Impact Statement
Motivated by issues with existing baseball aerodynamics models, this experimental study investigated the influence of small asymmetric surface protrusions on cylinder aerodynamics near the critical Reynolds number. The researchers gathered wind tunnel measurements of the pressure over a circular cylinder with a small triangular bump, which demonstrate that the bump introduces a local favourable and then adverse pressure gradient. This reduces the near-wall momentum of the flow, and for small a bump close to the stagnation point, this develops the boundary layer. When a larger bump is farther from the stagnation point, the boundary layer fully separates from the surface. Across the full range of observations, the bump strongly influences the upstream pressure distribution but has less effect on the downstream pressure distribution. These findings provide a foundation for predicting the pressure distribution and resulting aerodynamic forces on baseballs and offer insights for similar bodies with small asymmetric surface geometries.
1. Introduction
Spoilers, also known as “lift dumpers,” are flow-control surfaces that significantly alter the aerodynamic forces on an airfoil or similar shape by fully separating the attached boundary layer from the suction surface. These control devices are often seen on the upper surface of large aircraft wings, as shown in figure 1(a), and are used to reduce lift for descent or upon landing. A recent study on baseball aerodynamics (Smith et al., Reference Smith, Garrett, Dufour and Francis2024) showed that baseball seams act as spoilers when they lie near a plane through the centre of the ball and perpendicular to the direction of travel of the ball. At specific orientations, this can lead to a net force on a spinning baseball similar to, but in a different direction than, the Magnus effect (Briggs, Reference Briggs1959; Lyu et al., Reference Lyu, Smith, Elliott and Kensrud2022).
Figure 1. (a) Commercial aircraft spoiler deployed at landing to eliminate lift and ensure that the aircraft remains on the ground. (b) A flow visualisation result with vorticity in colour demonstrating a baseball seam acting as a spoiler, indicated by boundary-layer separation and ensuing shear layer at the seam on top. Note that the boundary layer on the bottom side of the ball separates farther downstream.
For the purpose of modelling the effect of baseball seams, it would be convenient to assume that the surface pressure behaves similarly to potential flow up to the separation point and then assumes the wake value. However, attempts to model forces on a baseball in this way, informed by experimentally determined separation points, have not been successful. The present study seeks to elucidate the pressure behaviour up and downstream of a small bump over a similar bluff body. To simplify the problem, a circular, non-spinning cylinder will be studied.
As a canonical flow, circular cylinders have been studied extensively. We will focus on the results for the Reynolds number range near the transition to turbulence. The first modern study on a circular cylinder in cross-flow is from Achenbach (Reference Achenbach1968). The surface pressure and shear stress of a smooth cylinder were measured in a range of Reynolds numbers similar to that of the present work. For Re
$= V_{\infty }D/\nu = 10^5$
, where
$V_\infty$
is the velocity of the free stream,
$D$
is the diameter of the cylinder and
$\nu$
is the kinematic viscosity, they reported a laminar boundary-layer separation near
$\theta =78^\circ$
, where
$\theta =0$
is the stagnation point, as evidenced by the shear stress going to zero and the pressure assuming the base pressure value. For a larger Re of
$2.6 \times 10^5$
, the boundary layers remained laminar, but the separation point moved to
$94^\circ$
. For Re
$= 8.5\times 10^5$
, a laminar separation bubble formed behind the separation at
$94^\circ$
and reattachment. The final separation point was
$147^\circ$
. For Reynolds numbers sufficiently large to cause turbulent boundary layers on the smooth cylinder (Re
$= 3.6\times 10^6$
), the separation point was
$115^\circ$
.
Three years later, Achenbach (Reference Achenbach1971) continued this work with measurements on uniformly roughened cylinders. A rough surface tends to move the “drag crisis,” or the precipitous drop in drag owing to the transition to turbulence of the boundary layers and subsequent reduced wake, to lower values of Reynolds number. As the Reynolds number was increased further, drag was found to increase again to a value that became insensitive to Reynolds number. This final value was found to increase with surface roughness. The surface pressure on a rough cylinder was shown to be strong function of Reynolds number in the range
$1 \times 10^5 \lt$
Re
$\lt 3 \times 10^6$
. The present measurements are within this range.
Igarashi (Reference Igarashi1986) investigated the role of placing circular “tripping” wires on the surface of a circular cylinder in trans-critical cross-flow in a wind tunnel. These trips were placed symmetrically relative to the stagnation and the effects of relative roughness height and Re were measured through measurement of the Strouhal number, surface pressure distributions, smoke flow visualisation and oil film visualisation. These experiments demonstrated that the trips resulted in four “patterns” which are presented in order of increasing Re for a given trip: (i) a laminar separation bubble, boundary-layer reattachment and laminar separation downstream of the reattachment; (ii) a laminar separation bubble, turbulent transition, turbulent boundary-layer reattachment and then turbulent separation; (iii) a laminar separation bubble, turbulent transition, turbulent boundary-layer reattachment and the turbulent separation point moves in the decreasing
$\theta$
direction with increasing Re; and (iv) the turbulent boundary layer separates at the trip. These findings are similar to the findings of this study, but at a lower range of Re and with only symmetric “trips.”
In Nebres & Batill (Reference Nebres and Batill1993), a circular wire was added to the surface of a cylinder to examine the impact on the oscillation frequency of the wake. The surface pressure distribution that resulted from a wire 9 % of the diameter of the cylinder placed at various angles along the surface was also reported for Re
$=3\times 10^4$
. They found that when the wire was close to the stagnation point (
$\lt 43^\circ$
), the wire caused separation and reattachment, leading to a final separation point far downstream than that of a smooth cylinder at this low Reynolds number. With the wire beyond this point, the wire caused boundary-layer separation, similar to the findings of this study.
The effect of roughness on the velocity profile of the boundary layer was reported by Güven et al. (Reference Güven, Farell and Patel1980). Generally, a smooth cylinder with a trip resulted in a more energetic boundary layer near the wall at the point of minimum pressure than the boundary layer on a cylinder with evenly distributed roughness. Similar results are observed for grooved surfaces (Seo et al., Reference Seo, Nam, Han and Hong2013).
Nakamura & Tomonari (Reference Nakamura and Tomonari1982) investigated the difference between a “trip,” as used in this study, and distributed roughness for flow over circular cylinders. Both of these changes to the cylinder move the drag crisis to lower values of Re. They concluded that a circular cylinder at Reynolds numbers as low as
$3\times 10^5$
can behave as trans-critical when a trip is employed around
$50^\circ$
, but that distributed roughness results in a different behaviour. The findings of this study similarly show that the tripped pressure distribution is different from the pressure distribution for a uniformly roughened sphere at the same Re.
West & Apelt (Reference West and Apelt1993) investigated pressure fluctuations on a smooth cylinder as a function of Reynolds number, turbulence level and blockage ratio. They found that the fluctuations were sensitive to Reynolds number and peaked near Re
$=8\times 10^4$
. In addition, these fluctuations reached their maximum near
$\theta = 75^\circ$
.
Recent investigations into cylinders in cross-flow near the critical Reynolds number have included the work of Pasam et al. (Reference Pasam, Tudball Smith, Holmes, Burton and Thompson2023), who considered the effect of relative roughness on cylinders with low blockage ratio to extend and improve on prior measurements of similar flows. Their results included a thorough set of data for this canonical flow to include mean and time-history pressures and forces, wake velocity distributions and momentum thicknesses. The data demonstrate a collapse of the base pressure, Strouhal number, Reynolds number, and wake angle with
$Re_k=\rho V_\infty k /\mu$
for post-critical flows, where
$\rho$
represents the air density and
$k$
represents the roughness height. Similarly, Desai et al. (Reference Desai, Mittal and Mittal2020) combined surface pressure measurements and particle image velocimetry data from the wake to identify an antisymmetric and a symmetric mode in the cylinder wake. The antisymmetric mode, responsible for the von Kármán vortex shedding, decreased relative to the symmetric mode as the flow transitioned from trans-critical to critical.
Many flow features including transition of a cylinder in cross-flow may be controlled passively by modifying the cylinder surface. Choi et al. (Reference Choi, Jeon and Kim2008) present a comprehensive review of passive control over bluff bodies, including circular cylinders. One relevant example discussed was a helical strake, or wire wrapped around a cylinder to prevent coherent vortex shedding from occurring over the full cylinder. Similar vortex shedding mitigation devices include spoiler plates, small plates normal to the surface distributed uniformly around the cylinder (Bianchi et al., Reference Bianchi, Silva, Cenci, Hirabayashi, Suzuki and Gonçalves2020).
Chopra and Mittal (Reference Chopra and Mittal2022) conducted a large eddy simulation of a cylinder with two trip heights (0.25 % and 1.0 % the cylinder diameter,) for Re from
$2\times 10^3$
to
$5 \times 10^5$
. These observations sought to better understand the “patterns” A, B/C and D in Igarashi (Reference Igarashi1986) and included a trip placed on a single side, with a smooth cylinder on the other. This selection was in part motivated by the relative lack of asymmetric trip locations in the prior literature which similarly motivates the present study. Results demonstrated that the boundary layer undergoes either natural transition through the formation of the laminar separation bubble for the smallest trip, or direct transition for the largest trip. A two-stage drag crisis was observed, owing to the boundary-layer transition on the opposite sides occurring at different values of Re.
In Lin et al. (Reference Lin, Meng, Yang and Gao2025), a device described as a “spoiler” was used to passively control the flow around a rectangular cylinder. The spoilers were plates on the leading edge of the rectangular cylinder angled
$45^\circ$
with respect to the surface of the cylinder. The effect of the spoilers on lift and drag as well as the time evolution of the flow was investigated. A recent example of passive flow control on a cylinder can be found in Gong et al. (Reference Gong, Wang, Liu and Jiang2024). They reported that cylinder drag can be reduced by placing a small rod parallel to and behind the cylinder. Other locations were also tested.
Small spoilers have also been considered as one of several alternatives to control flow separation in many aerodynamics applications. Small rectangular “mini spoilers” or “mini tabs” protruding controllable extents normal from a leading or trailing edge of an airfoil have recently been demonstrated as a means to control aerodynamic forces on a wing (Blaylock et al., Reference Blaylock, Chow, Cooperman and van Dam2014; Heathcote et al., Reference Heathcote, Gursul and Cleaver2020) without the elaborate design requirements and slow response time typical for larger spoilers (figure 1 a). Similarly, spoilers and synthetic jets (Smith & Glezer, Reference Smith and Glezer1998) are flow-control methods to actively separate the boundary layer and reduce dynamic stall in gust and/or flapping conditions (Barnes, Reference Barnes2024; Qian et al., Reference Qian, Wang and Gursul2023).
Spoilers have also emerged as a method for improving hydraulic turbine designs. Specifically, Bourgeois & Houde (Reference Bourgeois and Houde2023) numerically investigated spoilers as a means to limit discharge for spin no-load turbines. This study identified that the spoilers were effective in increasing head loss at the turbine as desired.
Finally, devices also referred to as spoilers have been applied in piping systems with closed-branch T-junctions to reduce pulsations due to the resonating acoustic field with periodic vortex shedding at the junction(s) (Bruggeman et al., Reference Bruggeman, Hirschberg, van Dongen, Wijnands and Gorter1989). In this context, Bruggeman et al. (Reference Bruggeman, Hirschberg, van Dongen, Wijnands and Gorter1991) identified a pulse reduction of 30–40 dB by placing a spoiler upstream of a second T-junction in cases where pulsations depend more on the absorption of the shed vortex energy than shear-layer stabilisation. The spoilers did not reduce pulsations when placed upstream of the first junction, and are limited in other T-junction cases by the relative importance of shear-layer stability (Botros et al., Reference Botros, Clavelle and Satish2022).
However, these devices act to disrupt the boundary layer and do not necessarily fully separate the boundary layer from the surface. Due to this ambiguity, this manuscript will maintain the language of “bump” to describe the selected geometries extending from the cylinder surface. The term “spoiler” will be reserved for cases where the bump acts to fully separate the boundary layer. The term “trip” will be reserved for cases where the bump does not fully separate the boundary layer.
Overall, these studies demonstrate the dependence of the separation location on the small surface features and the potential for trips and spoilers as a flow-control method in a variety of applications. However, the literature regarding the influence of small, asymmetrically placed spanwise surface features on a circular cylinder is underdeveloped. Specifically, the influence of a small (
$1\,\% \leq \delta \leq 5\,\%$
,) triangular bump, placed on a single side of a circular cylinder, similar to the geometry of a baseball seam, has not been experimentally observed. Thus, the present study examines the effect of a small, triangular-shaped bump on the surface pressure due to flow over a cylinder. In what follows, we will first describe the experimental set-up. This will be followed by results, a discussion of the results and conclusions.
2. Experimental set-up
2.1. Test article
The test article was a 75-mm-diameter, smooth aluminium cylinder with a 5-mm slot milled in the longitudinal direction. This slot received one of the 3-D printed bumps as shown in figure 2. The bumps are isosceles triangle cross-sections, with 10-mm end-to-end width in the direction tangent to the cylinder surface, and protrusion(s) 1-, 2- and 4-mm in the direction normal to the cylinder surface, beginning at the cylinder surface. The surface pressure distribution was measured as a function of Reynolds number, bump size and bump position.
Figure 2. Schematics of the three bump geometries used in this study. The bumps were isosceles-triangle-shaped with 10-mm width and protruded from the 75-mm diameter cylinder 1-, 2- and 4-mm.
The relative bump sizes
$\delta$
are 1.33 %, 2.66 % and 5.33 % of the cylinder diameter. We note that baseball seams, which motivate this study, are approximately 1 % of the diameter of a baseball. The most similar study the authors identified of a bump on the surface of a cylinder included circular cross-section bumps that were much larger:
$\delta \geq 9\,\%$
(Nebres & Batill, Reference Nebres and Batill1993).
2.2. Free-stream flow field
The cylinder was mounted in an Engineering Lab Designs 407A recirculating wind tunnel with a 0.6
$\times$
0.6-m test section. The manufacturer’s specification for streamwise turbulence intensity level is
$\leq$
0.25 % of the mean tunnel velocity
$V_\infty$
.
The Reynolds number range investigated in this study is less than a factor of two. However, we note that the flow is quite sensitive to the Reynolds number in this range. The maximum value was chosen to match the baseline case of the baseball study by Smith et al. (Reference Smith, Garrett, Dufour and Francis2024). The minimum value was selected to represent the lower limit of baseballs pitched in competitive sports (i.e., secondary school-age pitchers). For each test, the tunnel was started for 30 s before data collection to ensure that the free-stream velocity was in steady state for the target value of Reynolds number.
Barometric pressure and ambient temperature were measured daily to find the air density and viscosity. Due to the large number of samples for the time-averaged method of setting Reynolds number, the random uncertainty of the mean is insignificant.
We note that the tunnel temperature increased with time (
$\Delta T \lt 5\, ^{\circ }$
C per test). As this affects the viscosity and density used in the Re calculation, we continuously compensated for changes in tunnel temperature with changes in tunnel velocity to maintain a fixed Re value. The tunnel was also allowed to cool between each test.
Acrylic discs of 150-mm diameter were mounted above and below the measurement section to suppress spanwise flow. Zig-zag turbulent trips at
$45^{\circ }$
from the stagnation point ensure that the boundary layer is turbulent at separation. The trips spanned the measurement section and were 0.25-mm tall, 6-mm peak-to-peak and 9-mm in the lateral direction. The cylinder spanned the height of the test section, resulting in a blockage ratio of 12 %. Figure 3(a) shows the cylinder mounted in the test section.
Figure 3. (a) Cylinder mounted in the wind tunnel test section showing the acrylic disks, the trip and the three rows of pressure ports. (b) Close up of the cylinder on the bench showing the three rows of pressure ports and the largest bump. Note that the trip is not applied in this image.
2.2.1. Free-stream flow field uncertainty
Temperature variations are sources of systematic error; the density may vary by
$1.67 \times 10^{-2}$
kg m
$^{-3}$
and the viscosity by
$2.37 \times 10^{-7}$
kg m
$^{-1}$
s
$^{-1}$
. In addition, the wind tunnel velocity was calculated using a Pitot probe in the entrance to the test section connected to differential pressure transducers:
$V=\sqrt {2\Delta P/\rho }$
. One transducer was used for pressure differences up to 750 Pa and a second transducer for pressure differences up to 3.7 kPa. The calibration certificate uncertainties for these transducers are 0.5 % of full scale.
To estimate the total uncertainty in the Reynolds numbers, we propagated these individual uncertainties using the Taylor series method (Coleman & Steele, Reference Coleman and Steele2009; Smith & Neal, Reference Smith and Neal2025) for the data reduction equation: Re
$=D\sqrt {2 \rho \Delta P} /\mu$
\begin{equation} u_{Re} = \sqrt { \left ( \frac {D \sqrt { \Delta P}}{\mu \sqrt {2 \rho }} u_{\rho } \right)^2 + \left ( \frac {D \sqrt {\rho }}{\mu \sqrt {2 \Delta P}} u_{\Delta P} \right)^2 + \left ( \frac {\sqrt {2 \rho \Delta P}}{\mu } u_{D} \right)^2 + \left ( \frac {D \sqrt {2 \rho \Delta P}}{\mu ^2} u_{\mu } \right)^2 + 2\left ( \frac {D^2 \Delta P}{\mu ^3} u_{\rho } u_{\mu } \right) }. \end{equation}
Temperature measurements were made using the same instrument, and we treat their errors as perfectly correlated
$u_{\rho \mu }=u_{\rho }u_{\mu }$
according to the recommendation of Coleman & Steele (Reference Coleman and Steele2009). This method provides the total uncertainty as
$1.2 \times 10^4$
,
$2.5 \times 10^4$
and
$2.6 \times 10^4$
for the Reynolds numbers
$1.1 \times 10^5$
,
$1.3 \times 10^5$
and
$1.8 \times 10^5$
, respectively. We note that the contribution of the uncertainty from the pressure transducers is an order of magnitude larger than the combined contributions of the uncertainties of all other terms (
$D$
,
$\rho$
and
$\mu$
).
2.2.2. Test article orientation uncertainty
We varied the bump position by rotating the cylinder on a lathe chuck which held the cylinder from below. The bump orientation measurements were based on aligning the longitudinal slot location with a protractor, which was fixed to the access port of the test section used to mount the cylinder. The protractor was aligned with the free stream through parallel lines to the test section walls and verified by rotating the cylinder to identify maximum (stagnation) pressure at the expected angle. Thus, we estimate the upper limit for the uncertainty of the angular location (
$\theta$
) as half the resolution of the pressure ports placed every
$5^{\circ }$
:
$u_\theta = 2.5^{\circ }$
. This mounting method also pressed the top of the cylinder against the top of the wind tunnel test section to eliminate vibration.
The range of bump locations for this study were limited by the presence of turbulent trips (that is,
$\theta _b=60^{\circ }$
) to the last value before the fully separated region (that is,
$\theta _b=120^{\circ }$
) and varied in increments of
$10^{\circ }$
.
2.3. Pressure measurements
The pressure ports were 0.79-mm diameter holes drilled every
$5^{\circ }$
around the circumference of the cylinder (figure 3
b). Brass tubes connected a plastic hose to each internal hole in the cylinder, and these hoses extended through the cylinder to a slot in the top of the wind tunnel test section. The hoses were then connected to the pressure sensor. The static port on the Pitot-static probe mounted at the entrance of the test section provided the static pressure
$p_\infty$
. Tunnel velocity was measured using the same Pitot-static probe and a separate differential pressure sensor.
The pressure difference for each port was measured by sampling the output voltage of a 100 Torr capacitance manometer connected to the desired port on the cylinder surface and the static port for 30 s at 100 Hz. From these data, the pressure coefficient
$C_p=2(p-p_\infty)/{\rho V_\infty ^2}$
was determined. We assume that the values for computing
$C_p$
from the pressure difference measurement are fixed at a given value of Re. Thus, to convert pressure difference measurements to
$C_p$
, we identified the constant required at each observed Re for the pressure coefficient to provide
$C_p = 1$
at
$\theta =0^{\circ }$
. These observations were made with the bump positioned in the wake (
$\theta _b=180^\circ$
) to eliminate the potential influence of the bump. Through this method, we did not include
$\rho$
or
$V_\infty$
directly to compute
$C_p$
.
To correct these measurements in confined flow according to the moderate blockage (the blockage ratio
$B$
= 12%) for the cylinder in the trans-critical regime (i.e.,
$1.1 \times 10^5 \leq$
Re
$1.8 \times 10^5$
), we applied the momentum correction method developed by Maskell (Reference Maskell1963) and validated by Farell et al. (Reference Farell, Guven, Carrasquel and Patel1977). Specifically, we used each measured
$C_{pm}$
to find the unconfined corrected surface pressure coefficient
$C_p$
by first defining the base pressure parameter
$k$
, which is related to the base pressure coefficient
$C_{pb}$
through
$k^2=1-C_{pb}$
. This parameter relates the measured (indicated by subscript
$m$
) base pressure parameter
$k_m^2=1-C_{pbm}$
to the corrected base pressure parameter
$k_c^2=1-C_{pbc}$
where the corrected value
$k_c$
is identified for iteration
$n$
using
\begin{equation} (k_{c}^{2})_{n}=\frac {k_m^{2}}{1+\frac {BC_{D1}}{(k_{c}^{2})_{n-1}-1}}. \end{equation}
We neglected the skin friction drag, which is relatively small for cylinders in the trans-critical regime, and numerically integrated the surface pressure to identify
$C_D$
. This method was iterated until the parameter converged at
$(k_c^2)_n -(k_c^2)_{n-1} \lt 1\times 10^{-6}$
. Then, we applied the ratio of measured to corrected dynamic pressures to identify the corrected base pressure, the corrected dynamic pressure, and the corrected surface pressure(s)
\begin{equation} \frac {q_{c}}{q_m}=1+\frac {B}{(C_{pb})_{c}} = \frac {C_{pc}}{C_p}. \end{equation}
In this study, the momentum-method-corrected values for the surface pressure, the resulting lift and the resulting drag coefficients are reported. The uncorrected values are omitted to maintain consistency.
2.3.1. Surface pressure measurement uncertainty
The capacitance manometer resolution is 10
$^{-6}$
of full scale (100 Torr). The lowest Re at the mean measured density of 1.006 kg m
$^{-3}$
and velocity of 26.55 ms−1 provides the minimum dynamic pressure of 2.66 Torr, which is 2.66 % of the full range. Converting to
$C_p$
yields a resolution in pressure coefficient of 3.76
$\times$
10
$^{-5}$
and a 68 % confidence random uncertainty due to resolution limits of half the resolution: 1.88
$\times$
10
$^{-5}$
. Time averaging the 3,000 samples per measurement is sufficient to render the random uncertainty of the mean (
$u_{r,C_p}=1\times 10^{-3}$
) insignificant.
Given the excellent pressure instrument, we claim that the main source of uncertainty in this measurement is the error in the stagnation pressure value due to the misalignment of the measurement port with
$\theta =0^{\circ }$
. Assuming that the pressure near stagnation follows the potential flow solution, we estimate that the maximum error due to misalignment of the port at
$\theta =0^\circ$
is
$\pm$
$ 1-C_{p}(2.5^\circ)=0.01$
. To evaluate repeatability, the baseline case of the bump oriented at
$180^{\circ }$
and Re = 1.8
$\times$
10
$^{5}$
was measured on two separate days. The mean surface pressure measurement differences across days were less than the pressure measurement uncertainty due to port misalignment. Thus
$u_{C_p} = 0.01$
at a 68 % confidence random uncertainty.
The full parameter space for this study is shown in table 1.
Table 1. Experimental parameters
3. Results and discussion
3.1. Baseline pressure results
We begin by examining a case where the bump is at
$180^\circ$
, in the wake, and has no observable effect on the flow. This forms the baseline case. The surface pressure distributions for the three values of Reynolds number are shown in figure 4. Only one side of the cylinder is plotted since the surface pressure distribution is symmetric when the bump is located at
$180^{\circ }$
. The potential flow pressure distribution is included for reference. Examining the present results compared with the studies of Achenbach (Reference Achenbach1968, Reference Achenbach1971), it is clear that the pressure distribution resulting from a tripped boundary layer on a smooth cylinder is not the same as that of a smooth or uniformly rough cylinder, as reported by Nakamura & Tomonari (Reference Nakamura and Tomonari1982).
Figure 4. Surface pressure coefficient as a function of angle with the bump at
$180^\circ$
for three values of Re. The black curve is the potential flow solution. Also included are results from a smooth cylinder study (Achenbach, Reference Achenbach1968) and a uniformly roughened cylinder (Achenbach, Reference Achenbach1971). Uncertainty bands are omitted to maintain readability.
For each Re value, stagnation pressure (
$C_p = 1$
) is experienced at
$\theta = 0^{\circ }$
. Increasing Re results in more dissipation in the boundary layer. Compared with potential flow, the negative pressure gradient
${-\text{d}C_p}/{\text{d}\theta }$
is lower, and more so for larger Reynolds numbers, especially downstream of trips near
$45^\circ$
. Despite the increasing dissipation in the boundary layer with Re, the separation point does not change appreciably with Re and is near
$110^\circ$
. The base pressure (downstream of the separation point) is similar for each case with a value near
$C_p = -0.75$
.
3.2. The upstream effects of bump position and size
We now present the pressure data for the side of the cylinder with the bump. The range of bump locations is from 60
$^{\circ }$
, which is as far upstream as possible to avoid interaction with the trip, to 120
$^{\circ }$
, where the bump is at the edge of the wake and the spoiler does not influence the flow when positioned at greater angles. The pressure was not measured within 5
$^{\circ }$
of the turbulent trip tape (
$ 40^{\circ } \leq \theta \leq 50^{\circ }$
) to avoid spurious values due to blockage and/or local pressure gradients. To visualise these observations more carefully, we transform the
$x$
-axis into the ratio of the pressure port angle to the bump angle:
$\theta / \theta _b$
(figure 5). Note that the non-transformed pressure data for all cases with a bump are presented in the Appendix.
Figure 5. Surface pressure coefficient as a function of the bump position divided by the bump position angle with the bump angles ranging from
$60^\circ$
to
$120^\circ$
for the three sizes and three values of Re. The bump positions are
$60^\circ$
(
),
$70^\circ$
(
),
$80^\circ$
(
),
$90^\circ$
(
),
$100^\circ$
(
),
$110^\circ$
(
) and
$120^\circ$
(
). The solid lines at
$\theta / \theta _b=1$
indicate the bump location. Uncertainty bands are omitted to maintain readability.
Across all observations, the pressure distributions appear similar in the range
$0 \leq \theta / \theta _b \leq 1$
, and the pressure upstream of the bump is higher than the potential flow solution. This increase depends on the location of the bump. Generally, the pressure increases with a decrease in bump position angle (
$\theta _b$
) and an increase in bump size. Similarly, the pressure upstream of the bump generally increases with an increase in the size of the bump.
Based on the results of the surface pressure distribution in figure 5, the bump can have one of two effects after the bump:
$\theta / \theta _b \gt 1$
, each likely due to the local favourable and then adverse pressure gradient generated by the bump geometry.
-
(i) Causing complete separation of the boundary layer, indicated by the constant surface pressure after the bump. This is referred to as the bump acting as a spoiler.
-
(ii) Causing thickening of the attached boundary layer or separation with reattachment. In these cases, the surface pressure decreases then increases after the bump until a final separation point farther upstream than in the baseline case. This is referred to as the bump acting as a trip.
These effects (i) and (ii) are respectively aligned with the “patterns” C and D presented in the smaller circular trip wire observations by Igarashi (Reference Igarashi1986). The mechanisms are further elaborated through the large eddy simulation study results by Chopra and Mittal (Reference Chopra and Mittal2022).
3.3. Spoiler behaviour
We begin by discussing the range of bump locations that result in effect (i): the bump fully separates the boundary layer. For all Re values and all three sizes, the bump significantly increases the surface pressure upstream of the bump. This makes the pressure gradient more adverse than for the case of no bump at the same location. The pressure also increases upstream of the bump with an increase in bump size. Thus, we observe that a sufficiently large bump, positioned at a location where the bump creates an adverse pressure gradient, will act as a spoiler. We propose that this effect is due to a bump reducing the near-wall momentum to zero, fully separating the boundary layer. In this case, the pressure immediately increases to the base value after the bump. Figure 5 indicates that the bump acts as a spoiler for all observations except for the smallest bump (
$\delta = 1.33\,\%$
) placed at
$\theta _b=60^{\circ }$
and
$\theta _b=70^{\circ }$
.
This is the effect observed in Smith et al. (Reference Smith, Garrett, Dufour and Francis2024), where a baseball seam was found to act like a spoiler. The range of angles where seams were found to have this effect was roughly the same as the present results. A simple model fits the pressure distribution upstream of the spoilers. We fitted a modified version of the inviscid potential flow solution for a circular cylinder:
$C_p(\theta)=1-C_1\theta _b^2sin^2(C_2\theta / \theta _b)$
to the data for Re
$=1.8\times 10^5$
,
$\delta = 2.66\,\%$
. Figure 6 presents the resulting pressure distributions according to the least-squares best-fit result:
$C_p(\theta)=1-0.75\theta _b^2sin^2(2.4\theta /\theta _b)$
.
Figure 6. Fitted model curves of surface pressure coefficient as a function of the bump position divided by the bump position angle with the bump angles ranging from
$80^\circ$
to
$120^\circ$
for Re
$=1.8\times 10^5$
,
$\delta = 2.66\,\%$
. The bump positions are
$80^\circ$
(),
$90^\circ$
(),
$100^\circ$
(),
$110^\circ$
() and
$120^\circ$
(). The solid line at
$\theta / \theta _b=1$
indicates the bump location.
Figure 7. Surface pressure coefficient as a function of the bump position ranging from
$60^\circ$
to
$120^\circ$
for
$\delta = 1.33 \,\%$
, Re
$=1.1 \times 10^5$
. The bump positions are
$60^\circ$
(),
$70^\circ$
(),
$80^\circ$
(),
$90^\circ$
(),
$100^\circ$
(),
$110^\circ$
() and
$120^\circ$
(). The black line is the potential flow solution.
We expect the fitted curve presented here to provide a next step in predicting the surface pressure over a baseball according to a known orientation, given the model is appropriately adjusted for differences in cylinders and spheres (Yeung, Reference Yeung2009).
3.4. Trip behaviour
We now consider the bump positions and sizes that result in effect (ii): the bump acts as a trip and does not fully separate the boundary layer. Rather, we expect that the bump acts similarly to an isolated roughness element by further developing the already turbulent boundary layer. Specifically, that the local favourable then adverse pressure gradient introduced by the bump decreases, but does not reduce to zero, the near-wall momentum of the boundary layer. This development is evidenced by complete separation at a lower value of
$\theta$
than for the cylinder without the bump.
For the surface pressures observed at all values of Re in figure 5, the bump acts as a trip for the bump
$\delta = 1.33 \,\%$
placed at
$\theta _b=60^\circ$
and for the bump
$\delta = 1.33 \,\%$
placed at
$\theta _b=70^\circ$
. To assist the discussion of the trip behaviour, figure 7 shows the non-transformed surface pressure data for the bump side of the cylinder for
$\delta = 1.33 \,\%$
, Re
$=1.1 \times 10^5$
.
As shown in figure 7, the flow reattaches downstream of the bump, evidenced by the large decrease in pressure after the bump location. For the case of the bump located at
$60^\circ$
, the pressure also coincides with the potential flow solution at the bump and increases with increasing
$\theta$
until separation (indicated by constant surface pressure) near
$90^\circ$
. For the case of the bump located at
$70^\circ$
and size 1.33 %, the dissipation is higher than for the
$60^\circ$
case, but the final separation also occurs at
$90^\circ$
and the base pressure is the same for both positions.
These observations match the effect of roughness over supercritical spheres (Achenbach, Reference Achenbach1972; Elliott et al., Reference Elliott, Smith, Lyu and Smith2024; Norman & McKeon, Reference Norman and McKeon2011). Further, this result is opposite to that observed for subcritical cylinders (Nebres & Batill, Reference Nebres and Batill1993), where a cylindrical “spoiler” delayed boundary-layer separation compared with the case of no spoiler by transitioning the boundary layer to turbulent. This difference is owed to the boundary layer in this study being tripped to turbulent by both the trip tape at
$45^{\circ }$
and the larger Re value. For the larger bumps at these positions
$\theta _b \geq 60^{\circ }$
(
$\delta =2.66\,\%$
and
$5.33\,\%$
), the bump acts as a spoiler as the boundary layer separates and remains detached downstream of the bump.
3.5. Non-bump side pressures
The surface pressure distribution on the side opposite the bump is insensitive to the bump position, with some notable exceptions. The first of these exceptions is observed in the case of the intermediate bump size (
$\delta =2.66 \,\%$
) at all values of Re, shown in figure 8. Here, the pressure on the non-bump side of the cylinder is increased in the region
$240^\circ \leq \theta \leq 270^\circ$
compared with the other cases.
Figure 8. Surface pressure coefficient on the side of the cylinder without the bump as a function of the bump position ranging from
$60^\circ$
to
$120^\circ$
for
$\delta = 2.66 \,\%$
, Re
$=1.3 \times 10^5$
. The bump positions are
$60^\circ$
(),
$70^\circ$
(),
$80^\circ$
(),
$90^\circ$
(),
$100^\circ$
(),
$110^\circ$
() and
$120^\circ$
(). The black line is the potential flow solution.
Figure 9. Surface pressure coefficient on the side of the cylinder without the bump as a function of the bump position ranging from
$60^\circ$
to
$120^\circ$
for
$\delta = 5.33 \,\%$
, Re
$=1.3 \times 10^5$
. The bump positions are
$60^\circ$
(),
$70^\circ$
(),
$80^\circ$
(),
$90^\circ$
(),
$100^\circ$
(),
$110^\circ$
() and
$120^\circ$
(). The black line is the potential flow solution.
The opposite is seen for the largest bump
$\delta =5.33\,\%$
at the intermediate and highest Re:
$1.3 \times 10^5$
and
$1.8 \times 10^5$
. Figure 9 shows the result for Re =
$1.3 \times 10^5$
. Specifically, the boundary layer remains attached much farther in the streamwise direction than the other non-bump side cases for
$\theta _b=90^{\circ }$
. Further, the pressure in this region (
$220^\circ \leq \theta \leq 260^\circ$
) is lower than for the other cases which separate near the baseline separation point:
$\theta =240^{\circ }$
.
In Smith et al. (Reference Smith, Garrett, Dufour and Francis2024), it was reported that when a baseball at Re
$= 1.8\times 10^5$
has a seam near
$90^\circ$
and no seam on the opposite side of the sphere, the separation point moves toward a lower
$\theta$
on the non-seam side. Specifically, the separation from a baseball is normally about
$115^\circ$
(
$245^\circ$
in figure 8), but moves closer to
$90^\circ$
(
$270^\circ$
in figure 8) when the seam is at
$90^{\circ }$
. In this study, there is evidence that the same is true for a cylinder for the 2-mm (2.66 %) bump. As shown in figure 8, the separation point moves back to the common value near
$240^\circ$
for any bump location other than
$\theta _b=90^{\circ }$
, similar to the baseball result.
3.6. Base pressure
To supplement the discussion of base pressure, we present the typical base pressure measured through the mean surface pressure coefficient in the range
$120 \leq \theta \leq 240$
. Figure 10 shows the base pressure data, organised by bump size and Re.
Figure 10. Mean base pressure coefficient as a function of the bump position ranging from
$60^\circ$
to
$120^\circ$
for all three values of bump size and Re. The error bars represent the 95 % confidence random uncertainty of the mean.
Figure 11. Pressure integrated lift and drag coefficients as a function of bump position, size and Reynolds number. The force coefficients are integrated from the pressure coefficients, and thus have the same uncertainty
$ u_{C_F}=0.01$
while the location uncertainty is
$u_{\theta _b} =2.5 ^{\circ }$
.
As shown in figure 10, the base pressure generally increases with an increase in bump angle for the larger bumps:
$\delta = 2.66 \,\%$
and
$\delta =5.33 \,\%$
. For the smallest bump, the base pressure decreases with an increase in
$\theta _b$
to a local minimum at
$\theta _b=90^{\circ }$
. The base pressure increases with an increase in
$\theta _b$
through the range of remaining observed bump angles. Interestingly, the lowest values for the base pressure are observed for the largest bump when the bump is oriented the furthest upstream,
$\theta _b=60^\circ$
. Finally, the base pressure generally increases with an increase in Re, which aligns with expectations for circular cylinders.
3.7. Aerodynamic force results
The impact of the bump on the lift and drag, which is a function of the pressure around the cylinder, is shown in figure 11. We note that the fluid forces integrated to form these coefficients are only pressure forces, but the contribution of skin friction is negligible in all directions. Achenbach (Reference Achenbach1971) notes that skin friction amounts to less than 2 % of the total drag for a rough cylinder.
Generally, a bump on one side of a cylinder leads to lift toward the opposite side. The only exception is the bump of 2.66 % at
$120^\circ$
, which can cause a force in the opposite direction. For the two smallest bump sizes, the highest lift value is for a bump on the front of the cylinder (
$\theta _b \lt 90^\circ$
), while the pressure drag is not sensitive to the location of the bump.
The drag is less sensitive to the bump position. The largest changes in drag occur across the observed values of Re for the smallest bump at
$\theta = 60^\circ$
and
$\theta = 70^\circ$
. The boundary layer is not fully separated at the bump. Rather, the boundary layer reattaches, corresponding to a significantly lower pressure value than the baseline and higher observations of
$\theta _b$
. In the case of
$\theta _b=60^\circ$
, this leads to the lowest drag observed.
The delayed separation for the largest bump at
$90^\circ$
does not result in increased lift and also comes with a large drag penalty. The drag can be seen to depend only weakly on the bump position. However, it is also clear that drag increases with bump size, and that the drag is lowest for the smallest bump positioned farthest upstream.
4. Conclusions and recommendations
An experimental study of a smooth, tripped cylinder equipped with a spanwise bump on one side is reported. The Reynolds number range (
$1.1\times {10}^{5} \leq$
Re
$ \leq 1.8\times {10}^{5}$
) is chosen to lie near the drag crisis. The main result reported here is surface pressure and the forces it generates.
The baseline flow (with the bump in the wake, where it has no influence) resembles previously reported results for smooth, tripped cylinders. Viscous dissipation in the boundary layer was shown to increase with Reynolds number, while the separation point is near
$110^\circ$
and the base pressure remains constant with Re.
The smallest bump tested was only 1.33 % of the cylinder diameter. Even so, the pressure upstream of the bump is strongly dependent on the bump position for all observations. Overall, the pressure upstream of the bump increases with an increase in bump size. The pressure upstream of the bump also increases the farther the bump is positioned upstream. The pressure distributions upstream of the bump appear similar when the cylinder location variable
$\theta$
is transformed by the ratio to the bump position
$\theta /\theta _b$
. All three bumps removed the boundary layer from the surface when placed anywhere from
$80^\circ \text{ to } 120^\circ$
. As a result, the pressure distribution, and therefore the lift for bump positions near
$90^\circ$
, is significantly altered. The highest lift values resulted from a bump at less than
$90^\circ$
.
When the bump is sufficiently close to the stagnation point (
$60^\circ \lt \theta \lt 70^\circ$
), it acts as trip and further develops the already turbulent boundary layer. As a result, the final separation point moves to
$90^\circ$
compared with the case of no trip with separation at
$120^\circ$
. In this range, the favourable pressure gradient after the bump is sufficiently strong so that the bump cannot remove the boundary layer from the surface. However, while separation does not occur on the bump, the separation point is moved upstream compared with the baseline case.
Across observations, drag was not found to be a strong function of the bump position outside the low drag observed at
$\delta =1.33\,\%$
and
$\theta _b=60^{\circ }$
. In this case, the bump did not fully separate the boundary layer. In addition, drag increased significantly with bump size.
Acknowledgements
We would like to thank Mr. Terry Zollinger for his assistance in the design and construction of the test article.
Data availability statement
Raw data are available from the corresponding author (J.E.).
Author contributions
J.E. conducted the experimental design, data collection, data analysis and co-drafted the initial manuscript. A.N. conducted pressure measurement data collection. B.L.S. conceived of the study, co-drafted the initial manuscript, advised on data collection and advised on data analysis. All authors participated in contributing to the initial and revised manuscript. All authors approve of the content in this manuscript and agree to be held accountable for the work.
Funding statement
This study was not funded.
Declaration of interests
The authors declare no conflict of interest.
Ethical standards
The research meets all ethical guidelines, including adherence to the legal requirements of the study country.
Appendix
The full non-transformed pressure data for the cylinder with the bump placed from
$60^{\circ } \leq \theta _b \leq 120^{\circ }$
are provided.
Figure A1. Surface pressure coefficient as a function of angle with the bump at angles ranging from
$60^\circ$
to
$120^\circ$
for the three bumps and three values of Re. The bump positions are
$60^\circ$
(),
$70^\circ$
(),
$80^\circ$
(),
$90^\circ$
(),
$100^\circ$
(),
$110^\circ$
() and
$120^\circ$
(). The grey-shaded region indicates the side of the cylinder with no bump. The line is the potential flow solution. Uncertainty bands are omitted to maintain readability.
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