustion section there through into the impeller rear cavity in a direction substantially the same or opposite to the tangential direction of the pressurized air flow entering the impeller rear cavity at the impeller tip. Therefore, the angular momentum of both pressurized air flows will act on each other to change the angular momentum of the total pressurized air contained within the impeller rear cavity and thus the radial static pressure gradient. The numerical simulations were conducted for various β0 (0~0.8), λT (0.028~0.280) with and without control methods to investigate the control mechanisms of these two methods.Figure 1
Impeller rear cavity with control method.
(a)
The impeller rear cavity with baffle
(b)
The impeller rear cavity with swirl-controlled orifice


## 2. The Numerical Models

### 2.1. Geometry

The structures of the original cavity, the cavity with baffle, and the cavity with swirl-controlled orifice are, respectively, shown in Figures2(a)–2(c). RH is the inner radius of rotating disk, and R is the outer radius; RB is the inner radius of baffle; the axial distance between rotating and stationary disks varies from S1 to S2; the radius of axis of the orifice is RO; the diameter of the orifice is D; the number of the orifice is X; the angle between the axial direction of the orifice and the tangential direction is α (when the holes extend in a direction substantially opposite to the rotating direction of the rotor, α is positive). Table 1 shows the values of all the geometric parameters.Figure 2
(a) The cavity without control method. (b) The cavity with baffle. (c) The cavity with swirl-controlled orifice.
(a)
(b)
(c)Table 1
Geometric parameters.
R (mm)
144
RH (mm)
48
RO (mm)
132
D (mm)
0.9
X
30
α
30°
S1 (mm)
2.9 (without baffle)
1.9 (with baffle)
S2 (mm)
25.7
G1=S1/R
0.02 (without baffle)
0.0132 (with baffle)
G2=S2/R
0.178


### 2.2. Numerical Method

Steady state simulations were performed using commercial code CFX v13 with the k-ω-SST turbulence model and wall function approach. A periodic condition was imposed so that an axisymmetric 3D sector was modelled.Different grid sizes were used to study the grid independency for the cavity with and without control methods. The calculation results show that the variation of outlet pressure coefficient is less than 2% for cases with different grid sizes. At last, three meshes with 480000, 900000, and 2000000 cells are chosen for the model in Figures2(a)–2(c) separately. The first cell size of the wall is 1×10−6m for all the three models; for the cavity with swirl-controlled orifice, the O-type mesh is used in the orifice. The wall y+ values of all the numerical cases are smaller than 3 and suitable for the wall functions. Figure 3 shows the mesh model for the cavity with swirl-controlled orifice.Figure 3
The CFD mesh for the cavity with swirl-controlled orifice.


### 2.3. Boundary Conditions and Dimensionless Parameters

All the walls of the cavity are set to adiabatic and no slip condition. For cases in the cavity with swirl-controlled orifice, the mass flow rate ratio of inlet2 and inlet1 is set to 0.1/0.2/0.3. The values of dimensionless parameters and boundary conditions for the numerical cases in the current paper are listed in Table2. In recent years, many researchers such as Liu et al. [15] find that for any impeller rear cavity, when β0 and λT are the same, the difference of Cp, between the conditions with different combination of Cw and Reφ, is ignorable. Therefore, the dimensionless flow parameters discussed in the current paper are β0 and λT.Table 2
The values of parameters.
Location
Conditions
Inlet1
Total pressure:Pt=600000PaTotal temperature: Tt=479K
Inlet2
Mass flow rate,m2m2/m−m2=Ra=0.1/0.2/0.3
Outlet
Mass flow rate,m: 25.8~253 (g/s)
Walls
Adiabatic and no slip
Parameters
Range
Rotational speed of rotating wall,N
5000~30000 (rpm)
β0
0~0.8
Reφ
1.83×106~1.11×107
Cw
6.9×103~4.8×104
λT
0.028~0.280


### 2.4. Verification of the Numerical Model

The experimental data from Poncet et al. [5] in a rotor-stator cavity with centripetal throughflow was chosen for verification. The rotor-stator cavity consisted of a smooth stationary disk of 506 mm diameter and a smooth rotating disk of 500 mm diameter, shown in Figure 4. The distance between the stationary and rotating disks can be changed from 3 to 12 mm. The rotating disk is driven by a 5.5 kW electric servo motor. Because the flow in the cavity is water, the cavity pressure is maintained at 2 bar by a buffer and two pressure sensors to avoid cavitation. The temperature of the water is kept constant (23°C) by a heat exchanger to achieve the unchanged density ρ and dynamic viscosity μ. The water enters the cavity through 48 angled holes of 10 mm diameter and thus has preswirl. The mean inlet swirl ratio β0 of the flow in prerotation ranges from 0.43 to 0.54.Figure 4
Schematic diagram of verification case.The tangential and radial velocities in the cavity are measured by a two-dimension laser Doppler anemometer. The pressure on the stator at the dimensionless radial positions 0.186, 0.22, 0.28, 0.34, 0.4, and 0.46 is measured by six piezoresistive transducers. The comparison here is for two different throughflow bleeds (Cw=5929,9881) with an axial gap of 9 mm and Reφ=1.0×106. The inlet swirl ratio β0 is 0.5.A 4° sector mesh shown in Figure5 and the same numerical software as above were chosen for the verification. The structured mesh was chosen, and the first cell size of the wall is 2×10−6m. The mesh with 327229 cells was used for the model after the grid independence research. The verification test was carried out using the different turbulent models including Spalart-Allmaras, standard k-ε, and SST k-ω. The results using the SST k-ω model were found to show the best agreement.Figure 5
The mesh for verification case.At the inlet, the total temperature, total pressure, and flow velocity direction were set. At the outlet, the mass flow rate was set. At all the walls, the adiabatic and no slip condition was set. Figures6(a) and 6(b) compare the current computational results for the radial variation of static pressure coefficient Cp and swirl ratio β with the experimental data of Poncet. The CFD results agree well with the experimental data.Figure 6
Comparison of radial variation ofCp and β between numerical results using SST turbulence model and experimental data.
(a)
Cp
(b)
β


## 2.1. Geometry

The structures of the original cavity, the cavity with baffle, and the cavity with swirl-controlled orifice are, respectively, shown in Figures2(a)–2(c). RH is the inner radius of rotating disk, and R is the outer radius; RB is the inner radius of baffle; the axial distance between rotating and stationary disks varies from S1 to S2; the radius of axis of the orifice is RO; the diameter of the orifice is D; the number of the orifice is X; the angle between the axial direction of the orifice and the tangential direction is α (when the holes extend in a direction substantially opposite to the rotating direction of the rotor, α is positive). Table 1 shows the values of all the geometric parameters.Figure 2
(a) The cavity without control method. (b) The cavity with baffle. (c) The cavity with swirl-controlled orifice.
(a)
(b)
(c)Table 1
Geometric parameters.
R (mm)
144
RH (mm)
48
RO (mm)
132
D (mm)
0.9
X
30
α
30°
S1 (mm)
2.9 (without baffle)
1.9 (with baffle)
S2 (mm)
25.7
G1=S1/R
0.02 (without baffle)
0.0132 (with baffle)
G2=S2/R
0.178


## 2.2. Numerical Method

Steady state simulations were performed using commercial code CFX v13 with the k-ω-SST turbulence model and wall function approach. A periodic condition was imposed so that an axisymmetric 3D sector was modelled.Different grid sizes were used to study the grid independency for the cavity with and without control methods. The calculation results show that the variation of outlet pressure coefficient is less than 2% for cases with different grid sizes. At last, three meshes with 480000, 900000, and 2000000 cells are chosen for the model in Figures2(a)–2(c) separately. The first cell size of the wall is 1×10−6m for all the three models; for the cavity with swirl-controlled orifice, the O-type mesh is used in the orifice. The wall y+ values of all the numerical cases are smaller than 3 and suitable for the wall functions. Figure 3 shows the mesh model for the cavity with swirl-controlled orifice.Figure 3
The CFD mesh for the cavity with swirl-controlled orifice.


## 2.3. Boundary Conditions and Dimensionless Parameters

All the walls of the cavity are set to adiabatic and no slip condition. For cases in the cavity with swirl-controlled orifice, the mass flow rate ratio of inlet2 and inlet1 is set to 0.1/0.2/0.3. The values of dimensionless parameters and boundary conditions for the numerical cases in the current paper are listed in Table2. In recent years, many researchers such as Liu et al. [15] find that for any impeller rear cavity, when β0 and λT are the same, the difference of Cp, between the conditions with different combination of Cw and Reφ, is ignorable. Therefore, the dimensionless flow parameters discussed in the current paper are β0 and λT.Table 2
The values of parameters.
Location
Conditions
Inlet1
Total pressure:Pt=600000PaTotal temperature: Tt=479K
Inlet2
Mass flow rate,m2m2/m−m2=Ra=0.1/0.2/0.3
Outlet
Mass flow rate,m: 25.8~253 (g/s)
Walls
Adiabatic and no slip
Parameters
Range
Rotational speed of rotating wall,N
5000~30000 (rpm)
β0
0~0.8
Reφ
1.83×106~1.11×107
Cw
6.9×103~4.8×104
λT
0.028~0.280


## 2.4. Verification of the Numerical Model

The experimental data from Poncet et al. [5] in a rotor-stator cavity with centripetal throughflow was chosen for verification. The rotor-stator cavity consisted of a smooth stationary disk of 506 mm diameter and a smooth rotating disk of 500 mm diameter, shown in Figure 4. The distance between the stationary and rotating disks can be changed from 3 to 12 mm. The rotating disk is driven by a 5.5 kW electric servo motor. Because the flow in the cavity is water, the cavity pressure is maintained at 2 bar by a buffer and two pressure sensors to avoid cavitation. The temperature of the water is kept constant (23°C) by a heat exchanger to achieve the unchanged density ρ and dynamic viscosity μ. The water enters the cavity through 48 angled holes of 10 mm diameter and thus has preswirl. The mean inlet swirl ratio β0 of the flow in prerotation ranges from 0.43 to 0.54.Figure 4
Schematic diagram of verification case.The tangential and radial velocities in the cavity are measured by a two-dimension laser Doppler anemometer. The pressure on the stator at the dimensionless radial positions 0.186, 0.22, 0.28, 0.34, 0.4, and 0.46 is measured by six piezoresistive transducers. The comparison here is for two different throughflow bleeds (Cw=5929,9881) with an axial gap of 9 mm and Reφ=1.0×106. The inlet swirl ratio β0 is 0.5.A 4° sector mesh shown in Figure5 and the same numerical software as above were chosen for the verification. The structured mesh was chosen, and the first cell size of the wall is 2×10−6m. The mesh with 327229 cells was used for the model after the grid independence research. The verification test was carried out using the different turbulent models including Spalart-Allmaras, standard k-ε, and SST k-ω. The results using the SST k-ω model were found to show the best agreement.Figure 5
The mesh for verification case.At the inlet, the total temperature, total pressure, and flow velocity direction were set. At the outlet, the mass flow rate was set. At all the walls, the adiabatic and no slip condition was set. Figures6(a) and 6(b) compare the current computational results for the radial variation of static pressure coefficient Cp and swirl ratio β with the experimental data of Poncet. The CFD results agree well with the experimental data.Figure 6
Comparison of radial variation ofCp and β between numerical results using SST turbulence model and experimental data.
(a)
Cp
(b)
β


## 3. Numerical Results and Discussions

### 3.1. The Effect of the Baffle

#### 3.1.1. The Effect on the Flow Structure and Pressure Loss

The effect of the baffle on the flow structure and pressure loss has been carried out in the author’s previous research [15]. The results show that the biggest difference of flow characteristic in the cavity with and without baffle is that a big counterclockwise vortex exists in the stationary cavity composed of the stationary wall and the baffle surface. The existence of the big counterclockwise vortex leads to the diminution of the average swirl ratio of cavity. Thus, the pressure loss of cavity with the baffle reduces. More detailed analysis can be found in research [15].


#### 3.1.2. The Influence of Geometry Parameters of the Baffle

It is found by investigation in previous research that the baffle can reduce the outlet pressure loss of the impeller rear cavity, but whether it is any length, any space between the baffle and rotating disk wall, can the baffle play a role in reducing pressure losses? How to better design the baffle needs further research on the influence of the length of the baffle and the axial space between the baffle and rotating disk wall.(1) The Length of the Baffle. Figures 7(a) and 7(b) show the variation of βoutlet and Cp1 with λT when β0=0.8 of the cavity without and with three different baffles whose nondimensional lengths L∗ (L∗=1−RB/R) are 0.264, 0.403, and 0.542, respectively.Figure 7
The variation ofβoutlet and Cp1 with λT when β0=0.8 of the cavity without and with three different baffles of different lengths.
(a)
βoutlet
(b)
Cp1As shown in Figure7(a), when the length of the baffle is very short (L∗=0.264), βoutlet is the same as when there is no baffle; as the length of the baffle increases, βoutlet gradually decreases. As shown in Figure 7(b), when L∗=0.264, Cp1 is also the same as when there is no baffle; when L∗ increases from 0.264 to 0.403, Cp1 reduces; however, when L∗ increases from 0.403 to 0.542, Cp1 increases instead, which is different from the change rule of βoutlet.The swirl ratio contours and streamlines inr-z section of the cavity with three different baffles of different lengths under the condition λT=0.28, β0=0.8 are shown in Figure 8. It can be seen from Figure 8 that when the length of the baffle is very short (L∗=0.264), the stationary cavity formed by the stationary wall and the baffle is too small to cause great impact on the mainstream; the flow structure is essentially the same as the cavity without baffle; therefore, when L∗=0.264, βoutlet and Cp1 of the impeller rear cavity are the same as the cavity without baffle; when L∗ increases from 0.264 to 0.403, a large static cavity is formed between the baffle and the stationary wall; the main air flowing out from the small clearance mixes vigorously with the counterflow in the static cavity and leads to the diminution of βoutlet; when L∗ continues to increase from 0.403 to 0.542, the static cavity becomes larger; the reduction of βoutlet caused by the mixing is more pronounced because of the increase of the recirculating flow rate in the static cavity.Figure 8
The swirl ratio contours and streamlines inr-z section of the cavity with three different baffles of different lengths when λT=0.28, β0=0.8. (a) L∗=0.264. (b) L∗=0.403. (c) L∗=0.542.The above analysis can be verified from the comparison of the radial distribution of the averageβ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8, as shown in Figure 9(a). When L∗=0.264, the variation of β does not show the sudden decrease; when L∗=0.403, 0.542, β is significantly reduced at the exit position of the baffle, and the decrease is more noticeable when L∗=0.542.Figure 9
Comparison between the radial distribution ofβ, Cp, and Vr∗ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8.
(a)
β
(b)
Cp
(c)
Vr∗Figures9(b) and 9(c) show the comparison of the radial variation of Cp and nondimensional radial velocity Vr∗ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8. When L∗=0.264, there is no sudden decrease of Cp, which is consistent with the change rule of β; when L∗ increases from 0.264 to 0.403, the mixing happens at the outlet of the baffle; therefore, β decreases and results in a decrease of Cp; when L∗ continues to increase from 0.403 to 0.542, βoutlet is further lowered, but Cp1 increases instead. The reason why the variations of βoutlet and Cp1 are inconsistent is that when L∗ increases from 0.403 to 0.542, in the radial region from L∗=0.403 to L∗=0.542, G=S/R of the cavity with baffle L∗=0.542 is 0.02 and much smaller than that of the cavity with baffle L∗=0.403 (G=0.18); hence, for the large flow rate conditions (corresponding to large λT), the radial velocity is greatly increased and cannot be ignored (shown in Figure 9(c)). At this time, the variation of static pressure is codetermined by the change of β, the radial velocity, and the hydraulic friction caused by the nonnegligible radial velocity. Since the radial velocity is gradually increased during the inward flow process and the large radial velocity causes the hydraulic friction loss, when L∗ increases from 0.403 to 0.542, although βoutlet reduces, Cp1 increases due to the increase of radial velocity.In summary, as the nondimensional length of the baffle increases,βoutlet is gradually reduced, but Cp1 is first reduced and then increased. Therefore, when designing the baffle, there is an optimal length to make the static pressure loss in the cavity the smallest.(2) The Space between the Baffle and Rotating Disk Wall WhenL∗=0.403. Figures 10(a) and 10(b) show the variation of βoutlet and Cp1 with λT when β0=0.8 of the cavity without and with four different baffles whose nondimensional space between the baffle and rotating disk wall G1 (G1=S1/R) is 0.02, 0.013, 0.006, and 0.003, respectively.Figure 10
The variation ofβoutlet and Cp1 with λT when β0=0.8 of the cavity without and with four different baffles of different spaces.
(a)
βoutlet
(b)
Cp1As shown in Figure10(a), when G1=0.02, βoutlet is smaller than when there is no baffle; when G1 reduces from 0.02 to 0.006, βoutlet is basically unchanged; when G1 continues to decrease to 0.003, βoutlet is slightly reduced. In Figure 10(b), when G1=0.02, Cp1 is smaller than when there is no baffle; when G1 reduces from 0.02 to 0.013, Cp1 is unchanged; when G1 reduces from 0.013 to 0.006, Cp1 increases; when G1 continues to decrease to 0.003, Cp1 increases significantly and is much larger than that of the cavity without and with other baffles. In addition, the larger λT is, the more intensely Cp1 changes with G1. Through comparison between Figures 10(a) and 10(b), it is found that the increase in outlet static pressure loss that occurs when G1 reduces to 0.003 is not caused by the increase of the swirl ratio.Figures11(a)–11(d) show the comparison of the radial distribution of the average β, Cp, nondimensional radial velocity Vr∗, and total pressure coefficient Cpt in cavity with no baffle and with different baffles of different G1 under the condition λT=0.28 and β0=0.8. As shown in Figure 11(a), when G1=0.02, 0.013, and 0.006, the distribution of β in the cavity is basically the same, when G1=0.003, the variation rate of β in the cavity is slowed down because the tangential motion of the airflow is limited by the stationary wall. As shown in Figure 11(b), when G1=0.02 and G1=0.013, the Cp distribution in the cavity is the same and smaller than that in the cavity without baffle; when G1 reduces to 0.006, although the β distribution is basically the same as G=0.02 and 0.013, the variation rate of Cp in the clearance between the baffle and the rotating wall is bigger than G1=0.02, 0.013; when G1 continues to decrease to 0.003, although β decreases, Cp increases significantly and is several times of that when G=0.02, 0.013, and 0.006.Figure 11
Comparison between the radial variation ofβ, Cp, Vr∗, and Cpt in cavity without and with different baffles of different G1 under the condition λT=0.28 and β0=0.8.
(a)
β
(b)
Cp
(c)
Vr∗
(d)
CptThe reasons for the inconsistency betweenβ and Cp are as follows. (1) The inward flow in the clearance is an acceleration process. The smaller G1 is, the larger the radial velocity is, and the more obvious the acceleration is, as shown in Figure 11(c). However, the increase of radial velocity will result in a decrease of static pressure. (2) The large radial velocity will cause an increase of the hydraulic friction loss in the radial flow process. As shown in Figure 11(d), as G1 decreases, the total pressure loss in the clearance increases and leads to a decrease in static pressure.In summary, the variation of the space between the baffle and the rotating wall under small amplitude has little impact onβoutlet and Cp1 of the impeller rear cavity; when G1 is reduced to 0.006 or even 0.003, the large radial velocity will lead to the high total pressure loss caused by the hydraulic friction and the acceleration process of radial inflow leads to a decrease in static pressure because of the increase of the dynamic pressure. These two factors work together, resulting in a large increase in the static pressure loss in the cavity.


### 3.2. The Effect of the Swirl-Controlled Orifice

#### 3.2.1. The Effect on the Flow Structure

The flow structure of the cavity with swirl-controlled orifice under the conditionλT=0.28, β0=0, and Ra=0.2 is analyzed. As shown in Figure 12, four sections are selected from the cavity to draw the streamlines, swirl ratio contours, and static pressure contours: the r-z section (section A), the section with z∗=0.01 (the middle yellow section between the rotor and the stator at the highest radius, section B), the section with r∗=0.92 (the green section whose radius is the same as the center of the orifice, section C), and the section with r∗=0.55 (the red section at the middle of the large clearance cavity, section D).Figure 12
The swirl ratio and static pressure contours and streamlines in different sections of cavity with swirl-controlled orifice under the conditionλT=0.28, β0=0.8, and Ra=0.2. (a) Sections schematic. (b) r∗=0.55 (section D). (c) r-z section. (d) z∗=0.01 (section B). (e) r∗=0.092 (section C).It can be seen from Figure12 that the jet is formed at the outlet of the orifice and jetted toward the rotating disk at a high speed which will suppress the centrifugal pumping effect and thus thinning the boundary layer of the rotating wall. In the current paper, the orifices on the stator extend axially and tangentially in a direction substantially opposite to the rotating direction of the rotor; thus, the high-speed jet at the exit of the orifice has a high reverse tangential speed. Therefore, when the main flow is mixed with the jet flow, the angular momentum of both pressurized air flows will act on each other and the angular momentum of the total pressurized air contained within the impeller rear cavity will reduce. In the region near the orifice, due to the existence of the complex three-dimensional vortex, the flow is nonaxisymmetric and completely different from the Batchelor flow pattern. As the flow develops inward, the mixing between main flow and jet flow becomes more and more complete; the three-dimensional vortex gradually disappears. Meanwhile, the flow structure in the cavity becomes the Batchelor flow pattern again, shown as the swirl ratio and static pressure contours in the r∗=0.55 section which indicate the swirl ratio and static pressure are substantially constant along the axial direction.When the mass flow rate ratio Ra is changed, the flow structure in the impeller rear cavity changes. Figures13(a) and 13(b) show the swirl ratio contours and streamlines in two sections (z∗=0.01 section and r∗=0.92 section) of another two conditions. The values of λT and β0 of the two conditions are both set as 0.28 and 0.8, the Ra are 0.1 and 0.3, respectively.Figure 13
The swirl ratio contours and streamlines in two sections (z∗=0.01 and r∗=0.92) under the condition λT=0.28, β0=0.8. (a) Ra=0.1. (b) Ra=0.3.Through comparison between Figure13(a) and Figure 12, both the axial velocity and the tangential velocity of the jet flow at the outlet of the orifice are found to be reduced when Ra is reduced from 0.2 to 0.1 (the accurate velocities under different Ra are shown in Table 3). With the decrease of the axial velocity of the jet flow, the influence region of the jet becomes smaller. With the decrease of the tangential velocity, the jet flow with reverse tangential velocity changes the flow direction quickly under the influence of the main flow. As a result, the vortex originally existing in the z∗=0.01 section disappears, which means the jet depth of the jet flow becomes shallower. The decrease of the tangential velocity and the shallower jet depth caused by the decrease of the jet flow rate increase the swirl ratio in the cavity.Table 3
The velocity at outlet of the orifice under different Ra.
Velocity at the outlet of the orifice (m/s)
Ra
0.1
0.2
0.3
Total velocity
218
364
462
Axial velocity
110
187
247
Tangential velocity
188
312
390The comparison between Figure13(b) and Figure 12 shows that both the axial velocity and the tangential velocity of the jet flow increase when Ra increases. Therefore, the jet depth of the jet flow increases, the vortex of the z∗=0.01 section becomes larger and more complicated, and the radial area affected by the jet correspondingly becomes larger. Because of the above reasons, the swirl ratio in the cavity is greatly reduced, even to a negative value.


#### 3.2.2. The Effect on the Pressure Loss

Figures14(a)–14(d) show the static pressure contours in the rotating disk of the cavity without and with swirl-controlled orifice. As shown in Figure 14(a), the static pressure distribution of the rotating disk is axisymmetric at all the radii when there is no swirl-controlled orifice in the cavity. However, for the cavity with swirl-controlled orifice shown in Figure 14(b), the static pressure of the rotating disk is nonuniformly distributed in the circumferential direction near the radial position of the orifice because of the influence of the jet flow from the orifice. The stagnation of the high-speed jet flow on the rotating disk causes the local high pressure zone, and the complex three-dimensional vortex caused by the jet gives rise to the low pressure recirculation zone. With the increase of Ra from 0.1 to 0.3, shown in Figures 14(b)–14(d), the influence area of the jet flow from the orifice increases, and thus, the uneven pressure region increases.Figure 14
The static pressure contours in the rotating disk of the cavity: (a) without orifice; (b) with orifice,Ra=0.1; (c) with orifice, Ra=0.2; (d) with orifice, Ra=0.3.However, as the flow develops radially inward, the main flow and the jet flow are fully blended; the static pressure distribution of the rotating wall becomes axisymmetric in the low radius region. It can be seen from Figure15 that under different conditions, there is a core region with a constant swirl ratio in the r∗=0.55 section. In addition, the radial velocity of the core zone is relatively small comparing with the tangential velocity. Therefore, it can be considered that the flow satisfies the simple radial equilibrium equation, which means the radial distribution of pressure in the cavity is decided by the central core swirl ratio β. The above results prove the conclusion made in the flow structure analysis that the flow structure at low radius in the impeller rear cavity with swirl-controlled orifice is of Batchelor type.Figure 15
The axial variations of swirl ratio and radial velocity atr∗=0.55 radius under conditions with different Ra and β0.Figures16(a) and 16(b) show the comparisons between the variation of the outlet swirl ratio βoutlet and the outlet pressure loss Cp1 with β0 of the impeller rear cavity with swirl-controlled orifice and the variation of βoutlet and Cp1 with β0 of the cavity without orifice.Figure 16
The comparisons between the variations ofβoutlet and Cp1 with β0 of the impeller rear cavity with swirl-controlled orifice and those of the cavity without orifice.
(a)
βoutlet
(b)
Cp1It can be seen from Figure16(a) that βoutlet increases with the increase of β0 regardless of whether there is swirl-controlled orifice in the cavity. When β0 is in the range of 0~0.8, βoutlet of the cavity with swirl-controlled orifice is smaller than that of the cavity without orifice and decreases as Ra increases. For the cases whose Ra increases to 0.3, βoutlet decreases to a negative value for low β0 conditions.It can be seen from Figure16(b) that Cp1 of the cavity with swirl-controlled orifice is smaller than that of the cavity without orifice and decreases with increasing Ra when Ra is in the range of 0.1~0.2, β0 is in the range of 0~0.8. However, when Ra increases to 0.3, although Cp1 on the condition with high β0 is still smaller than that of the condition with Ra=0.2, Cp1 on the condition with low β0 is bigger than that of the condition with Ra=0.2.The reason for the inconsistency between the variations ofCp1 and βoutlet with β0, for the conditions with Ra=0.3, β0<0.4, is that the flow at the low radius, where it is away from the orifice, satisfies the simple radial equilibrium equation −dp∗/dr∗=2β2r∗, which means the radial distribution of pressure in the cavity is decided by the absolute value distribution of central core swirl ratio β. When Ra=0.3, β0<0.4, although βoutlet is reduced (reduced to a negative value), its absolute value is actually increased (shown in Figure 16(a)), and thus, Cp1 increases.Because of the important impact of the static pressure distribution in the cavity on the high-pressure rotating assembly axial load, further researches of the static pressure and swirl ratio distributions have been done.Figures17 and 18 show the contrasts of the radial distribution of swirl ratio and average static pressure in the cavity with and without swirl-controlled orifice on the same conditions. Figures 17 and 18 show the comparisons of cases with λT=0.28 and β0=0.8, 0, respectively. As shown in Figure 17, when β0=0.8, due to the mixing effect of the reverse swirling jet flow at the outlet of the orifice, the main flow β is smaller than that of the cavity without orifice, and the larger Ra is, the lower main flow β is. Thus, the decrease of the main flow β leads to the reduction of Cp. In addition, the flow is very complicated due to the strong influence of the jet at the exit of the orifice when Ra is large and thus causes the fluctuation of the radial distribution of β and the drastic increase of local Cp. However, as the flow develops radially inward, the vorticity gradually disappears and Cp decreases.Figure 17
The contrasts of the radial distribution of average static pressure andβ in the cavity with and without swirl-controlled orifice when λT=0.28 and β0=0.8.
(a)
β
(b)
CpFigure 18
The contrasts of the radial variation of average static pressure andβ in the cavity with and without swirl-controlled orifice when λT=0.28 and β0=0.
(a)
β
(b)
CpAs shown in Figure18, when β0=0, the main flow β is also reduced under the influence of the jet, and the larger Ra is, the lower main flow β is. The difference between the condition with β0=0 and the condition with β0=0.8 is that under the influence of the jet, main flow β becomes a negative value and will decrease as the flow develops radially inwards (which means the increase of the absolute value of β) when Ra is large. Therefore, the increase in the absolute value of the main flow β leads to the increase of Cp.


#### 3.2.3. The Influence of Geometry Parameters of the Swirl-Controlled Orifice

The swirl-controlled orifice arranged on the stationary wall introduces the reverse swirling flow to mix with the high swirling main flow so that the swirl ratio of the main flow is greatly reduced and the deswirl effect is achieved. For swirl-controlled orifice, the geometry parameters which will influence the deswirl effect include the number, length, diameter, orientation, and radial position. In the current paper, the angle between the orifice axial and the tangential direction and the radial position are discussed to investigate their effects on the swirl ratio and static pressure distributions in the cavity.(1) The Orientation. Figures 19(a) and 19(b) show the variation of βoutlet and Cp1 with β0 when λT=0.28, Ra=0.2 of the cavity without and with three different swirl-controlled orifices whose angle α between the axial and the tangential directions is 30°, 45°, and 60°, respectively. For all the cavities, the change rule of Cp1 with β0 is the same as that of βoutlet with β0; when β0 is small, α increases from 30° to 45°, βoutlet increases, α continues to increase from 45° to 60°, and βoutlet is basically unchanged; when β0 is large, βoutlet gradually increases with increasing α.Figure 19
The variation ofβoutlet and Cp1 with β0 of the impeller rear cavity without and with three different orifices whose α is 30°, 45°, and 60°, respectively.
(a)
βoutlet
(b)
Cp1Figures20(a) and 20(b) show contrasts of the radial distribution of the average β and Cp in the cavity without and with different orifices of different orientations under the condition Ra=0.28 and β0=0.4. When there is a swirl-controlled orifice, β near the orifice shows a sudden drop. When α is 30°, β decreases the most; when α=45° and α=60°, β decreases substantially the same, which eventually leads to the variation law of βoutlet as shown in Figure 19(a). However, for the radial variation of Cp shown in Figure 20(b), Cp near the orifice increases instead because of the pressure loss of the mixing process. When α=30°, the area affected by the jet is significantly larger than that of α=45° and α=60°, and Cp is larger; as the flow progresses downward, the mixing is completed, and the flow field eventually becomes uniform. At this time, the radial variation of Cp is determined by β, so Cp1 and βoutlet change in the same manner.Figure 20
The contrasts between the radial distribution ofβ and Cp in cavity without and with different orifices of different α under the condition Ra=0.2 and β0=0.8.
(a)
β
(b)
CpFigures21(a)–21(c) show the streamlines and velocity contours in two sections (z∗=0.01 section and r∗=0.92 section) of the cavity with three different orifices of three orientations 30°, 45°, and 60°. It can be seen from the figure that when Ra is the same, the larger the angle is, the smaller the tangential velocity of jet flow is and the larger the axial velocity is. The decrease of the tangential velocity of the jet causes the weakening of the deswirl effect; the increase of the axial velocity of the jet causes more outlet flow of the orifice to be sprayed and stagnated on the rotating wall which means the influence of the jet on the mainstream is weakened. However, for the condition of Ra=0.2 and β0=0.4, when the angle increases to 45°, the jet flow has already all been sprayed on the rotating wall, the increasing angle (from 45° to 60°) has little effect on the flow field.Figure 21
The velocity contours and streamlines in two sections (z∗=0.01 and r∗=0.92) under the condition Ra=0.2, β0=0.4.
(a)
(b)
(c)In summary, when Ra is equal and the angle of the swirl-controlled orifice is small, the tangential velocity of the jet flow decreases as the angle increases, the deswirl effect of the jet on the mainstream is weakened; therefore,βoutlet and Cp1 gradually increase with the increase of angle. When the angle increases to a certain value, the jet flow has already all sprayed on the rotating wall; βoutlet and Cp1 are basically unchanged with increasing angle.(2) Radial Position. Figures 22(a) and 22(b) show the variation of βoutlet and Cp1 with β0 when λT=0.28, Ra=0.1, without and with four different swirl-controlled orifices whose nondimensional radial position H=RO/R is 0.72, 0.83, 0.92, and 0.97, respectively. It can be seen from the figure that when Ra=0.1 and β0 is in the range of 0~0.8, the radial position H of the swirl-controlled orifice has little impact on βoutlet and Cp1. Under different H, βoutlet and Cp1 are basically equal.Figure 22
The variation ofβoutlet and Cp1 with β0 of the impeller rear cavity without and with four different orifices whose radial position H is 0.72, 0.83, 0.92, and 0.97, respectively.
(a)
βoutlet
(b)
Cp1Figures23(a) and 23(b) show contrasts of the radial distribution of the average β and Cp in cavity with no orifice and with four different orifices of different H under the condition of Ra=0.1 and β0=0.8. The figure shows that for the cavity with swirl-controlled orifice, the radial distribution of β and Cp of mainstream in the area before reaching the region near the orifice is the same as that of the cavity without orifice. After reaching the region near the orifice, β and Cp of the mainstream appear to suddenly drop because of the impact by the jet from the orifice. Whether the radial position of the orifice is high or low, the radial distribution of β of the main flow after the mixing of the mainstream and the jet is substantially the same, so βoutlet and Cp1 are substantially equal under different H. For the cavity with different orifices of different H, the unmixed area from the inlet to the orifice increases as H decreases, because the static pressure loss in this area is the same as that of the cavity without orifice; therefore, although H has no effect on Cp1, it will change the static pressure distribution at the high radius of the rotating wall, thus changing the axial load of the rotor assembly. As H decreases, the axial load of the rotor assembly decreases.Figure 23
Comparison between the radial distribution ofβ and Cp in cavity without and with different orifices of different H under the condition Ra=0.1 and β0=0.8.
(a)
β
(b)
CpIn summary, when Ra is equal, regardless of the radial position of the swirl-controlled orifice, the radial distribution of main flow swirl ratio after mixing is the same, the radial position has little effect onβoutlet and Cp1. However, with the decrease of H, the unmixed high static pressure loss area between the inlet and the orifice increases, and the axial load of the rotor assembly decreases. Therefore, if the axial load of the rotor assembly needs to be adjusted without changing the outlet static pressure of the cavity, the adjustment of the radial position of the swirl-controlled orifice is a way to achieve it.


## 3.1. The Effect of the Baffle

### 3.1.1. The Effect on the Flow Structure and Pressure Loss

The effect of the baffle on the flow structure and pressure loss has been carried out in the author’s previous research [15]. The results show that the biggest difference of flow characteristic in the cavity with and without baffle is that a big counterclockwise vortex exists in the stationary cavity composed of the stationary wall and the baffle surface. The existence of the big counterclockwise vortex leads to the diminution of the average swirl ratio of cavity. Thus, the pressure loss of cavity with the baffle reduces. More detailed analysis can be found in research [15].


### 3.1.2. The Influence of Geometry Parameters of the Baffle

It is found by investigation in previous research that the baffle can reduce the outlet pressure loss of the impeller rear cavity, but whether it is any length, any space between the baffle and rotating disk wall, can the baffle play a role in reducing pressure losses? How to better design the baffle needs further research on the influence of the length of the baffle and the axial space between the baffle and rotating disk wall.(1) The Length of the Baffle. Figures 7(a) and 7(b) show the variation of βoutlet and Cp1 with λT when β0=0.8 of the cavity without and with three different baffles whose nondimensional lengths L∗ (L∗=1−RB/R) are 0.264, 0.403, and 0.542, respectively.Figure 7
The variation ofβoutlet and Cp1 with λT when β0=0.8 of the cavity without and with three different baffles of different lengths.
(a)
βoutlet
(b)
Cp1As shown in Figure7(a), when the length of the baffle is very short (L∗=0.264), βoutlet is the same as when there is no baffle; as the length of the baffle increases, βoutlet gradually decreases. As shown in Figure 7(b), when L∗=0.264, Cp1 is also the same as when there is no baffle; when L∗ increases from 0.264 to 0.403, Cp1 reduces; however, when L∗ increases from 0.403 to 0.542, Cp1 increases instead, which is different from the change rule of βoutlet.The swirl ratio contours and streamlines inr-z section of the cavity with three different baffles of different lengths under the condition λT=0.28, β0=0.8 are shown in Figure 8. It can be seen from Figure 8 that when the length of the baffle is very short (L∗=0.264), the stationary cavity formed by the stationary wall and the baffle is too small to cause great impact on the mainstream; the flow structure is essentially the same as the cavity without baffle; therefore, when L∗=0.264, βoutlet and Cp1 of the impeller rear cavity are the same as the cavity without baffle; when L∗ increases from 0.264 to 0.403, a large static cavity is formed between the baffle and the stationary wall; the main air flowing out from the small clearance mixes vigorously with the counterflow in the static cavity and leads to the diminution of βoutlet; when L∗ continues to increase from 0.403 to 0.542, the static cavity becomes larger; the reduction of βoutlet caused by the mixing is more pronounced because of the increase of the recirculating flow rate in the static cavity.Figure 8
The swirl ratio contours and streamlines inr-z section of the cavity with three different baffles of different lengths when λT=0.28, β0=0.8. (a) L∗=0.264. (b) L∗=0.403. (c) L∗=0.542.The above analysis can be verified from the comparison of the radial distribution of the averageβ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8, as shown in Figure 9(a). When L∗=0.264, the variation of β does not show the sudden decrease; when L∗=0.403, 0.542, β is significantly reduced at the exit position of the baffle, and the decrease is more noticeable when L∗=0.542.Figure 9
Comparison between the radial distribution ofβ, Cp, and Vr∗ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8.
(a)
β
(b)
Cp
(c)
Vr∗Figures9(b) and 9(c) show the comparison of the radial variation of Cp and nondimensional radial velocity Vr∗ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8. When L∗=0.264, there is no sudden decrease of Cp, which is consistent with the change rule of β; when L∗ increases from 0.264 to 0.403, the mixing happens at the outlet of the baffle; therefore, β decreases and results in a decrease of Cp; when L∗ continues to increase from 0.403 to 0.542, βoutlet is further lowered, but Cp1 increases instead. The reason why the variations of βoutlet and Cp1 are inconsistent is that when L∗ increases from 0.403 to 0.542, in the radial region from L∗=0.403 to L∗=0.542, G=S/R of the cavity with baffle L∗=0.542 is 0.02 and much smaller than that of the cavity with baffle L∗=0.403 (G=0.18); hence, for the large flow rate conditions (corresponding to large λT), the radial velocity is greatly increased and cannot be ignored (shown in Figure 9(c)). At this time, the variation of static pressure is codetermined by the change of β, the radial velocity, and the hydraulic friction caused by the nonnegligible radial velocity. Since the radial velocity is gradually increased during the inward flow process and the large radial velocity causes the hydraulic friction loss, when L∗ increases from 0.403 to 0.542, although βoutlet reduces, Cp1 increases due to the increase of radial velocity.In summary, as the nondimensional length of the baffle increases,βoutlet is gradually reduced, but Cp1 is first reduced and then increased. Therefore, when designing the baffle, there is an optimal length to make the static pressure loss in the cavity the smallest.(2) The Space between the Baffle and Rotating Disk Wall WhenL∗=0.403. Figures 10(a) and 10(b) show the variation of βoutlet and Cp1 with λT when β0=0.8 of the cavity without and with four different baffles whose nondimensional space between the baffle and rotating disk wall G1 (G1=S1/R) is 0.02, 0.013, 0.006, and 0.003, respectively.Figure 10
The variation ofβoutlet and Cp1 with λT when β0=0.8 of the cavity without and with four different baffles of different spaces.
(a)
βoutlet
(b)
Cp1As shown in Figure10(a), when G1=0.02, βoutlet is smaller than when there is no baffle; when G1 reduces from 0.02 to 0.006, βoutlet is basically unchanged; when G1 continues to decrease to 0.003, βoutlet is slightly reduced. In Figure 10(b), when G1=0.02, Cp1 is smaller than when there is no baffle; when G1 reduces from 0.02 to 0.013, Cp1 is unchanged; when G1 reduces from 0.013 to 0.006, Cp1 increases; when G1 continues to decrease to 0.003, Cp1 increases significantly and is much larger than that of the cavity without and with other baffles. In addition, the larger λT is, the more intensely Cp1 changes with G1. Through comparison between Figures 10(a) and 10(b), it is found that the increase in outlet static pressure loss that occurs when G1 reduces to 0.003 is not caused by the increase of the swirl ratio.Figures11(a)–11(d) show the comparison of the radial distribution of the average β, Cp, nondimensional radial velocity Vr∗, and total pressure coefficient Cpt in cavity with no baffle and with different baffles of different G1 under the condition λT=0.28 and β0=0.8. As shown in Figure 11(a), when G1=0.02, 0.013, and 0.006, the distribution of β in the cavity is basically the same, when G1=0.003, the variation rate of β in the cavity is slowed down because the tangential motion of the airflow is limited by the stationary wall. As shown in Figure 11(b), when G1=0.02 and G1=0.013, the Cp distribution in the cavity is the same and smaller than that in the cavity without baffle; when G1 reduces to 0.006, although the β distribution is basically the same as G=0.02 and 0.013, the variation rate of Cp in the clearance between the baffle and the rotating wall is bigger than G1=0.02, 0.013; when G1 continues to decrease to 0.003, although β decreases, Cp increases significantly and is several times of that when G=0.02, 0.013, and 0.006.Figure 11
Comparison between the radial variation ofβ, Cp, Vr∗, and Cpt in cavity without and with different baffles of different G1 under the condition λT=0.28 and β0=0.8.
(a)
β
(b)
Cp
(c)
Vr∗
(d)
CptThe reasons for the inconsistency betweenβ and Cp are as follows. (1) The inward flow in the clearance is an acceleration process. The smaller G1 is, the larger the radial velocity is, and the more obvious the acceleration is, as shown in Figure 11(c). However, the increase of radial velocity will result in a decrease of static pressure. (2) The large radial velocity will cause an increase of the hydraulic friction loss in the radial flow process. As shown in Figure 11(d), as G1 decreases, the total pressure loss in the clearance increases and leads to a decrease in static pressure.In summary, the variation of the space between the baffle and the rotating wall under small amplitude has little impact onβoutlet and Cp1 of the impeller rear cavity; when G1 is reduced to 0.006 or even 0.003, the large radial velocity will lead to the high total pressure loss caused by the hydraulic friction and the acceleration process of radial inflow leads to a decrease in static pressure because of the increase of the dynamic pressure. These two factors work together, resulting in a large increase in the static pressure loss in the cavity.


## 3.1.1. The Effect on the Flow Structure and Pressure Loss

The effect of the baffle on the flow structure and pressure loss has been carried out in the author’s previous research [15]. The results show that the biggest difference of flow characteristic in the cavity with and without baffle is that a big counterclockwise vortex exists in the stationary cavity composed of the stationary wall and the baffle surface. The existence of the big counterclockwise vortex leads to the diminution of the average swirl ratio of cavity. Thus, the pressure loss of cavity with the baffle reduces. More detailed analysis can be found in research [15].


## 3.1.2. The Influence of Geometry Parameters of the Baffle

It is found by investigation in previous research that the baffle can reduce the outlet pressure loss of the impeller rear cavity, but whether it is any length, any space between the baffle and rotating disk wall, can the baffle play a role in reducing pressure losses? How to better design the baffle needs further research on the influence of the length of the baffle and the axial space between the baffle and rotating disk wall.(1) The Length of the Baffle. Figures 7(a) and 7(b) show the variation of βoutlet and Cp1 with λT when β0=0.8 of the cavity without and with three different baffles whose nondimensional lengths L∗ (L∗=1−RB/R) are 0.264, 0.403, and 0.542, respectively.Figure 7
The variation ofβoutlet and Cp1 with λT when β0=0.8 of the cavity without and with three different baffles of different lengths.
(a)
βoutlet
(b)
Cp1As shown in Figure7(a), when the length of the baffle is very short (L∗=0.264), βoutlet is the same as when there is no baffle; as the length of the baffle increases, βoutlet gradually decreases. As shown in Figure 7(b), when L∗=0.264, Cp1 is also the same as when there is no baffle; when L∗ increases from 0.264 to 0.403, Cp1 reduces; however, when L∗ increases from 0.403 to 0.542, Cp1 increases instead, which is different from the change rule of βoutlet.The swirl ratio contours and streamlines inr-z section of the cavity with three different baffles of different lengths under the condition λT=0.28, β0=0.8 are shown in Figure 8. It can be seen from Figure 8 that when the length of the baffle is very short (L∗=0.264), the stationary cavity formed by the stationary wall and the baffle is too small to cause great impact on the mainstream; the flow structure is essentially the same as the cavity without baffle; therefore, when L∗=0.264, βoutlet and Cp1 of the impeller rear cavity are the same as the cavity without baffle; when L∗ increases from 0.264 to 0.403, a large static cavity is formed between the baffle and the stationary wall; the main air flowing out from the small clearance mixes vigorously with the counterflow in the static cavity and leads to the diminution of βoutlet; when L∗ continues to increase from 0.403 to 0.542, the static cavity becomes larger; the reduction of βoutlet caused by the mixing is more pronounced because of the increase of the recirculating flow rate in the static cavity.Figure 8
The swirl ratio contours and streamlines inr-z section of the cavity with three different baffles of different lengths when λT=0.28, β0=0.8. (a) L∗=0.264. (b) L∗=0.403. (c) L∗=0.542.The above analysis can be verified from the comparison of the radial distribution of the averageβ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8, as shown in Figure 9(a). When L∗=0.264, the variation of β does not show the sudden decrease; when L∗=0.403, 0.542, β is significantly reduced at the exit position of the baffle, and the decrease is more noticeable when L∗=0.542.Figure 9
Comparison between the radial distribution ofβ, Cp, and Vr∗ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8.
(a)
β
(b)
Cp
(c)
Vr∗Figures9(b) and 9(c) show the comparison of the radial variation of Cp and nondimensional radial velocity Vr∗ in cavity with different baffles of different L∗ under the condition λT=0.28 and β0=0.8. When L∗=0.264, there is no sudden decrease of Cp, which is consistent with the change rule of β; when L∗ increases from 0.264 to 0.403, the mixing happens at the outlet of the baffle; therefore, β decreases and results in a decrease of Cp; when L∗ continues to increase from 0.403 to 0.542, βoutlet is further lowered, but Cp1 increases instead. The reason why the variations of βoutlet and Cp1 are inconsistent is that when L∗ increases from 0.403 to 0.542, in the radial region from L∗=0.403 to L∗=0.542, G=S/R of the cavity with baffle L∗=0.542 is 0.02 and much smaller than that of the cavity with baffle L∗=0.403 (G=0.18); hence, for the large flow rate conditions (corresponding to large λT), the radial velocity is greatly increased and cannot be ignored (shown in Figure 9(c)). At this time, the variation of static pressure is codetermined by the change of β, the radial velocity, and the hydraulic friction caused by the nonnegligible radial velocity. Since the radial velocity is gradually increased during the inward flow process and the large radial velocity causes the hydraulic friction loss, when L∗ increases from 0.403 to 0.542, although βoutlet reduces, Cp1 increases due to the increase of radial velocity.In summary, as the nondimensional length of the baffle increases,βoutlet is gradually reduced, but Cp1 is first reduced and then increased. Therefore, when designing the baffle, there is an optimal length to make the static pressure loss in the cavity the smallest.(2) The Space between the Baffle and Rotating Disk Wall WhenL∗=0.403. Figures 10(a) and 10(b) show the variation of βoutlet and Cp1 with λT when β0=0.8 of the cavity without and with four different baffles whose nondimensional space between the baffle and rotating disk wall G1 (G1=S1/R) is 0.02, 0.013, 0.006, and 0.003, respectively.Figure 10
The variation ofβoutlet and Cp1 with λT when β0=0.8 of the cavity without and with four different baffles of different spaces.
(a)
βoutlet
(b)
Cp1As shown in Figure10(a), when G1=0.02, βoutlet is smaller than when there is no baffle; when G1 reduces from 0.02 to 0.006, βoutlet is basically unchanged; when G1 continues to decrease to 0.003, βoutlet is slightly reduced. In Figure 10(b), when G1=0.02, Cp1 is smaller than when there is no baffle; when G1 reduces from 0.02 to 0.013, Cp1 is unchanged; when G1 reduces from 0.013 to 0.006, Cp1 increases; when G1 continues to decrease to 0.003, Cp1 increases significantly and is much larger than that of the cavity without and with other baffles. In addition, the larger λT is, the more intensely Cp1 changes with G1. Through comparison between Figures 10(a) and 10(b), it is found that the increase in outlet static pressure loss that occurs when G1 reduces to 0.003 is not caused by the increase of the swirl ratio.Figures11(a)–11(d) show the comparison of the radial distribution of the average β, Cp, nondimensional radial velocity Vr∗, and total pressure coefficient Cpt in cavity with no baffle and with different baffles of different G1 under the condition λT=0.28 and β0=0.8. As shown in Figure 11(a), when G1=0.02, 0.013, and 0.006, the distribution of β in the cavity is basically the same, when G1=0.003, the variation rate of β in the cavity is slowed down because the tangential motion of the airflow is limited by the stationary wall. As shown in Figure 11(b), when G1=0.02 and G1=0.013, the Cp distribution in the cavity is the same and smaller than that in the cavity without baffle; when G1 reduces to 0.006, although the β distribution is basically the same as G=0.02 and 0.013, the variation rate of Cp in the clearance between the baffle and the rotating wall is bigger than G1=0.02, 0.013; when G1 continues to decrease to 0.003, although β decreases, Cp increases significantly and is several times of that when G=0.02, 0.013, and 0.006.Figure 11
Comparison between the radial variation ofβ, Cp, Vr∗, and Cpt in cavity without and with different baffles of different G1 under the condition λT=0.28 and β0=0.8.
(a)
β
(b)
Cp
(c)
Vr∗
(d)
CptThe reasons for the inconsistency betweenβ and Cp are as follows. (1) The inward flow in the clearance is an acceleration process. The smaller G1 is, the larger the radial velocity is, and the more obvious the acceleration is, as shown in Figure 11(c). However, the increase of radial velocity will result in a decrease of static pressure. (2) The large radial velocity will cause an increase of the hydraulic friction loss in the radial flow process. As shown in Figure 11(d), as G1 decreases, the total pressure loss in the clearance increases and leads to a decrease in static pressure.In summary, the variation of the space between the baffle and the rotating wall under small amplitude has little impact onβoutlet and Cp1 of the impeller rear cavity; when G1 is reduced to 0.006 or even 0.003, the large radial velocity will lead to the high total pressure loss caused by the hydraulic friction and the acceleration process of radial inflow leads to a decrease in static pressure because of the increase of the dynamic pressure. These two factors work together, resulting in a large increase in the static pressure loss in the cavity.


## 3.2. The Effect of the Swirl-Controlled Orifice

### 3.2.1. The Effect on the Flow Structure

The flow structure of the cavity with swirl-controlled orifice under the conditionλT=0.28, β0=0, and Ra=0.2 is analyzed. As shown in Figure 12, four sections are selected from the cavity to draw the streamlines, swirl ratio contours, and static pressure contours: the r-z section (section A), the section with z∗=0.01 (the middle yellow section between the rotor and the stator at the highest radius, section B), the section with r∗=0.92 (the green section whose radius is the same as the center of the orifice, section C), and the section with r∗=0.55 (the red section at the middle of the large clearance cavity, section D).Figure 12
The swirl ratio and static pressure contours and streamlines in different sections of cavity with swirl-controlled orifice under the conditionλT=0.28, β0=0.8, and Ra=0.2. (a) Sections schematic. (b) r∗=0.55 (section D). (c) r-z section. (d) z∗=0.01 (section B). (e) r∗=0.092 (section C).It can be seen from Figure12 that the jet is formed at the outlet of the orifice and jetted toward the rotating disk at a high speed which will suppress the centrifugal pumping effect and thus thinning the boundary layer of the rotating wall. In the current paper, the orifices on the stator extend axially and tangentially in a direction substantially opposite to the rotating direction of the rotor; thus, the high-speed jet at the exit of the orifice has a high reverse tangential speed. Therefore, when the main flow is mixed with the jet flow, the angular momentum of both pressurized air flows will act on each other and the angular momentum of the total pressurized air contained within the impeller rear cavity will reduce. In the region near the orifice, due to the existence of the complex three-dimensional vortex, the flow is nonaxisymmetric and completely different from the Batchelor flow pattern. As the flow develops inward, the mixing between main flow and jet flow becomes more and more complete; the three-dimensional vortex gradually disappears. Meanwhile, the flow structure in the cavity becomes the Batchelor flow pattern again, shown as the swirl ratio and static pressure contours in the r∗=0.55 section which indicate the swirl ratio and static pressure are substantially constant along the axial direction.When the mass flow rate ratio Ra is changed, the flow structure in the impeller rear cavity changes. Figures13(a) and 13(b) show the swirl ratio contours and streamlines in two sections (z∗=0.01 section and r∗=0.92 section) of another two conditions. The values of λT and β0 of the two conditions are both set as 0.28 and 0.8, the Ra are 0.1 and 0.3, respectively.Figure 13
The swirl ratio contours and streamlines in two sections (z∗=0.01 and r∗=0.92) under the condition λT=0.28, β0=0.8. (a) Ra=0.1. (b) Ra=0.3.Through comparison between Figure13(a) and Figure 12, both the axial velocity and the tangential velocity of the jet flow at the outlet of the orifice are found to be reduced when Ra is reduced from 0.2 to 0.1 (the accurate velocities under different Ra are shown in Table 3). With the decrease of the axial velocity of the jet flow, the influence region of the jet becomes smaller. With the decrease of the tangential velocity, the jet flow with reverse tangential velocity changes the flow direction quickly under the influence of the main flow. As a result, the vortex originally existing in the z∗=0.01 section disappears, which means the jet depth of the jet flow becomes shallower. The decrease of the tangential velocity and the shallower jet depth caused by the decrease of the jet flow rate increase the swirl ratio in the cavity.Table 3
The velocity at outlet of the orifice under different Ra.
Velocity at the outlet of the orifice (m/s)
Ra
0.1
0.2
0.3
Total velocity
218
364
462
Axial velocity
110
187
247
Tangential velocity
188
312
390The comparison between Figure13(b) and Figure 12 shows that both the axial velocity and the tangential velocity of the jet flow increase when Ra increases. Therefore, the jet depth of the jet flow increases, the vortex of the z∗=0.01 section becomes larger and more complicated, and the radial area affected by the jet correspondingly becomes larger. Because of the above reasons, the swirl ratio in the cavity is greatly reduced, even to a negative value.


### 3.2.2. The Effect on the Pressure Loss

Figures14(a)–14(d) show the static pressure contours in the rotating disk of the cavity without and with swirl-controlled orifice. As shown in Figure 14(a), the static pressure distribution of the rotating disk is axisymmetric at all the radii when there is no swirl-controlled orifice in the cavity. However, for the cavity with swirl-controlled orifice shown in Figure 14(b), the static pressure of the rotating disk is nonuniformly distributed in the circumferential direction near the radial position of the orifice because of the influence of the jet flow from the orifice. The stagnation of the high-speed jet flow on the rotating disk causes the local high pressure zone, and the complex three-dimensional vortex caused by the jet gives rise to the low pressure recirculation zone. With the increase of Ra from 0.1 to 0.3, shown in Figures 14(b)–14(d), the influence area of the jet flow from the orifice increases, and thus, the uneven pressure region increases.Figure 14
The static pressure contours in the rotating disk of the cavity: (a) without orifice; (b) with orifice,Ra=0.1; (c) with orifice, Ra=0.2; (d) with orifice, Ra=0.3.However, as the flow develops radially inward, the main flow and the jet flow are fully blended; the static pressure distribution of the rotating wall becomes axisymmetric in the low radius region. It can be seen from Figure15 that under different conditions, there is a core region with a constant swirl ratio in the r∗=0.55 section. In addition, the radial velocity of the core zone is relatively small comparing with the tangential velocity. Therefore, it can be considered that the flow satisfies the simple radial equilibrium equation, which means the radial distribution of pressure in the cavity is decided by the central core swirl ratio β. The above results prove the conclusion made in the flow structure analysis that the flow structure at low radius in the impeller rear cavity with swirl-controlled orifice is of Batchelor type.Figure 15
The axial variations of swirl ratio and radial velocity atr∗=0.55 radius under conditions with different Ra and β0.Figures16(a) and 16(b) show the comparisons between the variation of the outlet swirl ratio βoutlet and the outlet pressure loss Cp1 with β0 of the impeller rear cavity with swirl-controlled orifice and the variation of βoutlet and Cp1 with β0 of the cavity without orifice.Figure 16
The comparisons between the variations ofβoutlet and Cp1 with β0 of the impeller rear cavity with swirl-controlled orifice and those of the cavity without orifice.
(a)
βoutlet
(b)
Cp1It can be seen from Figure16(a) that βoutlet increases with the increase of β0 regardless of whether there is swirl-controlled orifice in the cavity. When β0 is in the range of 0~0.8, βoutlet of the cavity with swirl-controlled orifice is smaller than that of the cavity without orifice and decreases as Ra increases. For the cases whose Ra increases to 0.3, βoutlet decreases to a negative value for low β0 conditions.It can be seen from Figure16(b) that Cp1 of the cavity with swirl-controlled orifice is smaller than that of the cavity without orifice and decreases with increasing Ra when Ra is in the range of 0.1~0.2, β0 is in the range of 0~0.8. However, when Ra increases to 0.3, although Cp1 on the condition with high β0 is still smaller than that of the condition with Ra=0.2, Cp1 on the condition with low β0 is bigger than that of the condition with Ra=0.2.The reason for the inconsistency between the variations ofCp1 and βoutlet with β0, for the conditions with Ra=0.3, β0<0.4, is that the flow at the low radius, where it is away from the orifice, satisfies the simple radial equilibrium equation −dp∗/dr∗=2β2r∗, which means the radial distribution of pressure in the cavity is decided by the absolute value distribution of central core swirl ratio β. When Ra=0.3, β0<0.4, although βoutlet is reduced (reduced to a negative value), its absolute value is actually increased (shown in Figure 16(a)), and thus, Cp1 increases.Because of the important impact of the static pressure distribution in the cavity on the high-pressure rotating assembly axial load, further researches of the static pressure and swirl ratio distributions have been done.Figures17 and 18 show the contrasts of the radial distribution of swirl ratio and average static pressure in the cavity with and without swirl-controlled orifice on the same conditions. Figures 17 and 18 show the comparisons of cases with λT=0.28 and β0=0.8, 0, respectively. As shown in Figure 17, when β0=0.8, due to the mixing effect of the reverse swirling jet flow at the outlet of the orifice, the main flow β is smaller than that of the cavity without orifice, and the larger Ra is, the lower main flow β is. Thus, the decrease of the main flow β leads to the reduction of Cp. In addition, the flow is very complicated due to the strong influence of the jet at the exit of the orifice when Ra is large and thus causes the fluctuation of the radial distribution of β and the drastic increase of local Cp. However, as the flow develops radially inward, the vorticity gradually disappears and Cp decreases.Figure 17
The contrasts of the radial distribution of average static pressure andβ in the cavity with and without swirl-controlled orifice when λT=0.28 and β0=0.8.
(a)
β
(b)
CpFigure 18
The contrasts of the radial variation of average static pressure andβ in the cavity with and without swirl-controlled orifice when λT=0.28 and β0=0.
(a)
β
(b)
CpAs shown in Figure18, when β0=0, the main flow β is also reduced under the influence of the jet, and the larger Ra is, the lower main flow β is. The difference between the condition with β0=0 and the condition with β0=0.8 is that under the influence of the jet, main flow β becomes a negative value and will decrease as the flow develops radially inwards (which means the increase of the absolute value of β) when Ra is large. Therefore, the increase in the absolute value of the main flow β leads to the increase of Cp.


### 3.2.3. The Influence of Geometry Parameters of the Swirl-Controlled Orifice

The swirl-controlled orifice arranged on the stationary wall introduces the reverse swirling flow to mix with the high swirling main flow so that the swirl ratio of the main flow is greatly reduced and the deswirl effect is achieved. For swirl-controlled orifice, the geometry parameters which will influence the deswirl effect include the number, length, diameter, orientation, and radial position. In the current paper, the angle between the orifice axial and the tangential direction and the radial position are discussed to investigate their effects on the swirl ratio and static pressure distributions in the cavity.(1) The Orientation. Figures 19(a) and 19(b) show the variation of βoutlet and Cp1 with β0 when λT=0.28, Ra=0.2 of the cavity without and with three different swirl-controlled orifices whose angle α between the axial and the tangential directions is 30°, 45°, and 60°, respectively. For all the cavities, the change rule of Cp1 with β0 is the same as that of βoutlet with β0; when β0 is small, α increases from 30° to 45°, βoutlet increases, α continues to increase from 45° to 60°, and βoutlet is basically unchanged; when β0 is large, βoutlet gradually increases with increasing α.Figure 19
The variation ofβoutlet and Cp1 with β0 of the impeller rear cavity without and with three different orifices whose α is 30°, 45°, and 60°, respectively.
(a)
βoutlet
(b)
Cp1Figures20(a) and 20(b) show contrasts of the radial distribution of the average β and Cp in the cavity without and with different orifices of different orientations under the condition Ra=0.28 and β0=0.4. When there is a swirl-controlled orifice, β near the orifice shows a sudden drop. When α is 30°, β decreases the most; when α=45° and α=60°, β decreases substantially the same, which eventually leads to the variation law of βoutlet as shown in Figure 19(a). However, for the radial variation of Cp shown in Figure 20(b), Cp near the orifice increases instead because of the pressure loss of the mixing process. When α=30°, the area affected by the jet is significantly larger than that of α=45° and α=60°, and Cp is larger; as the flow progresses downward, the mixing is completed, and the flow field eventually becomes uniform. At this time, the radial variation of Cp is determined by β, so Cp1 and βoutlet change in the same manner.Figure 20
The contrasts between the radial distribution ofβ and Cp in cavity without and with different orifices of different α under the condition Ra=0.2 and β0=0.8.
(a)
β
(b)
CpFigures21(a)–21(c) show the streamlines and velocity contours in two sections (z∗=0.01 section and r∗=0.92 section) of the cavity with three different orifices of three orientations 30°, 45°, and 60°. It can be seen from the figure that when Ra is the same, the larger the angle is, the smaller the tangential velocity of jet flow is and the larger the axial velocity is. The decrease of the tangential velocity of the jet causes the weakening of the deswirl effect; the increase of the axial velocity of the jet causes more outlet flow of the orifice to be sprayed and stagnated on the rotating wall which means the influence of the jet on the mainstream is weakened. However, for the condition of Ra=0.2 and β0=0.4, when the angle increases to 45°, the jet flow has already all been sprayed on the rotating wall, the increasing angle (from 45° to 60°) has little effect on the flow field.Figure 21
The velocity contours and streamlines in two sections (z∗=0.01 and r∗=0.92) under the condition Ra=0.2, β0=0.4.
(a)
(b)
(c)In summary, when Ra is equal and the angle of the swirl-controlled orifice is small, the tangential velocity of the jet flow decreases as the angle increases, the deswirl effect of the jet on the mainstream is weakened; therefore,βoutlet and Cp1 gradually increase with the increase of angle. When the angle increases to a certain value, the jet flow has already all sprayed on the rotating wall; βoutlet and Cp1 are basically unchanged with increasing angle.(2) Radial Position. Figures 22(a) and 22(b) show the variation of βoutlet and Cp1 with β0 when λT=0.28, Ra=0.1, without and with four different swirl-controlled orifices whose nondimensional radial position H=RO/R is 0.72, 0.83, 0.92, and 0.97, respectively. It can be seen from the figure that when Ra=0.1 and β0 is in the range of 0~0.8, the radial position H of the swirl-controlled orifice has little impact on βoutlet and Cp1. Under different H, βoutlet and Cp1 are basically equal.Figure 22
The variation ofβoutlet and Cp1 with β0 of the impeller rear cavity without and with four different orifices whose radial position H is 0.72, 0.83, 0.92, and 0.97, respectively.
(a)
βoutlet
(b)
Cp1Figures23(a) and 23(b) show contrasts of the radial distribution of the average β and Cp in cavity with no orifice and with four different orifices of different H under the condition of Ra=0.1 and β0=0.8. The figure shows that for the cavity with swirl-controlled orifice, the radial distribution of β and Cp of mainstream in the area before reaching the region near the orifice is the same as that of the cavity without orifice. After reaching the region near the orifice, β and Cp of the mainstream appear to suddenly drop because of the impact by the jet from the orifice. Whether the radial position of the orifice is high or low, the radial distribution of β of the main flow after the mixing of the mainstream and the jet is substantially the same, so βoutlet and Cp1 are substantially equal under different H. For the cavity with different orifices of different H, the unmixed area from the inlet to the orifice increases as H decreases, because the static pressure loss in this area is the same as that of the cavity without orifice; therefore, although H has no effect on Cp1, it will change the static pressure distribution at the high radius of the rotating wall, thus changing the axial load of the rotor assembly. As H decreases, the axial load of the rotor assembly decreases.Figure 23
Comparison between the radial distribution ofβ and Cp in cavity without and with different orifices of different H under the condition Ra=0.1 and β0=0.8.
(a)
β
(b)
CpIn summary, when Ra is equal, regardless of the radial position of the swirl-controlled orifice, the radial distribution of main flow swirl ratio after mixing is the same, the radial position has little effect onβoutlet and Cp1. However, with the decrease of H, the unmixed high static pressure loss area between the inlet and the orifice increases, and the axial load of the rotor assembly decreases. Therefore, if the axial load of the rotor assembly needs to be adjusted without changing the outlet static pressure of the cavity, the adjustment of the radial position of the swirl-controlled orifice is a way to achieve it.


## 3.2.1. The Effect on the Flow Structure

The flow structure of the cavity with swirl-controlled orifice under the conditionλT=0.28, β0=0, and Ra=0.2 is analyzed. As shown in Figure 12, four sections are selected from the cavity to draw the streamlines, swirl ratio contours, and static pressure contours: the r-z section (section A), the section with z∗=0.01 (the middle yellow section between the rotor and the stator at the highest radius, section B), the section with r∗=0.92 (the green section whose radius is the same as the center of the orifice, section C), and the section with r∗=0.55 (the red section at the middle of the large clearance cavity, section D).Figure 12
The swirl ratio and static pressure contours and streamlines in different sections of cavity with swirl-controlled orifice under the conditionλT=0.28, β0=0.8, and Ra=0.2. (a) Sections schematic. (b) r∗=0.55 (section D). (c) r-z section. (d) z∗=0.01 (section B). (e) r∗=0.092 (section C).It can be seen from Figure12 that the jet is formed at the outlet of the orifice and jetted toward the rotating disk at a high speed which will suppress the centrifugal pumping effect and thus thinning the boundary layer of the rotating wall. In the current paper, the orifices on the stator extend axially and tangentially in a direction substantially opposite to the rotating direction of the rotor; thus, the high-speed jet at the exit of the orifice has a high reverse tangential speed. Therefore, when the main flow is mixed with the jet flow, the angular momentum of both pressurized air flows will act on each other and the angular momentum of the total pressurized air contained within the impeller rear cavity will reduce. In the region near the orifice, due to the existence of the complex three-dimensional vortex, the flow is nonaxisymmetric and completely different from the Batchelor flow pattern. As the flow develops inward, the mixing between main flow and jet flow becomes more and more complete; the three-dimensional vortex gradually disappears. Meanwhile, the flow structure in the cavity becomes the Batchelor flow pattern again, shown as the swirl ratio and static pressure contours in the r∗=0.55 section which indicate the swirl ratio and static pressure are substantially constant along the axial direction.When the mass flow rate ratio Ra is changed, the flow structure in the impeller rear cavity changes. Figures13(a) and 13(b) show the swirl ratio contours and streamlines in two sections (z∗=0.01 section and r∗=0.92 section) of another two conditions. The values of λT and β0 of the two conditions are both set as 0.28 and 0.8, the Ra are 0.1 and 0.3, respectively.Figure 13
The swirl ratio contours and streamlines in two sections (z∗=0.01 and r∗=0.92) under the condition λT=0.28, β0=0.8. (a) Ra=0.1. (b) Ra=0.3.Through comparison between Figure13(a) and Figure 12, both the axial velocity and the tangential velocity of the jet flow at the outlet of the orifice are found to be reduced when Ra is reduced from 0.2 to 0.1 (the accurate velocities under different Ra are shown in Table 3). With the decrease of the axial velocity of the jet flow, the influence region of the jet becomes smaller. With the decrease of the tangential velocity, the jet flow with reverse tangential velocity changes the flow direction quickly under the influence of the main flow. As a result, the vortex originally existing in the z∗=0.01 section disappears, which means the jet depth of the jet flow becomes shallower. The decrease of the tangential velocity and the shallower jet depth caused by the decrease of the jet flow rate increase the swirl ratio in the cavity.Table 3
The velocity at outlet of the orifice under different Ra.
Velocity at the outlet of the orifice (m/s)
Ra
0.1
0.2
0.3
Total velocity
218
364
462
Axial velocity
110
187
247
Tangential velocity
188
312
390The comparison between Figure13(b) and Figure 12 shows that both the axial velocity and the tangential velocity of the jet flow increase when Ra increases. Therefore, the jet depth of the jet flow increases, the vortex of the z∗=0.01 section becomes larger and more complicated, and the radial area affected by the jet correspondingly becomes larger. Because of the above reasons, the swirl ratio in the cavity is greatly reduced, even to a negative value.


## 3.2.2. The Effect on the Pressure Loss

Figures14(a)–14(d) show the static pressure contours in the rotating disk of the cavity without and with swirl-controlled orifice. As shown in Figure 14(a), the static pressure distribution of the rotating disk is axisymmetric at all the radii when there is no swirl-controlled orifice in the cavity. However, for the cavity with swirl-controlled orifice shown in Figure 14(b), the static pressure of the rotating disk is nonuniformly distributed in the circumferential direction near the radial position of the orifice because of the influence of the jet flow from the orifice. The stagnation of the high-speed jet flow on the rotating disk causes the local high pressure zone, and the complex three-dimensional vortex caused by the jet gives rise to the low pressure recirculation zone. With the increase of Ra from 0.1 to 0.3, shown in Figures 14(b)–14(d), the influence area of the jet flow from the orifice increases, and thus, the uneven pressure region increases.Figure 14
The static pressure contours in the rotating disk of the cavity: (a) without orifice; (b) with orifice,Ra=0.1; (c) with orifice, Ra=0.2; (d) with orifice, Ra=0.3.However, as the flow develops radially inward, the main flow and the jet flow are fully blended; the static pressure distribution of the rotating wall becomes axisymmetric in the low radius region. It can be seen from Figure15 that under different conditions, there is a core region with a constant swirl ratio in the r∗=0.55 section. In addition, the radial velocity of the core zone is relatively small comparing with the tangential velocity. Therefore, it can be considered that the flow satisfies the simple radial equilibrium equation, which means the radial distribution of pressure in the cavity is decided by the central core swirl ratio β. The above results prove the conclusion made in the flow structure analysis that the flow structure at low radius in the impeller rear cavity with swirl-controlled orifice is of Batchelor type.Figure 15
The axial variations of swirl ratio and radial velocity atr∗=0.55 radius under conditions with different Ra and β0.Figures16(a) and 16(b) show the comparisons between the variation of the outlet swirl ratio βoutlet and the outlet pressure loss Cp1 with β0 of the impeller rear cavity with swirl-controlled orifice and the variation of βoutlet and Cp1 with β0 of the cavity without orifice.Figure 16
The comparisons between the variations ofβoutlet and Cp1 with β0 of the impeller rear cavity with swirl-controlled orifice and those of the cavity without orifice.
(a)
βoutlet
(b)
Cp1It can be seen from Figure16(a) that βoutlet increases with the increase of β0 regardless of whether there is swirl-controlled orifice in the cavity. When β0 is in the range of 0~0.8, βoutlet of the cavity with swirl-controlled orifice is smaller than that of the cavity without orifice and decreases as Ra increases. For the cases whose Ra increases to 0.3, βoutlet decreases to a negative value for low β0 conditions.It can be seen from Figure16(b) that Cp1 of the cavity with swirl-controlled orifice is smaller than that of the cavity without orifice and decreases with increasing Ra when Ra is in the range of 0.1~0.2, β0 is in the range of 0~0.8. However, when Ra increases to 0.3, although Cp1 on the condition with high β0 is still smaller than that of the condition with Ra=0.2, Cp1 on the condition with low β0 is bigger than that of the condition with Ra=0.2.The reason for the inconsistency between the variations ofCp1 and βoutlet with β0, for the conditions with Ra=0.3, β0<0.4, is that the flow at the low radius, where it is away from the orifice, satisfies the simple radial equilibrium equation −dp∗/dr∗=2β2r∗, which means the radial distribution of pressure in the cavity is decided by the absolute value distribution of central core swirl ratio β. When Ra=0.3, β0<0.4, although βoutlet is reduced (reduced to a negative value), its absolute value is actually increased (shown in Figure 16(a)), and thus, Cp1 increases.Because of the important impact of the static pressure distribution in the cavity on the high-pressure rotating assembly axial load, further researches of the static pressure and swirl ratio distributions have been done.Figures17 and 18 show the contrasts of the radial distribution of swirl ratio and average static pressure in the cavity with and without swirl-controlled orifice on the same conditions. Figures 17 and 18 show the comparisons of cases with λT=0.28 and β0=0.8, 0, respectively. As shown in Figure 17, when β0=0.8, due to the mixing effect of the reverse swirling jet flow at the outlet of the orifice, the main flow β is smaller than that of the cavity without orifice, and the larger Ra is, the lower main flow β is. Thus, the decrease of the main flow β leads to the reduction of Cp. In addition, the flow is very complicated due to the strong influence of the jet at the exit of the orifice when Ra is large and thus causes the fluctuation of the radial distribution of β and the drastic increase of local Cp. However, as the flow develops radially inward, the vorticity gradually disappears and Cp decreases.Figure 17
The contrasts of the radial distribution of average static pressure andβ in the cavity with and without swirl-controlled orifice when λT=0.28 and β0=0.8.
(a)
β
(b)
CpFigure 18
The contrasts of the radial variation of average static pressure andβ in the cavity with and without swirl-controlled orifice when λT=0.28 and β0=0.
(a)
β
(b)
CpAs shown in Figure18, when β0=0, the main flow β is also reduced under the influence of the jet, and the larger Ra is, the lower main flow β is. The difference between the condition with β0=0 and the condition with β0=0.8 is that under the influence of the jet, main flow β becomes a negative value and will decrease as the flow develops radially inwards (which means the increase of the absolute value of β) when Ra is large. Therefore, the increase in the absolute value of the main flow β leads to the increase of Cp.


## 3.2.3. The Influence of Geometry Parameters of the Swirl-Controlled Orifice

The swirl-controlled orifice arranged on the stationary wall introduces the reverse swirling flow to mix with the high swirling main flow so that the swirl ratio of the main flow is greatly reduced and the deswirl effect is achieved. For swirl-controlled orifice, the geometry parameters which will influence the deswirl effect include the number, length, diameter, orientation, and radial position. In the current paper, the angle between the orifice axial and the tangential direction and the radial position are discussed to investigate their effects on the swirl ratio and static pressure distributions in the cavity.(1) The Orientation. Figures 19(a) and 19(b) show the variation of βoutlet and Cp1 with β0 when λT=0.28, Ra=0.2 of the cavity without and with three different swirl-controlled orifices whose angle α between the axial and the tangential directions is 30°, 45°, and 60°, respectively. For all the cavities, the change rule of Cp1 with β0 is the same as that of βoutlet with β0; when β0 is small, α increases from 30° to 45°, βoutlet increases, α continues to increase from 45° to 60°, and βoutlet is basically unchanged; when β0 is large, βoutlet gradually increases with increasing α.Figure 19
The variation ofβoutlet and Cp1 with β0 of the impeller rear cavity without and with three different orifices whose α is 30°, 45°, and 60°, respectively.
(a)
βoutlet
(b)
Cp1Figures20(a) and 20(b) show contrasts of the radial distribution of the average β and Cp in the cavity without and with different orifices of different orientations under the condition Ra=0.28 and β0=0.4. When there is a swirl-controlled orifice, β near the orifice shows a sudden drop. When α is 30°, β decreases the most; when α=45° and α=60°, β decreases substantially the same, which eventually leads to the variation law of βoutlet as shown in Figure 19(a). However, for the radial variation of Cp shown in Figure 20(b), Cp near the orifice increases instead because of the pressure loss of the mixing process. When α=30°, the area affected by the jet is significantly larger than that of α=45° and α=60°, and Cp is larger; as the flow progresses downward, the mixing is completed, and the flow field eventually becomes uniform. At this time, the radial variation of Cp is determined by β, so Cp1 and βoutlet change in the same manner.Figure 20
The contrasts between the radial distribution ofβ and Cp in cavity without and with different orifices of different α under the condition Ra=0.2 and β0=0.8.
(a)
β
(b)
CpFigures21(a)–21(c) show the streamlines and velocity contours in two sections (z∗=0.01 section and r∗=0.92 section) of the cavity with three different orifices of three orientations 30°, 45°, and 60°. It can be seen from the figure that when Ra is the same, the larger the angle is, the smaller the tangential velocity of jet flow is and the larger the axial velocity is. The decrease of the tangential velocity of the jet causes the weakening of the deswirl effect; the increase of the axial velocity of the jet causes more outlet flow of the orifice to be sprayed and stagnated on the rotating wall which means the influence of the jet on the mainstream is weakened. However, for the condition of Ra=0.2 and β0=0.4, when the angle increases to 45°, the jet flow has already all been sprayed on the rotating wall, the increasing angle (from 45° to 60°) has little effect on the flow field.Figure 21
The velocity contours and streamlines in two sections (z∗=0.01 and r∗=0.92) under the condition Ra=0.2, β0=0.4.
(a)
(b)
(c)In summary, when Ra is equal and the angle of the swirl-controlled orifice is small, the tangential velocity of the jet flow decreases as the angle increases, the deswirl effect of the jet on the mainstream is weakened; therefore,βoutlet and Cp1 gradually increase with the increase of angle. When the angle increases to a certain value, the jet flow has already all sprayed on the rotating wall; βoutlet and Cp1 are basically unchanged with increasing angle.(2) Radial Position. Figures 22(a) and 22(b) show the variation of βoutlet and Cp1 with β0 when λT=0.28, Ra=0.1, without and with four different swirl-controlled orifices whose nondimensional radial position H=RO/R is 0.72, 0.83, 0.92, and 0.97, respectively. It can be seen from the figure that when Ra=0.1 and β0 is in the range of 0~0.8, the radial position H of the swirl-controlled orifice has little impact on βoutlet and Cp1. Under different H, βoutlet and Cp1 are basically equal.Figure 22
The variation ofβoutlet and Cp1 with β0 of the impeller rear cavity without and with four different orifices whose radial position H is 0.72, 0.83, 0.92, and 0.97, respectively.
(a)
βoutlet
(b)
Cp1Figures23(a) and 23(b) show contrasts of the radial distribution of the average β and Cp in cavity with no orifice and with four different orifices of different H under the condition of Ra=0.1 and β0=0.8. The figure shows that for the cavity with swirl-controlled orifice, the radial distribution of β and Cp of mainstream in the area before reaching the region near the orifice is the same as that of the cavity without orifice. After reaching the region near the orifice, β and Cp of the mainstream appear to suddenly drop because of the impact by the jet from the orifice. Whether the radial position of the orifice is high or low, the radial distribution of β of the main flow after the mixing of the mainstream and the jet is substantially the same, so βoutlet and Cp1 are substantially equal under different H. For the cavity with different orifices of different H, the unmixed area from the inlet to the orifice increases as H decreases, because the static pressure loss in this area is the same as that of the cavity without orifice; therefore, although H has no effect on Cp1, it will change the static pressure distribution at the high radius of the rotating wall, thus changing the axial load of the rotor assembly. As H decreases, the axial load of the rotor assembly decreases.Figure 23
Comparison between the radial distribution ofβ and Cp in cavity without and with different orifices of different H under the condition Ra=0.1 and β0=0.8.
(a)
β
(b)
CpIn summary, when Ra is equal, regardless of the radial position of the swirl-controlled orifice, the radial distribution of main flow swirl ratio after mixing is the same, the radial position has little effect onβoutlet and Cp1. However, with the decrease of H, the unmixed high static pressure loss area between the inlet and the orifice increases, and the axial load of the rotor assembly decreases. Therefore, if the axial load of the rotor assembly needs to be adjusted without changing the outlet static pressure of the cavity, the adjustment of the radial position of the swirl-controlled orifice is a way to achieve it.


## 4. Conclusion

Two control methods, namely, baffle and swirl-controlled orifice, were proposed to regulate the pressure loss and distribution in an impeller rear cavity in the author’s previous [15] and the current papers. The numerical simulations were carried out to investigate the control mechanisms of these two methods. The control mechanism of the baffle is that the existence of the big counterclockwise vortex leads to the diminution of the average swirl ratio of cavity [15]. Thus, the pressure loss of cavity with baffle reduces.The swirl-controlled orifice which could deswirl the flow is more effective in regulating the pressure loss and its distribution in impeller rear cavity than baffle. The control mechanism of the swirl-controlled orifice is that the main air swirl ratio is directly reduced by introducing a jet which is from the combustion section and formed by the inclined orifice with a high reverse tangential velocity. However, more attention should be paid on the detailed design of the orifice, for the reason that too much jet flow will reduce the main flow swirl ratio to a negative value whose absolute value might be bigger than that of the cavity without orifice and thus causes the increase of the pressure loss.Furthermore, the influence of geometry parameters of the two methods including the length of baffle, the space between the baffle and rotating disk wall, the orientation, and radial position of swirl-controlled orifice was investigated. Through the researches, the main conclusions are made as follows.When designing the baffle, there is an optimal length to make the static pressure loss in the cavity the smallest. The small amplitude variation of the space between the baffle and the rotating wall and the radial position of the swirl-controlled orifice have little effect on the outlet static pressure loss of the cavity; however, the radial position of the swirl-controlled orifice will change the radial distribution of the static pressure on the rotating wall.



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*Source: 2187975-2020-02-22.xml*