## Abstract

Sweep in a transonic fan is conventionally used to reduce design point losses by inclining the passage shock relative to the incoming flow. However, future low pressure ratio fans operate to lower Mach numbers meaning the role of sweep at cruise is diminished. Instead, sweep might be repurposed to improve the performance of critical high Mach number off-design conditions such as high angle of attack (AOA). In this article, we use unsteady computational fluid dynamics to compare two transonic low pressure ratio fans, one radially stacked and one highly swept, coupled to a short intake design, at the high AOA flight condition. The AOA considered is 35 deg, which is sufficient to separate the intake bottom lip. The midspan of the swept fan was shifted upstream to add positive sweep to the outer span. Based on previous design experience, it was hypothesized that the swept fan would reduce transonic losses when operating at high AOA. However, it was found that the swept fan increased the rotor loss by 24% relative to the radial fan. Loss was increased through two key mechanisms. (i) Rotor choking: flow is redistributed around the intake separation and enters the rotor midspan with high Mach numbers. Sweeping the fan upstream reduced the effective intake length, which increased the inlet relative Mach number and amplified choking losses. (ii): Rotor-separation interaction (RSI): the rotor tip experiences low mass flow inside the separation, which increases the pressure rise across the casing to a point where the casing boundary layer separates. The swept fan diffused the casing streamtube, causing the casing separation to increase in size and persist in the passage for longer. High RSI loss indicated that the swept fan was operating closer to the rotating stall point.

## 1 Introduction

Future civil turbofan engines strive toward lower fan pressure ratios to improve propulsive efficiency. However, the cost of a low pressure ratio fan is a large engine diameter, which increases the system weight and drag. A way to mitigate these penalties is to shorten the axial length of the engine intake [1]. Yet, a key disadvantage of a short intake is that the flow will likely separate during sharp climb maneuvers when the aircraft angle of attack (AOA) is high. Current fans are not designed to ingest an intake separation at high AOA, and their capacity to deliver sufficient thrust would be compromised.

Future low pressure ratio fans should be designed to maintain pressure rise with an intake separation at high AOA so that the cruise fuel burn benefits of a short intake can be exploited. Reference [2] shows that the pressure rise at high AOA is limited by two key loss mechanisms that warrant the attention of fan designers: (i) rotor choking and (ii) rotor–separation interaction (RSI). These mechanisms are illustrated in Fig. 1. Both mechanisms occur in the lower half of the intake.

Fig. 1
Fig. 1
Close modal

(i) Rotor choking loss: Flow is accelerated around the intake bottom lip and is terminated by a strong shock that separates the flow entering the rotor tip. The intake flow is redistributed around the separation and enters the rotor midspan with high Mach numbers. Consequently, the midspan passage shock is fully swallowed, indicative of choked operation, leading to high loss. Previous studies have successfully reduced choking losses by weakening the passage shock. One method is to “open” the blade leading edge to increase the flow capacity and delay the onset of choking [1]. Another approach is to reduce the midspan camber to alleviate the pre-shock Mach number [2].

(ii) Rotor–separation interaction: RSI is the loss generated in the rotor tip and on the casing when passing through the intake separation. The rotor tip experiences high positive incidence [3], which separates the boundary layer on the blade tip and casing. These separations, and the loss they generate, are larger in fans designed with high tip static pressure rise [2].

In this article, we consider the effect of the fan rotor sweep design on these two high AOA fan loss mechanisms. Sweep is conventionally used to improve the design point losses by inclining the passage shock relative to the incoming flow. However, low pressure ratio fans operate at lower Mach numbers meaning the role of sweep at cruise is diminished [4]. As a result, sweep might be repurposed to improve off-design conditions such as high AOA. This article compares two low pressure ratio fan designs, one radially stacked and one highly swept, coupled to a short intake design at the separated high AOA flight condition. Analysis is conducted using unsteady, full annulus CFD.

In the swept fan design, the midspan was shifted upstream to add positive sweep to the outer span. Based on design wisdom of legacy high pressure ratio fans, it was hypothesized that this design change would reduce high Mach number choking losses relative to a radial fan. However, it was found that the swept fan generated 24% higher rotor loss than the radial fan. Contributing to this increase in loss were three key aerodynamic effects of sweep on the fan–intake flow, described by Captions (a)–(c) in Fig. 1.

First, in a compact fan–intake configuration, forward sweep effectively reduces the intake length. This was shown to increase the relative Mach number entering the swept fan, which outweighed any shock inclination benefits and amplified choking losses. Second, the swept fan redistributed the upstream intake bulk flow, further increasing the rotor inlet Mach number, swirl, and radial flow velocity distortion. Finally, we found that positive tip sweep worsened RSI loss. When operating inside the separation, the swept fan radially diffused the casing streamtube leading to a stronger rotor casing separation.

## 2 Numerical Methodology

The numerical methodology and CFD setup (Turbostream solver [5]) is identical to that described in Ref. [2], where more detailed information can be found. The numerical method has been extensively validated against test data of similar cases of fans running with inlet distortion [6,7].

Unsteady Reynolds-averaged Navier–Stokes CFD is used to simulate the high AOA condition. A schematic of the numerical domain used for the high AOA simulations is shown in Fig. 2(a). It consists of a fan–intake system situated in a large freestream environment. Inlet flow properties are defined far upstream of the engine at station 1. Station 2 is a constant axial plane located in the intake, 0.1 of the fan diameter upstream of the rotor tip. Stations 3 and 4 are curved planes that closely follow the rotor leading and trailing edges, respectively. Stations 5c and 5bp are located downstream of the core and bypass stators, respectively.

Fig. 2
Fig. 2
Close modal

The boundary conditions are defined at the maximum climb operating condition, altitude of 15,000 ft, and freestream Mach number of 0.3. The fan speed is approximately 8% higher than the cruise condition. The fan operating condition is matched to the working line by iterating the area of downstream choked core and bypass nozzles. The AOA value considered is αy,1 = 35 deg, which is large enough to produce a substantial lip separation.

The short intake geometry has a length-to-diameter ratio, L/D = 0.35 and was provided by Rolls-Royce plc. Two fan rotor geometries are considered: a radial fan (RF) and a swept fan (SF). For reference, the RF is identical to the design named “Fan A” in Ref. [2]. Both rotors were first designed in steady, clean flow (i.e., αy,1 = 0 deg), referring to the axisymmetric straight inlet duct domain shown in Fig. 2(b). The downstream bypass/core stators and the hub/casing lines are identical for both rotor designs.

## 3 Sweep Design Methodology

A comparison of the RF and SF designs is shown in the fan–intake environment in Fig. 2(a) and in isolation in Fig. 2(b). The midspan of the SF was shifted upstream to add positive sweep to the outer part of the span. A comparison of the blade sections at 50% span is shown in Fig. 3. Sweep was implemented by displacing the SF sections along the chord line, commonly termed “true sweep,” denoted v3. At 50% span, the SF is displaced by roughly a quarter of the chord upstream. Lean, defined as the displacement perpendicular to the chord line, is the same for both fans.

Fig. 3
Fig. 3
Close modal

Shifting the leading edge axial coordinate, x3 upstream inadvertently increases the inlet area of the SF and therefore, the choking flow capacity. Arguably, this desirable effect is a natural consequence of the blade stacking. However, increased flow capacity is known to reduce losses at high AOA and would collude the role of true sweep. Hence, it was necessary to correct the flow capacity by increasing the blade inlet angle (i.e., “close down”) of the SF midspan sections, as shown in Fig. 3. The blade exit angle was held fixed to maintain constant work input at the design point.

Radial profiles of v3 and the aerodynamic sweep angle Λ3 are plotted in Fig. 4. The mathematical definition of Λ3, first used in Ref. [8], can be found in the appendix of this paper. Positive Λ3 is defined when v3 is decreasing toward the casing. The SF was designed to a maximum value of Λ3 = +21 deg at 80% span. This radial height corresponds to the periphery of the intake separation at αy,1 = 35 deg where the inlet Mach numbers are highest and therefore, where the expected effect of sweep is the strongest. Strictly speaking, the RF outer span is designed with slight negative Λ3 at the casing.

Fig. 4
Fig. 4
Close modal

The value of x3 is also an important system-level design feature because it trades directly with the intake length. Figure 4(a) shows the SF extends axially up to 18% of the blade span upstream relative to the hub point. This equates to 19.4% of the intake length or 0.068 L/D. Hence, when coupled to the SF, the average intake length is effectively shorter. It will be shown that reduced effective intake length increases the level of inlet distortion and the choking losses at high AOA.

Aside from sweep, all other aspects of the SF design are kept the same as the RF where possible. At a one-dimensional level, both fans were designed to identical pressure ratio, mass flow, choking flow capacity, and nominally equal efficiency ($±0.3%$). The four corner points of the rotor are held fixed to maintain a common intake and spinner design with the RF. Along the span, both fans were designed to the same radial pressure ratio [2] and chord distribution. These design constraints mean the SF may not be a mechanically feasible design, but they do ensure a fair aerodynamic comparison, which is the objective of this study.

## 4 Loss Breakdown

### 4.1 Overall Fan–Intake Performance.

The mass-averaged pressure ratio characteristic measured across the entire fan stage–intake system, from stations 1–5, is shown in Fig. 5. The values are normalized by the clean flow design point condition. The fan-alone characteristics confirm that the two fans are designed with identical flow capacity. Furthermore, the SF exhibits reduced stall margin when operating with clean inlet flow. This is a natural artifact of a positive tip sweep design [9], and therefore, no attempt was made to restore the SF stall margin.

Fig. 5
Fig. 5
Close modal

At high AOA, the pressure ratio of the RF deteriorates by 3.8% relative to the clean flow design condition. This is due to a sharp increase in rotor loss when running with an intake separation. The mass flow of the RF also reduces by 5% because the choked nozzle exit boundary conditions operate to a fixed flow function, $m˙cPT0/AP0$. By comparison, the SF experiences a 4.4% and 5.8% reduction in pressure ratio and flow, respectively. This ultimately means the SF produces less thrust than the RF at high AOA.

### 4.2 Fan–Intake System Loss Breakdown.

The system performance deteriorates at high AOA because of an increase in loss generation across the intake and fan stage. Figure 6 presents the total fan–intake system loss and the breakdown of loss generated across each component. Loss is defined by the entropy function: 1 − eΔs/R, which is mass-averaged across the relevant station planes. The total system loss of the RF and SF operating at high AOA increases by 91% and 127%, respectively, relative to the clean flow design point. The loss breakdown shows that high AOA penalizes all components, but the dominant source of loss is the rotor, which contributes to roughly two-thirds of the total system loss. The key result of this study is that the SF generates 24% higher rotor loss than the RF at high AOA.

Fig. 6
Fig. 6
Close modal

Upstream of the rotor, the lip separation increases the intake loss. However, the contribution of the intake to the total loss is small ($<10%$), and so the intake itself does not significantly deteriorate the system pressure ratio. Instead, the intake should be considered primarily as a flow distortion generator to the rotor. Downstream of the rotor, the core and bypass stators generate roughly a quarter of the total system loss at high AOA. Comparing the two designs at high AOA, the stator losses scale with the rotor loss. This result indicates the flow exiting the SF rotor is less favorable, and subsequently, the stators operate further from design intent.

### 4.3 Rotor Loss Breakdown.

Substantial rotor loss at high AOA warrants further investigation. The rotor loss is categorized into two spatially distinct mechanisms: (i) rotor choking and (ii) RSI. A time-averaged streamline tracking method was used to quantify the contribution of each loss mechanism. Details of the numerical method are described in Ref. [2] based on the work of Ref. [10].

Figure 7 plots the spatial distribution of time-averaged rotor loss (measured between stations 3 and 4) for both fan designs. Loss is plotted against the streamline inlet coordinates to account for the mass redistribution through the rotor. The dashed lines indicate spatial zones (1)–(3), which roughly encompass each loss mechanism. Choking losses are generated primarily in the rotor midspan in the lower half of the intake where the intake Mach numbers are high. RSI losses are generated on the casing as the rotor tip exits the intake separation. The loss within each zone is mass averaged and presented in Fig. 6.

Fig. 7
Fig. 7
Close modal

Choking is the primary loss source at high AOA corresponding to two-thirds of the rotor loss and nearly half of the entire fan-intake system loss. The SF increases choking loss by 21% relative to the RF. RSI is the secondary loss source because it concerns a smaller portion of the total mass flow. Yet, the SF increases RSI loss by 81% relative to the RF and is a key disadvantage of a positive tip sweep fan design. In the following sections, we conduct a flow field analysis of the intake flow and key rotor loss mechanisms to understand why the SF generates more loss than the RF.

## 5 Intake Aerodynamics

A meridional view of the intake Mach number at high AOA with the RF is shown in Fig. 8. The intake flow is categorized into two distinct regions: bulk and separated flow. Generally speaking, the bulk flow distortion causes rotor choking loss and the separated flow distortion causes RSI loss.

Fig. 8
Fig. 8
Close modal

At high AOA, the captured streamtube enters the intake with a vertical velocity component. The short intake cannot turn the bulk streamtube completely axial. This leads to flow asymmetry about the longitudinal axis of the engine, termed “upwash.” Streamtube turning also accelerates the flow around the bottom lip to supersonic Mach numbers. This is terminated by a normal shock, which separates the flow entering the fan tip.

### 5.1 Bulk Flow Aerodynamics.

The time-averaged intake flow, coupled to the RF, at station 2 is shown in Figs. 9(a)9(d). Figure 9(a) shows that streamtube turning generates a positive bottom-to-top static pressure gradient. Figure 9(b) shows that this accelerates the bulk flow in the lower half of the intake and decelerates in the upper half. Figure 9(c) shows upwashing flow is co- or counter-swirling with or against the rotation of the fan creating a swirl velocity distortion pattern. Work input is increased in counter swirling flows, and the fan responds by imposing suction on the right-hand side of Fig. 9(a). Figure 9(d) shows that upwash also causes the intake flow to migrate radially toward the casing in the upper half of the intake and toward the hub in the lower half.

Fig. 9
Fig. 9
Close modal

The difference in the intake flow properties between the two fan designs is shown in Figs. 9(e)9(h). This comparison is performed at a constant axial plane rather than the leading edge (which are located at different positions) to isolate changes in the fan–intake coupling. The SF redistributes the intake flow by changing the intake static pressure field, as shown in Fig. 9(e). Regions of red indicate where intake pressure is higher when coupled to the SF. Fundamentally, fans impose high static pressure on the upstream flow in response to inlet distortion that decreases the work input (e.g., high axial velocity or co-swirling flow), and vice-versa [11]. This principle can be used to explain the differences in intake pressure between the two designs.

A key difference in the flow can be seen in the lower right part of Fig. 9(e), where the SF exhibits a region of higher pressure. This is because the leading edge of the SF is located further upstream where the effects of upwash are stronger. As a result, the mass flow entering the SF in the lower half of the intake increases and the work input reduces relative to the RF. The opposite is true in the upper half of the intake where the mass flow entering the SF is lower and so responds with high work input and lower pressure. As a result of these two effects, the SF redistributes the intake flow from bottom-to-top indicated by arrow A. Figure 9(f) shows that the SF draws higher Mach number in the upper half of the intake and less in the lower half. Hence, bottom-to-top flow redistribution alleviates the mass flow imbalance between the upper and lower halves of the intake.

However, Figs. 9(g) and 9(h) show that bottom-to-top intake flow redistribution amplifies the swirl and radial flow distortion. Enhanced swirl distortion increases the SF work input in the counter-swirl region and reduces the work input in the co-swirl region relative to the RF. Figure 9(e) shows that this creates a left-to-right static pressure gradient, which redistributes mass toward the counter-swirl region, indicated by arrows B and C. Left-to-right flow redistribution further amplifies the bulk flow swirl distortion and increases the Mach number entering the counter-swirl region.

### 5.2 Integral Distortion Indices.

Redistribution of the bulk flow extends axially throughout the intake. This is quantified using integral distortion indices (IDI) [6]. IDI measure how different a particular flow property is from the clean flow design condition. Equation (1) describes how an IDI is calculated for an arbitrary component of velocity, termed $DVϵ$. The L2 norm error between the high AOA and clean flow values is calculated at each (r, θ) coordinate on an axial plane and then integrated. The procedure is then repeated for a range of axial planes throughout the intake.
$DVϵ=1ρ3A3U3,tip∫A([ρVϵ]AOA−[ρVϵ]C)2dA$
(1)

Figures 10(a)10(c) plot absolute Mach number (DM), swirl ($DVθ$), and radial velocity ($DVr$) IDI calculated at axial planes through the intake. For both fans, DM peaks near the intake throat, indicating where the top-to-bottom mass flow imbalance is maximum. Downstream of the throat, the intake diffuses the flow toward design point conditions and DM reduces. By comparison, $DVθ$ and $DVr$ are maximum at the intake lip where the flow has not yet been turned. These metrics reduce as the streamtube is rotated toward the longitudinal axis of the engine. None of the metrics reach zero by station 3 implying residual upwash at the fan face.

Fig. 10
Fig. 10
Close modal

The redistribution effects of the rotor sweep design extend upstream to the intake lip. Consistent with the previous analysis, the SF reduces DM at a constant axial location. However, the SF does not redistribute the flow enough to outweigh a shorter effective intake length and the value of DM at station 3 is 15% higher than the RF. For swirl and radial flow distortion, the redistribution and intake length effects are complimentary. As a result, the SF increases $DVθ$ and $DVr$ by 36% and 34% relative to the RF, respectively.

### 5.3 Separated Flow Aerodynamics.

Figure 9(b) shows that the intake separation is characterized by a severe deficit in flow in the lower half of the intake. Low inlet velocity increases the rotor pressure rise, which is partly achieved by reducing the inlet static pressure, shown at the bottom of Fig. 9(a). Low inlet static pressure redistributes mass, circumferentially and radially, toward the separation. Figure 9(c) shows the rotor tip experiences strong co-swirling flows entering the separation and counter-swirling flows exiting the separation. The latter is a critical region in the flow, where the rotor imparts maximum pressure rise on low momentum inlet flow and is the origin of RSI loss. Radially, the rotor redistributes the bulk flow toward the casing. It will be shown that radial flows play a beneficial role in reducing RSI losses.

The axial development of the separation through the intake is quantified using a total pressure IDI, $DP0$. Total pressure isolates the effect of the separation because redistribution of the bulk flow is an inviscid phenomena [12]. Equation (2) describes how $DP0$ is calculated. In this instance, it was more meaningful to use a mass average and normalize by the inlet total pressure.
$DP0=1ρ3A3Vx3P01∫A([P0]AOA−[P0]C)2dm˙$
(2)

Figure 10(d) plots $DP0$ showing a near-linear growth in the separation as it approaches the fan face. The SF limits the growth of the intake separation because its leading edge is located further upstream than the RF. As a result, the final size of the intake separation at station 3 is, in fact, smaller than the RF. This result demonstrates that the intake separation size and RSI loss (discussed previously in Fig. 6) do not necessarily correlate.

A circumferential distribution of total pressure, mass-averaged over 80–100% span, at station 3 is shown in Fig. 11. The SF reduces the separation peak deficit by 12%. Furthermore, the SF shifts the separation clockwise by 7 deg. This is caused by a circumferential redistribution of the bulk flow streamtube described by arrow D in Fig. 9(e).

Fig. 11
Fig. 11
Close modal

## 6 Rotor Choking Loss

### 6.1 Description of Loss Mechanism and Effect of Sweep.

Turning of the intake bulk flow increases the Mach number entering the lower half of the intake, as shown in Fig. 9(b). Furthermore, flow is redistributed around the intake separation to a smaller flow area, further increasing the inlet Mach number entering the rotor midspan. This leads to passage choking and high loss [2].

Snapshots of loss downstream of the rotor at station 4 are shown in Fig. 12 for the two designs. Intake flow that is redistributed radially around the separation chokes the rotor hub and midspan. Intake flow that is redistributed circumferentially around the separation chokes the rotor outer midspan and tip before it enters the separation. Figure 12(b) shows the SF generates lower choking losses in the hub/lower midspan, but increases outer midspan/tip choking losses as the rotor approaches the separation.

Fig. 12
Fig. 12
Close modal

### 6.2 Linking Choking Loss to Inlet Mach Number and Post-Shock Diffusion.

The flow at two span fractions, 40% and 75%, is investigated in depth to understand the underlying reasons behind a spanwise variation in choking loss between the RF and SF designs. Figure 13 shows circumferential distributions of time-averaged inlet relative Mach number, M3,rel, and rotor loss. Flow properties are plotted against rotor inlet streamline coordinates at station 3.

Fig. 13
Fig. 13
Close modal

Effect of Inlet Mach Number at 75% Span: Figure 13(a) shows the SF ingests higher M3,rel at 75% span between θ3 = 90 − 270 deg, and as a result, Fig. 13(b) shows the SF generates higher loss. This region of the flow corresponds to the periphery of the intake separation where the upstream gradients of Mach number are high, Fig. 8. As a result, M3,rel is especially sensitive to the fan leading edge axial position and increased M3,rel into the SF is due to a reduction in effective intake length. This penalizing effect clearly outweighs any loss benefit related to the inclination of the passage shock in the SF.

The left-to-right intake flow redistribution effect, described in Sec. 6.1, compounds the increase in M3,rel from θ3 = 90 − 140 deg. As a result, the SF chokes earlier than the RF causing the losses to rise at a faster rate. Both M3,rel and loss peak at a similar value for both designs near θ3 = 180 deg. This suggests that both fans have reached their maximum flow capacity, which is, by design, the same.

Effect of Post-Shock Diffusion at 40% Span: Far from the intake separation, the streamwise gradients of Mach number are comparatively small. Both fans experience similar M3,rel, but the SF generates lower loss. The blade suction surface static pressure at θ = 180 deg is shown in Fig. 14. A streamline entering the SF at 40% span experiences reduced diffusion downstream of the passage shock. A weaker adverse pressure gradient accounts for the smaller separation size and lower loss observed in the SF.

Fig. 14
Fig. 14
Close modal

Two factors contribute to a reduction in midspan exit static pressure in the SF. First, Fig. 2(a) shows the trailing edge is shifted upstream. This design change reduces the exit area locally in the midspan and increases the flow velocity toward the trailing edge. Second, it will be shown in the following section that RSI drives radial flow redistribution from the midspan to the casing. This has a beneficial effect of contracting the casing streamtube, but adversely diffuses the midspan streamtube. It will be shown the RF enhances radial flow redistribution, which further diffuses the flow at 40% span.

Consolidating these two effects, it was discussed previously in Fig. 6 that the SF generates higher mass-averaged choking loss. Hence, the loss penalty at 75% span outweighs the loss saving at 40% span. This is for two reasons. First, Fig. 13(b) shows the loss delta at 75% span is nominally larger than at 40% span. Second, the mass flow per unit span is higher at 75% span and thus carries more weight on a mass-averaged basis. In general, the SF trades lower choking loss in the inner span for higher choking loss in the outer span, which is overall detrimental.

## 7 Rotor–Separation Interaction Loss

### 7.1 Description of Loss Mechanism and Effect of Sweep.

The casing flow is investigated in Fig. 15. In this view, the rotor is travelling from right to left. The loss generated during RSI can be split into four chronological phases:

1. Entering the separation, co-swirling flows help keep the rotor pressure rise low, the adverse pressure gradient across the casing is relatively weak and the casing boundary layer remains attached.

2. Progressing through the separation, the rotor pressure rise increases, separating the casing boundary layer leading to high loss generation.

3. Exiting the separation, the rotor experiences counter-swirling flows and the pressure rise is maximum. The casing separation reaches its largest size. The adverse pressure gradient across the casing causes high entropy flow to reverse upstream and interact with the intake separation.

4. After the rotor has fully exited the separation, the rotor pressure rise reduces, the casing boundary layer reattaches and the rotor gradually recovers.

Despite ingesting a slightly smaller intake separation, Fig. 15(b) shows the SF exacerbates the size of the casing separation, loss generation, and upstream flow reversal. Figure 12 shows the SF casing separation persists inside the passage for roughly a quarter of the annulus longer than the RF. Aside from the increased steady losses, delayed rotor recovery after exiting the intake separation is indicative of reduced rotating stall margin [7,13]. Rotating stall can be expected if the rotor does not recover before re-entering the intake separation.

Fig. 15
Fig. 15
Close modal

### 7.2 Linking Rotor–Separation Interaction Loss to Streamtube Contraction Ratio.

The casing separation size and rotor recovery distance are determined by the level of streamtube diffusion during RSI. Diffusion is defined by the casing streamtube contraction ratio (SCR), ρ4V4,rel/ρ3V3,rel and can be quantified using the streamline tracking method.

The combined effect of the intake separation and the rotor sweep design on the casing SCR is complex. Hence, the problem is broken down into two parts. First, the effect of the intake separation on SCR is analyzed using the RF. Second, the effect of sweep is considered where changes to SCR are linked to radial static pressure gradients in the flow.

Effect of the Intake Separation on RF Casing SCR: Figure 16 shows the RF rotor flow when passing through the intake separation at θ3 = 170 deg. Values in clean flow are shown for reference. Figure 16(a) shows the rotor tip responds to the intake separation by imposing suction. As a result, mass is redistributed through the rotor passage shown by the time-averaged streamlines in Fig. 16(c). Low momentum inlet flow is accelerated axially through the passage, and mass is redistributed radially from the midspan to the casing. Both of these redistribution effects strongly contract and add momentum to the casing streamtube. Figure 16(b) shows SCR peaks at a value of 2 near the casing, significantly higher than in the clean flow. High SCR is a natural response of the rotor to the intake separation and acts to alleviate the casing diffusion. This is a beneficial effect that encourages the rotor to recover.

Fig. 16
Fig. 16
Close modal

Effect of the Sweep Design on Casing SCR: Sweep affects the radial mass redistribution through the rotor during RSI. Figure 17(a) quantifies the radius change, r4/r3 of a midspan streamtube defined from 60–80% inlet span. The spike in r4/r3 at θ3 = 170 deg indicates radial mass redistribution from the midspan to the casing. The SF reduces r4/r3, indicating that it adds less momentum to the casing flow. As a result, Figure 17(b) shows the SF exhibits lower casing SCR inside and after exiting the separation. This leads to higher diffusion across the casing line, which drives a stronger casing separation and higher RSI loss.

Fig. 17
Fig. 17
Close modal

There are two reasons why the SF redistributes less mass toward the casing during RSI. The first reason is related to changes in the upstream intake flow. Figure 9(h) shows that the flow enters the SF midspan with higher hub-ward radial velocity in the lower half of the intake. Figure 17(a) shows that this has a broad effect on r4/r3, reducing the SF value from θ3 = 90 − 300 deg.

The second reason is related to the radial static pressure gradients inside the blade row. Figure 18 shows a meridional view of the fan–intake static pressure field at θ3 = 170 deg for both designs. The flow has been time averaged in the absolute frame of reference. Figure 18(a) shows that high incidence inside the separation causes the RF tip passage shock to move upstream to the leading edge. Consequently, the shock line along the outer part of the span is swept in the negative direction. This establishes a radial static pressure gradient, ∂P/∂r inside the blade row that enhances radial mass redistribution from the midspan to the casing. Figure 18(b) shows the positive tip sweep design of the SF counters this effect and the shock line exhibits near-zero sweep. As a result, the SF imposes a weaker ∂P/∂r than the RF. Consequently, Fig. 17(a) shows the SF significantly reduces the radial mass redistribution from the midspan to the casing at θ3 = 170 deg.

Fig. 18
Fig. 18
Close modal

### 7.3 A Generic Design Framework for Rotor–Separation Interaction.

We consolidate the results presented in this article and previous work published by the authors in Ref. [2] into a generic design framework for RSI. Figure 16(c) shows the casing streamtube is shaped like a nozzle. A simple model of this streamtube is illustrated in Fig. 19. The nozzle contraction can be controlled either geometrically with the casing line or aerodynamically with the bounding tip streamline. In Ref. [2], we considered the former and showed that casing lines designed with less contraction recover slowly from the intake separation. By comparison, this article showed that positive sweep radially diffused the bounding aerodynamic streamline, which also led to delayed recovery. These two design studies are aerodynamically equivalent because they both reduced the casing SCR, which increased the casing separation size, rotor recovery distance, and RSI loss.

Fig. 19
Fig. 19
Close modal

It is true that both studies have inadvertently explored negative design changes relative to the RF. This has helped define “keep out zones” in a broader separation-tolerant rotor design methodology. Nevertheless, future design studies should seek to maximize the casing SCR to reduce both RSI loss and the rotor recovery distance.

## 8 Conclusions

This article compared the aerodynamic performance of a radial (RF) and a swept fan (SF) coupled to a short intake at the separated high angle of attack (AOA) condition. Contrary to expectation, the SF generated 24% higher rotor loss than the RF at high AOA. Loss was increased through two key mechanisms: (i) rotor choking and (ii) rotor–separation interaction.

(i) Rotor choking: Flow is redistributed around the separation and enters the rotor with high Mach number. This leads to passage choking and is the dominant loss source at high AOA, contributing to two-thirds of the total rotor loss. Sweep was added to the SF by displacing the midspan forward while maintaining a fixed tip position. This design change inclined the passage shock in the outer span and, based on previous design experience of legacy high speed fans, was expected to reduce loss. However, in modern compact fan–intake configurations, forward sweep considerably reduces the effective intake length. This increased the inlet relative Mach number entering the SF and amplified choking loss.

(ii) Rotor–separation interaction: Inside the intake separation, the rotor tip experiences a combination of low axial and counter swirl velocity. This increases the pressure rise across the casing to a point where the casing boundary layer separates. The RF responded by redistributing mass from the midspan to the casing, adding momentum to the casing streamtube. This alleviated the casing separation size and the RF recovered quickly from the intake separation. By comparison, the SF weakened the radial static pressure gradients in the flow that drive this beneficial effect. Instead, the SF diffused the casing streamtube, which increased the casing separation size and loss. The casing separation also persisted inside the passage for longer, indicating that the SF was operating closer to the stall point.

## Acknowledgment

The authors acknowledge Rolls-Royce plc. and Innovate UK for funding and providing permission to publish this work. Special thanks are given to Turbostream Ltd. for supporting the use of their CFD solver.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The authors attest that all data for this study are included in the paper. Data provided by a third party listed in Acknowledgment.

## Nomenclature

r =

s =

entropy, J/kg/K

v =

displacement along chord line, i.e., “true sweep”

x =

axial coordinate, m

A =

area, m2

D =

fan diameter, m

L =

intake length, m

P =

pressure, Pa

R =

specific gas constant

T =

temperature, K

U =

V =

velocity, m/s

$m˙$ =

mass flowrate, kg/s

M =

Mach number

αy,1 =

angle of attack

β =

relative swirl flow angle

ζ =

θ =

circumferential coordinate

ρ =

density, kg/m3

Ω =

### Subscripts

0 =

total quantity

1/3/4 =

value at the domain inlet/rotor inlet/rotor exit plane

5bp/5c =

value at the bypass/core stator exit plane

C =

value in “clean,” axisymmetric flow at the design point

rel =

value in the rotating reference frame

x/θ/r =

### Appendix: Mathematical Definition of the Aerodynamic Sweep Angle, Adopted From Smith and Yeh (1963)

The most complete definition of the sweep angle in a transonic fan is the angle between the passage shock surface and the local flow vector just upstream in three-dimensional space. However, this approach requires complex shock identification techniques. A simpler approach is to assume that the shock line follows the rotor leading edge. This is largely true apart from in the endwall regions where the shock must intersect the casing perpendicularly [9]. Leading edge quantities are easily obtainable and can provide a useful proxy for sweep during design.

The leading edge aerodynamic sweep angle, Λ3 is shown in Eq. (A1) and is defined as the cross product of the leading edge geometric and passage-wise averaged flow vectors. This definition of sweep was first considered in Ref. [8], where a full derivation of Λ3 can be found. A diagram defining the terms of Eq. (A1) is shown in Fig. 20. The rotor inlet radial and relative swirl flow velocity angles are denoted as ζ3 and β3, respectively.
$Λ3=sin−1[tanζ3+tanμx,3+tanμθ,3tanβ3(1+tan2μx,3+tan2μθ,3)(1+tan2β3+tan2ζ3)]$
(A1)
Geometric parameters such as axial stacking angle, μx,3 and tangential stacking angle, μθ,3 are defined as follows:
$μx,3=tan−1(∂x3∂r3)$
(A2)
$μθ,3=tan−1(∂r3θ3∂r3)$
(A3)
Fig. 20
Fig. 20
Close modal

## References

1.
Peters
,
A.
,
Spakovszky
,
Z. S.
,
Lord
,
W.
, and
Rose
,
B.
,
2015
, “
Ultrashort Nacelles for Low Fan Pressure Ratio Propulsors
,”
ASME J. Turbomach.
,
137
(
2
), p.
021001
.
2.
Mohankumar
,
B.
,
Hall
,
C. A.
, and
Wilson
,
M. J.
,
2021
, “
Fan Aerodynamics With a Short Intake at High Angle of Attack
,”
ASME J. Turbomach.
,
143
(
5
), p.
051003
.
3.
,
N. R.
,
Cao
,
T.
,
Watson
,
R.
, and
Tucker
,
P. G.
,
2019
, “
Toward Future Installations: Mutual Interactions of Short Intakes With Modern High Bypass Fans
,”
ASME J. Turbomach.
,
141
(
1
), p.
081013
.
4.
Moyon
,
F.
,
Wilson
,
M. J.
, and
Schnell
,
R.
,
2016
, “
Low Pressure Ratio Fan Design—Challenges, Fan Design Strategy and Results for Ultra-High Bypass Ratio Engines
,”
Greener Aviation Conference
,
Brussels, Belgium
,
Oct. 11–13
.
5.
Brandvik
,
T.
, and
Pullan
,
G.
,
2011
, “
An Accelerated 3D Navier-Stokes Solver for Flows in Turbomachines
,”
ASME J. Turbomach.
,
133
(
2
), p.
021025
.
6.
Gunn
,
E. J.
,
2015
, “
Aerodynamics of Boundary Layer Ingesting Fans
,” Ph.D. thesis,
University of Cambridge
,
Cambridge, UK
.
7.
Perovic
,
D.
,
Hall
,
C. A.
, and
Gunn
,
E. J.
,
2019
, “
Stall Inception in a Boundary Layer Ingesting Fan
,”
ASME J. Turbomach.
,
141
(
9
), p.
091007
.
8.
Smith
,
L. H.
, and
Yeh
,
H.
,
1963
, “
Sweep and Dihedral Effects in Axial-Flow Turbomachinery
,”
ASME J. Basic. Eng.
,
85
(
3
), pp.
401
414
.
9.
Denton
,
J. D.
, and
Xu
,
L.
,
2002
, “
The Effects of Lean and Sweep on Transonic Fan Performance: A Computational Study
,”
Proceedings of ASME Turbo Expo 2002, Amsterdam, Netherlands
, Paper No. GT2002-30327.
10.
Fidalgo
,
V. J.
,
Hall
,
C. A.
, and
Colin
,
Y.
,
2012
, “
A Study of Fan-Distortion Interaction Within the NASA Rotor 67 Transonic Stage
,”
ASME J. Turbomach.
,
134
(
5
), p.
051011
.
11.
Longley
,
J. P.
, and
Greitzer
,
E. M.
,
1992
, “
Inlet Distortion Effects in Aircraft Propulsion System Integration
,”
AGARD Lecture Series, pp 6-1-6-18
.
12.
Defoe
,
J. J.
,
,
M.
, and
Hall
,
D. K.
,
2018
, “
Fan Performance Scaling With Inlet Distortions
,”
ASME J. Turbomach.
,
140
(
7
), p.
071009
.
13.
Lee
,
K. B.
,
Dodds
,
J.
,
Wilson
,
M.
, and
Vahdati
,
M.
,
2018
, “
Validation of a Numerical Model for Predicting Stalled Flows in a Low-Speed Fan: Part II Unsteady Analysis
,”
ASME J. Turbomach.
,
140
(
5
), p.
051009
.