# How do the finite-size particles modify the drag in Taylor-Couette turbulent
flow

Cheng Wang1  Lei Yi1  Linfeng Jiang1  Chao Sun1,2<EMAIL_ADDRESS>1Center for Combustion Energy, Key Laboratory for Thermal Science and Power
Engineering of Ministry of Education, Department of Energy and Power
Engineering, Tsinghua University, Beijing 100084, China 2Department of
Engineering Mechanics, School of Aerospace Engineering, Tsinghua University,
Beijing 100084, China

###### Abstract

We experimentally investigate the drag modification by neutrally buoyant
finite-size particles with various aspect ratios in a Taylor-Couette (TC)
turbulent flow. The current Reynolds number, $Re$, ranges from $6.5\times
10^{3}$ to $2.6\times 10^{4}$, and the particle volume fraction, $\Phi$, is up
to $10\%$. Particles with three kinds of aspect ratio, $\lambda$, are used:
$\lambda=1/3$ (oblate), $\lambda=1$ (spherical) and $\lambda=3$ (prolate).
Unlike the case of bubbly TC flow (van Gils et al., 2013; Verschoof et al.,
2016), we find that the suspended finite-size particles increase the drag of
the TC system regardless of their aspect ratios. The overall drag of the
system increases with increasing $Re$, which is consistent with the
literature. In addition, the normalized friction coefficient,
$c_{f,\Phi}/c_{f,\Phi=0}$, decreases with increasing $Re$, the reason could be
that in the current low volume fractions the turbulent stress becomes dominant
at higher $Re$. The particle distributions along the radial direction of the
system are obtained by performing optical measurements at $\Phi=0.5\%$ and
$\Phi=2\%$. As $Re$ increases, the particles distribute more evenly in the
entire system, which results from both the greater turbulence intensity and
the more pronounced finite-size effects of the particles at higher $Re$.
Moreover, it is found that the variation of the particle aspect ratios leads
to different particle collective effects. The suspended spherical particles,
which tend to cluster near the walls and form a particle layer, significantly
affect the boundary layer and result in maximum drag modification. The minimal
drag modification is found in the oblate case, where the particles
preferentially cluster in the bulk region, and thus the particle layer is
absent. Based on the optical measurement results, it can be concluded that, in
the low volume fraction ranges ($\Phi=0.5\%$ and $\Phi=2\%$ here),  the larger
drag modification is connected to the near-wall particle clustering. The
present findings suggest that the particle shape plays a significant role in
drag modification, and the collective behaviors of rigid particles provide
clues to understand the bubbly drag reduction.

###### keywords:

Taylor-Couette, turbulence, multiphase flow

##  1 Introduction

Particle-laden flow is ubiquitous both in nature and industry, including
plankton in the ocean (Pedley & Kessler, 1992), dust and virus dispersed in
the atmosphere (Mittal et al., 2020) and catalytic particles in industrial
settings (Wang et al., 2019, 2020). For the suspension of rigid spheroidal
particles, the system can be characterized by the Reynolds number of the flow,
$Re$, and the particle parameters, which include the density, $\rho_{p}$, the
diameter, $d_{p}$, the aspect ratio, $\lambda$, and the volume fraction of the
particle, $\Phi$. According to the ranges of $d_{p}$ and $\Phi$, the mechanism
of the fluid-particle interaction can be roughly classified into two types:
(i) one-way coupled and (ii) two-/four-way coupled (Elghobashi, 1994; Voth &
Soldati, 2017). When $d_{p}\ll\eta_{K}$ (the dissipative length scale of the
flow) and $\Phi$ is low, the fluid and the particles can be treated as one-way
coupled, hence the fluid is unaffected. In this regime, the particle-laden
flow can be described by the point-particle model, which has been extensively
verified and used in the simulation studies (Saw et al., 2008; Rusconi et al.,
2014; Frankel et al., 2016; Park et al., 2018; Lohse, 2018; Lovecchio et al.,
2019). For $d_{p}\ll\eta_{K}$ but $\Phi$ is high enough, the particles can
still be modeled as point-particles but would instead affect the surrounding
fluid since the fluid and particles are two-/four-way coupled now. However,
when $d_{p}$ exceeds $\eta_{K}$ (typically $d_{p}>10\eta_{K}$ (Voth & Soldati,
2017)), the particles, which are referred to as finite-size particles, can
modify the surrounding flow field by two-way or four-way coupling way. To
resolve the flow field around the finite-size particles, experiments and
fully-resolved simulations, which have been conducted to study the physics of
the finite-size effects and the particle dynamics (Magnaudet & Eames, 2000;
Peskin, 2002; Uhlmann, 2008; Tagawa et al., 2013; Wang et al., 2017b; Bakhuis
et al., 2018; Jiang et al., 2020; Will et al., 2021; Assen et al., 2021), are
required.

The finite-size effects on the microscopic scale can cause turbulence
modulation on the macroscopic scale. It has been reported that tremendous drag
reduction can be achieved by a small amount of large bubble injection (Van den
Berg et al., 2005; van den Berg et al., 2007; van Gils et al., 2013; Verschoof
et al., 2016; Ezeta et al., 2019), however, of which the mechanism is still
not fully understood. The main difficulty in studying the bubbly flow in the
experiments is the deformability of the bubble, which makes it difficult to
fix the bubble shape and size. On the contrary, through performing density
matching, suspended rigid spheroidal particles can be used to partially solve
the difficulty above, making it possible to delve into the mechanism of bubbly
drag reduction.

Indeed, recent studies have hinted that the spherical particles are promising
in achieving drag modification both in channel flow (Lashgari et al., 2014;
Picano et al., 2015) and duct flow (Zade et al., 2018). However, on the one
side, few studies have directly measured the drag of the flow, under what
conditions the particles will increase or decrease the turbulence drag is
still unknown. Bakhuis et al. (2018) experimentally investigated the effects
of finite-size rigid spherical particles on the drag of a Taylor-Couette
turbulent flow, where they found that the overall drag does not vary much in
their explored high Reynolds number range and the low particle volume fraction
range. While in a later study, Ardekani & Brandt (2019) varied the aspect
ratios of the suspended particles in wall-bounded turbulence and found
turbulence attenuation (compared to the single-phase flow) in prolate and
oblate cases. In their study, an overall drag reduction was also found for the
oblate particle with $\lambda\leq 1/3$ when compared to the single-phase case.
It should be noted that turbulence attenuation is not necessary to connect to
an overall drag reduction and vice versa. For example, the turbulence
attenuation but overall drag enhancement might be achieved at the same time at
the cost of high particle volume fractions since the particle-induced stress
is greatly enhanced (Picano et al., 2015). Given the importance of the
boundary layer for turbulent stress and drag, an explanation was proposed by
Ardekani & Brandt (2019) for the mechanism of turbulence modulation in terms
of the near-wall dynamics of different particles. On the other side, studies
in recent years have shed some light on the physics of the turbulence
modulation induced by particles. For example, Ardekani et al. (2017) performed
simulations in turbulent channel flow laden with oblate particles up to a
volume fraction of $\Phi=15\%$, and they have observed an overall drag
reduction. In their study, two possible mechanisms are found to be responsible
for the particle-induced drag reduction: (i) the absence of the near-wall
particle layer and (ii) the alignment of the major axes of the oblate
particles to the wall. Besides, experimental findings have also suggested that
the collective effects of the particles and bubbles can significantly affect
the flow properties (Calzavarini et al., 2008; Colin et al., 2012; van Gils et
al., 2013; Maryami et al., 2014; Alméras et al., 2017; Mathai et al., 2018).

Among various flow geometries, a closed setup, where drag can be directly
measured, is convenient for evaluating the drag modification of the flow
induced by suspended particles. In this work, we employ a TC system (Grossmann
et al., 2016) \- the flow between two coaxial cylinders - to suspend the
particles. The Reynolds number, $Re$, the particle volume fraction, $\Phi$,
and the particle aspect ratio, $\lambda$, are varied to study their effects on
the drag. To find out the mechanism of the drag modification, optical
measurements are performed to obtain the particle distribution in the radial
direction of the system.

Figure 1:  $(a)$ The sketch of the Taylor-Couette facility. The gap between
the two coaxial cylinders is filled with glycerine-water solution to match the
particle density. The neutrally buoyant particles (blue dots) are recorded by
the CCD camera. The outer cylinder is surrounded by a PMMA cubic circulating
water bath, which keeps the temperature of the system at $T=22\pm 0.1$ ℃
during the experiments. $(b)$ shows the sketches and sizes of the particles
used in this work.

##  2 Experiment

###  2.1 Experimental facility

The TC facility used in the present work is shown by the sketch in figure
1(a). The inner cylinder is made of aluminum, while the outer one is made of
PMMA (polymethyl methacrylate) to perform optical measurements. The outer
cylinder is surrounded by a PMMA cubic circulating bath, which keeps the
system temperature at $T=22\pm 0.1$ ℃ during the experiments. The radius of
the inner and outer cylinder is $r_{i}$ = 25 mm and $r_{o}$ = 35 mm,
respectively, giving the gap width $d$ = $r_{o}-r_{i}$ = 10 mm and the radius
ratio $\eta=r_{i}/r_{o}=0.714$. The height of the inner cylinder is $L$ = 75
mm, which gives the aspect ratio of the system $\Gamma=L/d=7.5$.

During the experiments, the outer cylinder is fixed, while the inner cylinder
is connected to and driven by a rheometer (Discovery Hybrid Rheometer, TA
Instruments), and the overall torque of the system is measured at the same
time by the torque sensor of the rheometer. The control parameter of TC flow
is the Reynolds number defined by:

$Re=\frac{\omega_{i}r_{i}d}{\nu},$ (1)

where $\omega_{i}$ is the angular velocity of the inner cylinder and $\nu$ is
the kinematic viscosity of the fluid. In the present work, the $\omega_{i}$
ranges from $50$ to $200$ rad/s, which gives the $Re$ ranges from $6.5\times
10^{3}$ to $2.6\times 10^{4}$.

The overall torque of the system, $\tau_{total}$, that needed to drive the
inner cylinder at a constant angular velocity $\omega_{i}$, can be divided
into two parts: (i) the torque, $\tau$, due to the sidewall of the inner
cylinder (TC flow), (ii) the torque, $\tau_{end}$, contributed from the von
Kármán flow at the end plates. Since the aspect ratio of the system is
relatively small here, the rotation of the end plates generates secondary
vortices that contribute to the torque measurements (Bagnold, 1954; Hunt et
al., 2002). The calibration of the end effect due to the von kármán flow
between the bottom and top lids of the inner and outer cylinder can be found
in Appendix A. Here, only $\tau$ is used, and it can be non-dimensionalized
as:

$G=\frac{\tau}{2\pi L\rho_{f}\nu^{2}},$ (2)

where $L$ is the length of the inner cylinder and $\rho_{f}$ is the fluid
density.

In the experiments, the gap between the bottom and top lids of the inner and
outer cylinders is 2 mm and larger than the particle diameter, the particles
therefore would enter in and escape from the bottom and top gaps between the
inner and outer cylinders. For each experiment, the system is initially
started from a static state, and then the inner cylinder is imposed a constant
angular velocity by the motor of the rheometer. Before measuring the torque,
the inner cylinder is kept rotating to ensure the establishment of a
statistically stationary state. For each $\omega_{i}$, the torque measurements
are repeated 3 times, and the averaged value is used, of which the standard
deviations are less than $1\%$.

###  2.2 Preparation of the finite-size particles

The particles we used are printed with a 3D printer using photosensitive resin
(Elastic Resin of Formlabs. Inc) and are then cured at 60 ℃ for 60 mins. To
check their water-absorbing ability, the particles are immersed in the static
glycerin-water solution for 2 hours, and afterward the change in weight is
found to be negligible. The density of the particle is $\rho_{p}=1.06\times
10^{3}$ kg/m3 (averaged value based on more than 1000 particles). The particle
volume fraction, $\Phi$, ranges from $0\%$ to $10\%$ with a spacing of $2\%$.
In addition, optical measurements and additional torque measurements are
performed at $\Phi=0.5\%$. To study the shape effect of the finite-size
particles, we change the particle aspect ratio, $\lambda=h_{p}/d_{p}$, where
$d_{p}$ is the length of the symmetric axis of the particle, and $h_{p}$ is
the length that perpendicular to it. In this work, $\lambda$ is designed to be
equal to 1/3, 1, and 3, corresponding to the oblate, spherical and prolate,
respectively (see figure 1(b)). We fix the volume of each particle the same
for three cases of aspect ratio. The equivalent diameter of the particle based
on the volume, $d_{e}$, is equal to the diameter of the spherical particle,
i.e., $d_{e}=d_{s}=1$ mm. Note that the particles are verified to be finite-
size particles. For example, the dissipative length scale of the TC flow,
$\eta_{K}$, can be estimated as around $0.075$ mm when $\omega_{i}=50$ rad/s,
which gives $d_{e}\textgreater 10\eta_{K}$ and satisfies the assumption of the
finite-size model (Voth & Soldati, 2017).

To eliminate the effect of the gravity and the buoyancy force, the density of
the particle and the fluid are matched using glycerin-water solution (the
weight fraction of the glycerin is $w_{t}=25\%$). The solution density is
$\rho_{f}=1.0598\times 10^{3}$ kg/m3 and the kinematic viscosity is
$\nu=1.913\times 10^{-6}$ m2/s at $T=22$ ℃ (Cristancho et al., 2011), giving a
0.02% density mismatch from the particle density. Since the temperature of the
system is well controlled by the circulating water bath, the effects of the
temperature variation on the density and viscosity of the solution can be
neglected in the present work.

The particle motion is recorded by a CCD camera (MD028MU-SY, Ximea.Inc) at a
frequency $f_{c}=15$ Hz, and then the particle positions are obtained by
performing particle detection. The flow domain is illuminated by a light
source, which is shown in figure 1(a). The details of the detection methods
and examples can be found in Appendix C.

Figure 2:  The normalized friction coefficient of the Taylor-Couette system,
$c_{f,\Phi}/c_{f,\Phi=0}$, for (a) $\lambda=1/3$ (oblate), (b) $\lambda=1$
(spherical) and (c) $\lambda=3$ (prolate), where $c_{f,\Phi=0}$ is the
friction coefficient for the single-phase case. The accuracy of the
experiments is indicated by the error bars, which are typically less than 1%.

##  3 Results

###  3.1 Drag modification

Firstly, we study the effects of changing the Reynolds number on the drag of
the system. For the global analysis of the drag modification by bubbles or
particles, the friction coefficient, $c_{f,\Phi}$, which evaluates the skin
frictional drag of the flow system, has been extensively used in various flow
geometries (Sanders et al., 2006; Verschoof et al., 2016; Olivucci et al.,
2021). In the TC system, the friction coefficient is defined as (Lathrop et
al., 1992; Van Gils et al., 2011):

$c_{f,\Phi}=\frac{(1-\eta)^{2}}{\pi\eta^{2}}\frac{G}{Re^{2}}.$ (3)

Figure 2 shows the normalized friction coefficients of the system,
$c_{f,\Phi}/c_{f,\Phi=0}$, where $c_{f,\Phi=0}$ is the friction coefficient of
the single-phase case. It is found that the drag modification increases with
increasing $\Phi$ for a given $Re$. In the investigated ranges, the greatest
drag enhancement is found to be around $20\%$, which is observed in the
spherical case at $Re=6.5\times 10^{3}$ and $\Phi=10\%$ (figure 2(b)).
Additionally, $c_{f,\Phi}/c_{f,\Phi=0}$ decreases as the $Re$ increasing,
which has also been found and is referred to as the shear-thinning effect in
the suspension of deformable particles (Adams et al., 2004) and the emulsions
(Yi et al., 2021; Rosti & Takagi, 2021). Note that, the overall drag of the
system ($G$ or $\tau$, which are not shown here), increases with increasing
$Re$ and is consistent with the literature (Stickel & Powell, 2005; Fall et
al., 2010; Picano et al., 2013).

The modification of the friction coefficient is related to the changes of the
wall stress, which can be decomposed into three parts when no external force
and torque is applied on particles:

$\tau_{w,\Phi}=\tau_{v}+\tau_{T}+\tau_{p}=\tau_{v}+\tau_{T_{f}}+\tau_{T_{p}}+\tau_{p},$
(4)

where $\tau_{v}$ the viscous stress of the fluid phase, $\tau_{p}$ the
particle-induced stress, and $\tau_{T}=\tau_{T_{f}}+\tau_{T_{p}}$ the
turbulent Reynolds stress of the combined phase, $\tau_{T_{f}}$ and
$\tau_{T_{p}}$ the turbulent Reynolds stress of fluid and particulate phase,
respectively. Following the studies in Zhang & Prosperetti (2010) and Picano
et al. (2015), the explicit expression of each term above in a Couette flow
(Batchelor, 1970; Wang et al., 2017a) can be written as:

$\tau_{v}=\mu(1-\Phi)\frac{\mathrm{d}U_{f}}{\mathrm{d}r},$ (5)
$\tau_{T_{f}}=-\rho(1-\Phi)\langle u^{\prime}_{f}v^{\prime}_{f}\rangle,$ (6)
$\tau_{T_{p}}=-\rho\Phi\langle u^{\prime}_{p}v^{\prime}_{p}\rangle,$ (7)
$\tau_{p}=\Phi\langle\sigma^{p}_{xy}\rangle,$ (8)

where $\mu$ the dynamic viscosity of the fluid, $U_{f}$ the mean fluid
velocity in the azimuthal direction, $u^{\prime}$ and $v^{\prime}$ the
velocity fluctuation in the azimuthal and radial direction with the subscripts
$f$ and $p$ denoting fluid and particulate phase, respectively,
$\sigma^{p}_{xy}$ the general stress in the particulate phase, normal to the
cylindrical surface and pointing in the radial direction. Here we note that
the contribution to fluid viscous stress due to velocity in the axial
direction is neglected since it is a minor effect.

At a fixed $Re$, the wall stress of single-phase case,
$\tau_{w,\Phi=0}=\mu\frac{\mathrm{d}U}{\mathrm{d}r}|_{r=r_{i}}$, is a
constant, and the particle-induced stress ($\tau_{p}$) increases with
increasing $\Phi$. In addition, it has been reported that in channel flow
(Picano et al., 2015), for a fixed $Re$ in the current low particle volume
fraction ranges, the viscous stress ($\tau_{v}$) weakly depends on $\Phi$, and
the turbulent Reynolds stress of the combined phase ($\tau_{T}$) increases
with increasing $\Phi$. Though there are differences between the channel flow
and the TC flow, the result in the channel flow is instructive for the
understanding of the current study. Considering the dependence above of the
stress on $\Phi$ at a fixed $Re$, the normalized friction coefficient
increases with increasing $\Phi$, which is consistent with the trends in
figure 2. On the other hand, for a fixed low $\Phi$ (as in this work), the
turbulent Reynolds stress of fluid phase in single-phase flow
($\tau_{T_{f},\Phi=0}$) increases greatly as $Re$ increases, which makes the
contribution of particulate phase ($\tau_{T_{p}}$ and $\tau_{p}$) relatively
insignificant and therefore results in the decreasing trends of normalized
friction coefficients with increasing $Re$. Another feature of the normalized
friction coefficients in figure 2 is that, as $Re$ increases, the differences
between various $\Phi$ decrease. Specifically, when $Re$ is small, the
contributions of particulate phase to the wall stress are non-negligible,
hence the normalized wall stress (friction coefficients) highly depends on
$\Phi$ through $\tau_{T_{p}}$ and $\tau_{p}$. However, when $Re$ is high
enough and $\Phi$ is low (as in this work), the turbulent Reynolds stress due
to fluid phase in particle-laden flow and single-phase flow ($\tau_{T_{f}}$
and $\tau_{T_{f},\Phi=0}$) plays the dominant role while $\tau_{T_{p}}$ and
$\tau_{p}$ become minor, therefore the contributions from particles become
less and less important as $Re$ increases. Hence, the effect of changing
$\Phi$ on the normalized friction coefficients becomes smaller at higher $Re$
in the current parameter regimes.

On the other side, taking the particle-laden flow as a continuous effective
fluid, the interaction between the particles and the resulting particle
distributions are related to the rheology of a particle-laden flow, which can
be quantified by the effective viscosity, $\nu_{eff}$. In the Stokes regime
($Re\ll 1$), the rheology of dense granular suspensions has been extensively
investigated, and the dependence of the effective viscosity on the particle
volume fraction has been discussed (Guazzelli & Pouliquen, 2018). In the
current semi-dilute regime ($\Phi\leq 10\%$), the normalized effective
viscosity of the granular flow in the Stokes regime, $\nu^{S}_{eff}$, can be
approximated using the Krieger & Dougherty (K-D) formula (Krieger & Dougherty,
1959):

${\nu^{S}_{eff}\over{\nu_{f}}}=(1-\frac{\Phi}{\Phi_{m}})^{-[\eta]\Phi_{m}},$
(9)

where $\nu_{f}$ the viscosity of the fluid, $\Phi_{m}$ the maximum packing
particle fraction ($\Phi_{m}=0.65$ is used here as done in Stickel & Powell
(2005)) and $[\eta]={5\over 2}$ for rigid spheres. In this work, the
$\nu_{eff}$ was calculated using the same method as in previous works (Bakhuis
et al., 2021; Yi et al., 2021), and the details can be found in Appendix B. As
shown in figure 3, we compare the experimental results with the K-D formula.
Though the model captures the increasing trend of the effective viscosity, the
$Re$-dependence of the effective viscosity is missing, indicating that the
relation in the Stokes regime is no longer valid in the current situation. The
disparity found between the experimental data and the model can be understood
since equation 9 was obtained based on the assumptions that the flow is
inertialess and the particles distribute uniformly in the Stokes regime.
However, for the current turbulent flow ($Re\sim 10^{4}$) and the suspended
finite-size particles, the particle inertia is non-negligible and can be
measured by the Stokes number, which is far beyond unity as shown in the later
section. Moreover, as has been reported in previous numerical studies (Picano
et al., 2015; Ardekani & Brandt, 2019), the particles show collective effects,
which are also found in our experiments and will be discussed later. Note that
when $Re=6.5\times 10^{3}$, the flow could be in the classical regime with
laminar boundary layers and a turbulent bulk with Taylor vortex (Grossmann et
al., 2016), which accounts for the more rapidly increasing trend than the
model and other experimental data. Using the effective viscosity, the shear-
thinning effect of the particle-laden flow is also examined, which can be well
described by the Herschel–Bulkley model (Herschel & Bulkley, 1926), and the
details can be found in Appendix B.

Figure 3:  The non-dimensional effective viscosity, $\nu_{eff}/\nu_{f}$, as a
function of the particle volume fraction, $\Phi$, for (a) $\lambda=1/3$
(oblate), (b) $\lambda=1$ (spherical) and (c) $\lambda=3$ (prolate), where
$\nu_{f}$ is the kinematic viscosity of the solution.

###  3.2 Effects of the particle aspect ratio

Next, we investigate the effects of changing the particle aspect ratio on the
drag of the system. Particles with three kinds of aspect ratio are used:
$\lambda=1/3$ (oblate), $\lambda=1$ (spherical) and $\lambda=3$ (prolate). The
results are already given in figure 2 and figure 3. It is found that the
particles could increase the drag of the system regardless of their aspect
ratio, which is attributed mostly to the hydrodynamics interactions and rarely
to the frictional contact between the particles in the current low $\Phi$
range (Guazzelli & Pouliquen, 2018). The shear-thinning effect and the
increasing trend of the drag modification with increasing $\Phi$ are found to
be ubiquitous in all cases.

It is remarkable, however, that particles with different aspect ratios could
affect the drag of the system to different degrees, even for the same $Re$ or
$\Phi$. As shown in figure 2, for a given $\Phi$, the
$c_{f,\Phi}/c_{f,\Phi=0}$ of the oblate case decrease much more rapidly than
that of the spherical and prolate cases, indicating that the suspended oblate
particles result in a more pronounced shear-thinning effect, which can also be
verified by the effective viscosity (see Appendix B). Moreover, for a given
$Re$ and $\Phi$, the suspensions of the spherical, prolate and oblate
particles result in the greatest, moderate and minimal drag, respectively. In
the investigated ranges, the largest discrepancy of $c_{f,\Phi}/c_{f,\Phi=0}$
between suspensions of particles with different aspect ratios is $4\%$, which
occurs at $\Phi=10\%$ and $Re=1.3\times 10^{4}$ in the spherical and oblate
cases. Given the impressive accuracy of the drag measurements (less than 1%)
and the relatively low $\Phi$, this disparity in the drag modification is
quite noticeable. In addition, the difference of $c_{f,\Phi}/c_{f,\Phi=0}$
increases with increasing $\Phi$, which is due to the increasing importance of
particle-induced stress at higher $\Phi$ (Ardekani & Brandt, 2019). Therefore,
it is reasonable to speculate that, as $\Phi$ further increases, the
differences of the drag modification between different aspect ratios would
become larger. Note that, this result is different from the particle-laden
channel flow in the previous study (Ardekani & Brandt, 2019), where they found
that only the spherical particles increase the drag and the other two types of
particles reduce the drag.

The dependence of the drag on the particle aspect ratio provides an
experimental clue to the understanding of the mechanisms of bubbly drag
reduction. Flow with dispersed bubbles can, under certain conditions, result
in significant drag reduction (Van den Berg et al., 2005; van den Berg et al.,
2007; Ezeta et al., 2019). However, bubbles are deformable, making it
impossible to fix the bubble shape and therefore to isolate the effects of the
bubble shape. van Gils et al. (2013) and Verschoof et al. (2016) have reported
that the bubble deformation is crucial for achieving significant drag
reduction, but the contributions of (i) the deformation process and (ii) the
ultimate bubble shape after the deformation remain unknown. Obviously, the
rigid particle suspensions are significantly different from bubbly flow,
including the slip conditions at the surface, the resistance of the dispersed
phase to straining motion, the polydispersity, the presence/absence of
contaminants (surfactants), etc, and therefore a one-to-one comparison between
these two types of flow is also unrealistic. However, the one that should be
emphasized is that, as done in this work, the shape effect of rigid spheroidal
finite-size particles on the overall drag provides a relatively effortless
implement to study the shape effects of bubbles during the deformation
process. Notwithstanding how simplistic the rigid particles are compared to
bubbles, these particles (rigid particles and bubbles) behave somehow similar
in such as the kinematic motion (Mathai et al., 2020), making the study of the
rigid particles a reasonable choice to provide a reference case for bubbly
flow studies. In this work, the rigid spheroidal particles are used to study
their shape effect on drag. Due to the frictional contact between solid
surfaces, rigid particles dispersed in the flows result in the drag
enhancement (Guazzelli & Pouliquen, 2018), which is contrary to the drag
reduction in the bubbly flow. However, the fact that the particle aspect ratio
affects the drag modification in the current particle-laden flow, also hints
that the bubble shape could affect the drag of the bubbly flow. Given that the
shape effect on the overall drag is relatively small (compared to the drag
modulation amplitude in bubbly flow, which is around $40$% at $\Phi=4\%$
(Verschoof et al., 2016)), one would expect that the bubbles can also modulate
the turbulence through other mechanisms next to the change of their shapes.
Therefore, the unique features of bubbly flow relative to rigid particle-laden
flow are worthy of attention for future studies.

###  3.3 The collective effects of particles

Figure 4:  The spherical particle positions which are obtained from different
frames for $\Phi=0.5\%$ at (a) $Re=6.5\times 10^{3}$ and (b) $Re=1.3\times
10^{4}$. The value of the color bar means the number of times that the
particles appear at the position denoted by the points in the graph. The
green, magenta and yellow rectangles represent the injected region, vortex-
center region and the ejected region, respectively, and the width of which is
around $1.7d_{e}$. Note that most of the points in the graph are corresponding
to values of $1\sim 2$ in the color bar. $(c)$ shows the sketch of flow
structures and the particle positions (dots) at $Re=6.5\times 10^{3}$. The
injected and ejected plumes are represented by the red and blue arrows,
respectively. Note that the particle positions in the sketch are not
experimental data and for demonstration only.

To reveal the physical mechanism of the drag modification, we look into the
particle distribution by performing optical measurements. It should be noted
that, even at the minimal particle volume fraction ($\Phi=2\%$), the particles
cause violent light scattering and cannot be accurately detected by
algorithms. Therefore, we start with a smaller volume fraction ($\Phi=0.5\%$,
the number of particles $\simeq 1700$) to reduce the intensity of the light
scattering, so that the particles in the images can be detected using the
ellipse detection algorithms (Lu et al., 2020). One may question that whether
the particle distribution obtained at this low volume fraction could
qualitatively represent that at higher volume fractions since the particle
dynamics change greatly with increasing $\Phi$. To assuage this misgiving, we
perform torque measurements at $\Phi=0.5\%$ and the results have been shown in
figures 2,3,8,9,10. It can be seen that the quantities related to the drag of
the system at $\Phi=0.5\%$ (including $c_{f}$, $\nu_{eff}$ and $G$) show
similar trends to that at higher volume fractions, hinting that the particles
behave in similar ways at the low and high volume fractions in the current
parameter regimes. Here, as depicted in figure 4(a,c), we define the region
where the plumes are ejected from the inner (outer) boundary layer to the bulk
as the ejected (injected) region, and the region between them is defined as
the vortex-center region. The spherical particle positions which are obtained
from different frames when $\Phi=0.5\%$ at $Re=6.5\times 10^{3}$ and
$Re=1.3\times 10^{4}$ are given in figure 4(a) and figure 4(b), respectively.
When $Re=6.5\times 10^{3}$, it is found that the particles distribute non-
uniformly, and the pattern of the particle distributions reminisces about the
Taylor vortices in TC flow (Grossmann et al., 2016). The particle
distributions show a lower clustering near the inner wall in the ejected
region, while in the injected region, the lower clustering emerges near the
outer wall. However, when the $Re$ is increased to $1.3\times 10^{4}$, the
particle distribute nearly homogeneously in the entire system (figure 4(b)).

To quantitatively evaluate the collective effects of the particles, we choose
three typical regions of the flow structures (i.e., the injected region,
ejected region, and the vortex-center region) and calculated the PDF of the
particle radial positions. As shown in figure 5, the PDF is consistent with
the pattern of the particle distributions in figure 4. When $Re=6.5\times
10^{3}$, the PDF has the minimal value near the inner wall in the ejected
region, indicating the emergence of the lower clustering region. While in the
injected region, the PDF peaks near the inner wall (i.e., highly clustering
region) and approaches the lowest value near the outer wall. Not surprisingly,
as shown in figure 5(b), the PDF curves tend to overlap with each other when
the $Re$ increases, indicating that the distribution of the particles becomes
less non-uniform in the entire system at higher $Re$. Note that, the inner
wall peak appearing in the ejected region at higher $Re$ (figure 5b), which is
opposite to the behavior found at low $Re$ (figure 5a), and this might result
from the slight shift of flow structure positions since the positions of the
Taylor vortex could be not exactly the same at low and high $Re$.

Figure 5:  The PDF of the particles position for $\lambda=1$ (spherical) at
$(a)$ $Re=6.5\times 10^{3}$ and $(b)$ $Re=1.3\times 10^{4}$. The two red
dashed vertical lines in each figure indicate the position of an equivalent
radius of the particles (i.e., $r_{e}=0.5d_{e}$) away from the walls.

The difference of the particle distributions at different $Re$ can be
interpreted from the perspective of the evolution of flow structures and the
finite-size effect of the particles. On the one side, though the TC flow
displays flow structure at high $Re$ (Huisman et al., 2014), the Taylor
vortices become turbulent and the velocity fluctuations increase as $Re$
increasing (Grossmann et al., 2016), resulting in the more vigorous particle
motion. On the other side, the finite-size effect of the particle can be
characterized by the particle Reynolds number. Since the slip velocity of the
particles is not accessible in the current experiments, the particle Reynolds
number is estimated using the bulk velocity of the flow $u_{b}$, i.e.,
$Re_{p}=u_{b}d_{e}/\nu$, where $u_{b}$ can be estimated as $u_{b}\simeq
0.4\cdot\omega_{i}r_{i}$ in the present Reynolds number regime (Grossmann et
al., 2016). Considering that the flow Reynolds number is defined by equation
1, one can obtain the particle Reynolds number as:

$Re_{p}=0.4{\frac{d_{e}}{d}}Re.$ (10)

Hence, the $Re_{p}$ ranges from $2.6\times 10^{2}$ to $10^{3}$ in the
experiments, and the finite-size effects of the particle become more
pronounced at higher $Re$.

Further, the particle inertia can also be measured by the particle Stokes
number, $St=\tau_{p}/\tau_{\eta}$, where $\tau_{p}$ and $\tau_{\eta}$ are the
inertia response time of the particles and the Kolmogorov timescale of the
flow, respectively. For spherical particles suspended in TC flow, the Stokes
number is reduced to:

$St={\frac{\rho_{p}d_{p}^{2}}{18\rho_{f}[(r_{o}^{2}-r_{i}^{2})r_{i}d]^{1/2}}(GRe)^{1/2}},$
(11)

i.e., the $St$ (or, the particle inertia) increases with increasing $G$ and
$Re$. For non-spherical particles, $St_{non}=c\cdot St$, where $c=f(\lambda)$
is a constant only depends on $\lambda$ (Voth & Soldati, 2017). Since the
suspension is dilute here ($\Phi=0.5\%$), the non-dimensional torque $G$ can
be approximated to that of the single-phase case, $G_{sp}$, giving the $St$
ranging from $10$ to $60$. Therefore, in the current $Re_{p}$ and $St$ ranges,
the suspended particles could induce unsteady wakes and exhibit inertia
clustering (Toschi & Bodenschatz, 2009; Mathai et al., 2020). Specifically,
for the case of $Re=6.5\times 10^{3}$ in figure 4(a) (correspondingly,
$Re_{p}=2.6\times 10^{2}$ and $St=10$), the particles are principally driven
by the strong plumes released from the boundary layer, which are depicted by
the arrows in figure 4(c). While for the case of $Re=1.3\times 10^{4}$ in
figure 4(b) (correspondingly, $Re_{p}=5.2\times 10^{2}$ and $St=25$), the
particles with the increased inertia can escape more easily from the flow
structures and distribute more uniformly.

Since the particle distributions are inhomogeneous in the axial direction of
the system, we use the averaged PDF, which is obtained by calculating the
arithmetic average value of the three typical regions, to quantitatively
represent the collective effects of particles in the entire system. As shown
in figure 6(a-c), for a given $\lambda$, the trends of the averaged PDF curves
remain when the $Re$ increases from $6.4\times 10^{3}$ to $Re=1.3\times
10^{4}$, suggesting that the increasing turbulent intensity has negligible
effects on the averaged particle migration in the radial direction of the
system in the current situation.

Nevertheless, for different $\lambda$, the averaged PDF curves show distinct
differences regardless of the $Re$. In other words, particles with different
$\lambda$ show different collective behaviors near the walls and thereby are
expected to affect the boundary layer to different degrees. Indeed, the
formation of particle layers has been reported in the particle-laden channel
flow in the previous simulation works (Costa et al., 2016; Ardekani et al.,
2017; Ardekani & Brandt, 2019). Ardekani & Brandt (2019) have shown that the
spherical particles form a particle layer, which could enhance the near-wall
Reynolds stress. While for the cases of the oblate and prolate particles, the
near-wall Reynolds stress is attenuated due to the absence of the particle
layer. In the present work in TC flow, as indicated in figure 5 and figure
6(b), the spherical particles preferentially cluster and form a particle layer
near the inner wall, where the boundary layer exists. Therefore, the maximum
drag modification is observed in the flow laden with spherical particles.
However, the near-wall clustering phenomenon disappears in the oblate case
(figure 6(a)), of which the PDF peaks in the bulk and has the lowest value
near the walls. The averaged PDF curves indicate that the oblate particles
prefer to cluster in the bulk and thereby have a smaller effect on the
boundary layer, accounting for the observations of the minimal drag
modification in figure 2 and figure 3.

Figure 6:  The averaged PDF of the particles position (a,d) for $\lambda=1/3$
(oblate), (b,e) for $\lambda=1$ (spherical), (c,f) for $\lambda=3$ (prolate).
(a-c) are obtained at $\Phi=0.5\%$ by calculating the arithmetic average value
of the three typical regions in figure 4, while (d-f) are obtained at
$\Phi=2\%$ by manually detecting the particle positions. The two red dashed
vertical lines in each figure are the same as in figure 5.

However, one more question remains since so far the analyses of particle
distribution are based on the optical measurements at $\Phi=0.5\%$: will the
particle preferential clustering persist at even higher $\Phi$? To bridge the
gap of volume fractions between the torque measurements ($\Phi\geq 2\%$) and
optical measurements ($\Phi=0.5\%$), we further conduct optical measurements
at higher volume fractions. Since the domain is illuminated from the back, the
light intensity decreases greatly at higher volume fractions, making the
particles hard to be distinguished from the background fluid. At higher volume
fractions, the feasible method to detect the particles is manual detection,
which is of relatively low accuracy but provides reliable information. The
averaged PDF curves of particle distribution at $\Phi=2\%$ are shown in figure
6(d-f). For each case, 100 frames are used and the total number of detected
particles is more than 3000. For even higher volume fractions ($\Phi\geq
4\%$), the enormous amount of unfocused particles make the particles inside
the focal plane invisible, therefore no useful data can be obtained.

One can see in figure 6(d-f) that the spherical particles still preferentially
cluster near the inner wall and therefore form a particle layer, which is
consistent with the result obtained at $\Phi=0.5\%$. Additionally, at
$\Phi=2\%$, the distribution of spherical particles becomes more non-uniform
in the radial direction than that at $\Phi=0.5\%$, which has also been
reported in Fornari et al. (2016), hinting that the spherical particles tend
to move toward the walls as $\Phi$ increases. This growing non-uniform
distribution possibly results from the stronger shear-induced particle-
particle interactions at higher $\Phi$, and could partially account for the
increasing drag differences compared with other particle shapes as $\Phi$
increases. Moreover, as $\Phi$ increases, the particles might relaminarize the
bulk flow, and thus suppress the Reynolds stress (Fornari et al., 2016). This
Reynolds stress suppression could therefore yield a stronger $Re$-dependence
of the drag at higher $\Phi$, which is verified by the stronger shear-thinning
effects of normalized friction coefficient (figure 2) and the normalized
effective viscosity (figure 10). On the other hand, for oblate and prolate
cases, it is clear that most of the particles distribute in the bulk region.
The near-wall clustering phenomenon disappears and therefore the particle
layer is absent, which is similar to that of $\Phi=0.5\%$ and accounts for
their similar overall drag.

So far, the optical measurements performed at $\Phi=0.5\%$ and $\Phi=2\%$ lead
to the same conclusion that the larger drag modification is connected to the
near-wall particle clustering in the current system. Though the result and
conclusion of particle preferential clustering might not be directly
extrapolated further to higher volume fractions, one reasonable speculation
would be that it will play a significant role in the drag modulation at higher
$\Phi$. Of course, further studies are needed to confirm it in future work.

##  4 Conclusion

In this study, we experimentally investigated the drag modification by
neutrally buoyant finite-size particles in the Taylor-Couette turbulent flow.
The Reynolds number ranges from $6.5\times 10^{3}$ to $2.6\times 10^{4}$, and
the particle volume fraction ranges from $0\%$ to $10\%$. To study the shape
effects of the finite-size particle, we conduct experiments using particles
with aspect ratio equals to $\lambda=1/3$ (oblate), $\lambda=1$ (spherical),
and $\lambda=3$ (prolate). It is found that, different from the cases in
bubbly TC flow, the rigid particles increase the drag of the system due to the
frictional contact between solid surfaces, and the particle-laden flow somehow
exhibits the shear-thinning effect since the turbulent stress becomes dominant
at higher Reynolds number in the current low volume fraction ranges. The drag
modification by the particles was also interpreted from the perspective of the
effective viscosity, which shows a discrepancy from the Krieger & Dougherty
formula due to the non-negligible flow inertia and the non-uniform particle
distributions at high $Re$ and $\Phi$ in the current study. Through varying
the particle aspect ratios, we found that the suspensions of the spherical,
prolate, and oblate particles result in the greatest, moderate and minimal
drag, respectively. The dependence of the drag modification on the particle
aspect ratio also hints that the bubble shape might affect the drag of the
flow to some extent in bubbly flow.

Furthermore, we performed optical measurements at low volume fractions
($\Phi=0.5\%$ and $\Phi=2\%$) and found that the drag modification induced by
the suspended particles is related to the particle collective effects. For
$Re=6.5\times 10^{3}$ (correspondingly, $Re_{p}=2.6\times 10^{2}$ and $St=10$)
at $\Phi=0.5\%$, the particles could follow the motion of the flow and the
distributions of the particle positions obtained from different frames reflect
the Taylor vortices. However, when $Re$ increases to $1.3\times 10^{4}$
(correspondingly, $Re_{p}=5.2\times 10^{2}$ and $St=25$), the Taylor vortices
become turbulent and the finite-size effects of the particle increase,
allowing the particles to escape more easily from the flow structures and
resulting in the more uniform distributions. Additionally, it is found that
the particle aspect ratio affects the particle collective effects. The
spherical particles preferentially cluster near the walls and form a particle
layer, while which are absent in the oblate case. This particle preferential
clustering is verified to hold at $\Phi=2\%$. Based on the results, it can be
concluded that, for particles with different aspect ratios at low volume
fractions ($\Phi=0.5\%$ and $\Phi=2\%$ here), the different preferential
collective effects could affect the boundary layer to different degrees, and
finally result in the different drag modifications. More studies are needed to
further explore how particles modify the overall drag at higher volume
fractions.

## Acknowledgement

This work was supported by the Natural Science Foundation of China under grant
nos.11988102, 91852202.

##  Appendix A Torque measurement and the end effect calibration

The torque of system, $\tau_{total}$, can be divided into two parts: (i) the
torque, $\tau$, due to the sidewall of the inner cylinder (TC flow), (ii) the
torque, $\tau_{end}$, contributed from the von Kármán flow at the end plates.
Since $\tau$ increases linearly with the height of the inner cylinder
(Greidanus et al., 2011; Hu et al., 2017), the $\tau_{end}$ can be obtained
through the vertical intercept of the fitting lines. We conduct experiments to
measure the torque using three apparatus with different heights of $L$,
$1.5L$, $2L$, and the results are shown in figure 7. In these calibration
experiments, the single-phase glycerin-water solution is used (i.e.,
$\Phi=0$). For different Reynolds numbers, the ratio of $\tau_{end}$ to
$\tau_{total}$ is found to be around a constant (25%). Here we assume that for
$\Phi>0$ the ratio of $\tau_{end}$ to $\tau_{total}$ is the same as that for
single-phase case ($\Phi=0$).

Figure 7:  The calibration of the torque measurements. The torque contribution
from the von Kármán flow at the ends of the system can be determined as the
vertical intercept of the fitting line. Here the particle volume fraction
$\Phi=0$, i.e., the single-phase glycerin-water solution, is used.  Figure 8:
The dependence of the modified dimensionless torque, $G_{m}$, on the modified
Reynolds number, $Re_{m}$, for (a) $\lambda=1/3$ (oblate), (b) $\lambda=1$
(spherical), (c) $\lambda=3$ (prolate). The insets show $G_{m}$ compensated
with $Re_{m}^{-1.6}$.

##  Appendix B The calculation of the effective viscosity

The rheology of multiphase flow can be characterized using the effective
viscosity, $\nu_{eff}$. For single-phase TC turbulent flow ($\Phi=0\%$), a
simple scaling law exists between $G$ and $Re$: $G\propto Re^{\alpha}$
(Eckhardt et al., 2000). Assuming that this relation is still valid for
particle-laden flow ($\Phi>0\%$) here, the following equation can be derived:

${\nu_{eff}\over\nu_{f}}={({\tau\over{\tau_{f}}})^{1\over{2-\alpha}}},$ (12)

where $\nu_{f}$ is the viscosity of the fluid (i.e., the single-phase flow),
and $\tau$ and $\tau_{f}$ are the measured torque for the particle-laden flow
and the single-phase flow, respectively. As one could see from the derivation
above, the effective viscosity is a fitting parameter depending on the scaling
law between $G$ and $Re$. Using the equation above, the effective viscosity of
the particle-laden flow can be calculated. We define the modified
dimensionless torque, $G_{m}={\tau\over{2\pi l\rho_{f}\nu_{eff}^{2}}}$, and
the modified Reynolds number, $Re_{m}=\omega_{i}r_{i}d/\nu_{eff}$. As shown in
figure 8, it is found that the particle-laden flow satisfied the scaling law
$G_{m}\propto Re_{m}^{\alpha}$, where $\alpha\simeq 1.6$. The dependence of
the normalized friction coefficient on the modified Reynolds number is shown
in figure 9.

Figure 9:  The normalized friction coefficient of the Taylor-Couette system,
$c_{f,\Phi}/c_{f,\Phi=0}$, as a function of the modified Reynolds number,
$Re_{m}$, for (a) $\lambda=1/3$ (oblate), (b) $\lambda=1$ (spherical) and (c)
$\lambda=3$ (prolate), where $c_{f,\Phi=0}$ is the friction coefficient for
the single-phase case. The accuracy of the experiments is indicated by the
error bars, which are typically less than 1%. Figure 10:  The dependence of
the non-dimensional effective viscosity, $\nu_{eff}/\nu_{f}$, on the
characteristic shearing rate, $\dot{\gamma}$, for (a) $\lambda=1/3$ (oblate),
(b) $\lambda=1$ (spherical) and (c) $\lambda=3$ (prolate). The curves are
fitting results using the HB model. Insets: the decreasing flow index $n$ with
the increasing $\Phi$ indicates a more pronounced shear-thinning effect at
higher $\Phi$.

Using the effective viscosity, the shear-thinning effect of the particle-laden
flow can be quantified. The dependence of the non-dimensional effective
viscosity, $\nu_{eff}/\nu_{f}$, on the characteristic shearing rate,
$\dot{\gamma}=\omega_{i}r_{i}/d$, for various aspect ratios is shown in figure
10. To evaluate the shear-thinning effect of the particle-laden flow, we use
the Herschel-Bulkley (HB) model (Herschel & Bulkley, 1926):

$\mu_{eff}=k_{0}\dot{\gamma}^{n-1}+\tau_{0}\dot{\gamma}^{-1},$ (13)

where $\mu_{eff}$ is the effective dynamic viscosity of the particle-laden
flow, $k_{0}$ and $n$ represents the consistency and the flow index,
respectively, and $\tau_{0}$ is the yield shear stress. Since the flow is far
from the jamming state in the current system, the yield shear stress is
expected to be zero ($\tau_{0}=0$). As the density of the fluid and the
particle are matched, we take $\rho_{f}$ as the density of the particle-laden
flow, giving $\mu_{eff}/\mu_{f}$ = $\nu_{eff}/\nu_{f}$, where $\mu_{f}$ is the
dynamic viscosity of the single-phase flow. Consequently, the HB model can be
simplified as $\nu_{eff}/{\nu_{f}}=k_{0}\dot{\gamma}^{n-1}/\mu_{f}$ and the
fitting curves are shown in figure 10. Note that the fitting parameter $k_{0}$
is different for various particle aspect ratios and volume fractions. For the
single-phase case ($\Phi=0\%$), the normalized effective viscosity
$\nu_{eff}/\nu_{f}$ is around 1 for various $Re$. When the $\Phi$ increases,
the HB model agrees well with the experimental data, and the flow index $n$ of
the HB model decreases with the increasing $\Phi$, suggesting that the shear-
thinning effect becomes more pronounced at higher $\Phi$.

Figure 11:  The examples of particle detection for (a) $\lambda=1/3$ (oblate),
(b) $\lambda=1$ (spherical) and (c) $\lambda=3$ (prolate) at $Re=6.5\times
10^{3}$. Most particles inside the focal plane have been detected.

##  Appendix C Particle detection

During the optical measurements, we locate the focal plane of the camera at
the crossing plane of the axis and the light-line (the cyan shadow plane in
figure 1(a)). The depth of the field is around $0.21$ mm, which is smaller
than the particle diameter. Therefore the depth resolution in the azimuthal
direction is high enough. The central height of the camera is kept the same as
the apparatus so that the visible window is located at the central height of
the apparatus, therefore the ending effects in the axis direction are
eliminated.

The particle detection is performed using the ellipse detection method
proposed by Lu et al. (2020). The examples of particle detection are given in
figure 11. Inside the focal plane, most particles are detected and a few
others are not since the material used to print the particles is transparent.
Therefore, to ensure the accuracy of the data, 30000 frames are used to
calculate the cumulative spatial distribution (figure. 4) and the PDF curves
(figure. 5 and figure. 6) for each $Re$ case.

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#  Burt: A Chatbot for Interactive Bug Reporting

Yang Song1, Junayed Mahmud2, Nadeeshan De Silva1, Ying Zhou3,
Oscar Chaparro1, Kevin Moran2, Andrian Marcus3, Denys Poshyvanyk1  1William &
Mary (USA), 2George Mason University (USA), 3The University of Texas at Dallas
(USA)

###### Abstract

This paper introduces Burt, a web-based chatbot for interactive reporting of
Android app bugs. Burt is designed to assist Android app end-users in
reporting high-quality defect information using an interactive interface. Burt
guides the users in reporting essential bug report elements, i.e., the
observed behavior, expected behavior, and the steps to reproduce the bug. It
verifies the quality of the text written by the user and provides instant
feedback. In addition, Burt provides graphical suggestions that the users can
choose as alternatives to textual descriptions.

We empirically evaluated Burt, asking end-users to report bugs from six
Android apps. The reporters found that Burt’s guidance and automated
suggestions and clarifications are useful and Burt is easy to use. Burt is an
open-source tool, available at github.com/sea-lab-wm/burt/tree/tool-demo.

A video showing the full capabilities of Burt can be found at
https://youtu.be/SyfOXpHYGRo.

##  I Introduction

Bug reports are essential for successful software maintenance and evolution.
These reports are expected to provide clear and detailed information related
to a defect, including the system’s observed behavior (OB), the expected
behavior (EB), and the steps to reproduce the bug (S2Rs)[1]. Unfortunately,
bug reports are often unclear, incomplete, and/or ambiguous – often causing
delays during the bug resolution process [2, 3].

One main challenge that contributes to low-quality bug reports is the
knowledge gap between what reporters know and what developers need [4, 1].
This is especially true when the reporters are software end-users, who are
often unfamiliar with the system internals and do not know the information
elements important for developers (e.g., the OB, EB, and S2Rs) and how to
express them. Most bug reporting systems (e.g., GitHub Issues, Jira, or
Bugzilla) are not designed to address this knowledge gap, since they are
static web forms and templates that: (1) offer limited guidance on what
information needs to be reported, and how it needs to be reported; and (2) do
not provide feedback to end-users on whether the information they provide is
clear and complete. In consequence, the burden of providing high-quality bug
information rests mainly on the reporters.

We propose a web-based chatbot for interactive BUg repoRTing (or Burt). The
software engineering challenge addressed by Burt is ensuring high-quality bug
reporting by end-users, considering the above-mentioned limitations of
existing bug reporting systems. The envisioned users for Burt are end-users
who report problems with their app. Burt guides the users during reporting
essential bug report elements (i.e., OB, EB, and S2Rs), offering instant
quality verification, corrections, and graphical suggestions. Burt’s usage
methodology is described in detail in section II-B.

Burt implements techniques based on natural language processing, dynamic
software analysis, and automated bug report quality assessment. We designed
and instantiated Burt as a stand-alone web system for Android apps that
focuses on bugs manifesting in the app’s UI.

We empirically evaluated Burt, asking 18 end-users to report 12 bugs from six
Android apps using Burt, and assess their experience. The reporters found
Burt’s guidance and automated suggestions/clarifications to be useful,
accurate, and easy to use. Moreover, the bug reports collected by Burt are of
higher quality than reports collected via a traditional template-based bug
reporting system.

Burt is an open-source tool hosted on GitHub [5] that can be used for any
Android app project. More details about Burt’s algorithms and evaluation can
be found in its original research paper [6].

##  II The Burt Interactive Bug Reporting Tool

Burt is a standalone web-based chatbot, currently tailored for Android apps,
that aims to collect high-quality information from the reporter through a
guiding dialog. It generates a bug report with textual bug descriptions and
app screen captures.

Burt (i) guides the user in reporting essential bug report elements (the OB,
EB, and S2Rs), (ii) checks the quality of these elements and offers instant
feedback about issues, and (iii) provides graphical suggestions such as the
next S2Rs.

###  II-A Burt’s Graphical User Interface (GUI)

Burt’s GUI is composed of a standard chatbot interface and various panels for
interactive bug reporting (see figure 1). The Chat Box allows the reporter to
provide textual descriptions of the OB, EB, and S2Rs and select Burt’s
graphical suggestions (e.g., the next S2Rs via screenshots). The Reported
Steps Panel enumerates and displays the S2Rs that the user has reported,
allowing them to edit the steps to correct mistakes. The Screen Capture Panel
displays screen captures of the last three S2Rs. The Quick Action Panel
provides buttons to finish reporting the bug, restart the reporting session,
and (pre)view the bug report. The Tips Panel displays suggestions to reporters
on how to use Burt and how to better express the OB, EB, and S2Rs. The tips
change depending on the current stage of the conversation. Burt also provides
a Developer Panel that allows developers to add new apps to Burt (via the
Settings icon next to the Help button).

###  II-B Reporting a Bug with Burt

To report a bug, the user first selects the target app exhibiting the defect
by clicking on its icon—Burt lists the apps that it supports. Then, Burt
guides the reporter through three phases: OB, EB, and S2R reporting. In each
phase, Burt prompts the user to provide individual descriptions of the OB, EB,
and S2Rs, respectively. Burt automatically parses the descriptions and
verifies their quality by matching them to states of a GUI-level execution
model for the app (see Sec. III-C).

If the OB/EB/S2R is matched to an app screen from Burt’s execution model, Burt
asks the user to confirm the matched screen. If the user confirms, Burt
proceeds to the next phase of the conversation (e.g., asking for the EB or
next S2Rs); otherwise, Burt asks the user to rephrase the bug element.

If there are no app screen matches, Burt suggests the user to revise their
description and asks them to rephrase the OB/EB/S2R. With a new description,
the quality verification is re-executed. If there are multiple matches, Burt
provides a list of up to five app screenshots (derived from the app execution
model) that match the description. The user can then inspect the app screens
and select the one that she believes best matches her description of the bug
element. If none are selected, Burt suggests additional app screens, if any.
If the user selects one app screen, Burt saves the bug element description and
screen, and proceeds to prompt the user for the next bug element. After three
unsuccessful attempts to provide a high-quality description, Burt records the
(last) provided description for bug report generation. This process proceeds
for each bug element starting with the OB.

Burt includes an additional feature to help users save time writing S2Rs: it
suggests the probable next S2Rs that the user may have performed during actual
app usage. Burt suggests the first five S2Rs from the most likely path from
the current state to the OB state in the app execution model. This dialogue
flow uses a predictive algorithm that uses Burt’s execution model (see section
III-C). The suggestions are displayed as a list of generated app screens, each
screen representing a S2R. The generated screen is visually annotated with a
yellow oval highlighting the GUI component (e.g., a button) executed by the
step. The user can select none, one, or multiple of the suggested S2Rs. When a
S2R is selected, Burt suggests additional S2Rs, if any. When none are selected
and Burt has more suggestions, Burt asks the user if they want additional
suggestions. If so, Burt displays them. Otherwise, Burt prompts the user to
describe the next S2R.

###  II-C Adding New Apps to Burt

Developers can add new apps to Burt through the Developer Panel, which
requires the developer to upload the app icon and ZIP files containing app
execution data required by Burt to build the app execution model. Burt
uploads/extracts the files, parses the data to identify the app name and
version, verifies the data format, and stores the data for later use. Burt
provides feedback if there are any detected issues with the data.

##  III Burt’s Architecture & Implementation

Burt has three main components (see figure 2). The Natural Language Parser
(NL) parses users’ bug descriptions. The Dialogue Manager (DM) implements the
conversation flows for the reporting process. The Report Processing Engine
(RP) matches the parsed bug descriptions to the app execution model, to assess
bug element quality and provide suggestions.

###  III-A Natural Language Parser (NL)

Burt parses the textual OB/EB/S2R descriptions using dependency parsing via
the Stanford CoreNLP toolkit [7], which produces a tree of grammatical
dependencies between words. Burt first utilizes a heuristic-based approach
from our prior work [8] to identify the sentence type of each user message
(e.g., conditional, imperative, or passive voice). Then, Burt executes one of
its 16 parsing algorithms (one for each sentence type) that traverse the tree
to extract the relevant words from the sentences. This parsing is based on our
prior work on S2R quality assessment [9] and extracts a phrase using the
following format: [subject] [action] [object] [preposition] [object2]. For
example, for the Mileage app [10], the OB sentence “The fuel economy shows a
NaN value on page”, written in present tense, is parsed as [fuel economy]
[shows] [NaN value] [on] [page]. The S2R sentence “Save the car fillup”,
written imperatively, is parsed as [user] [saves] [car fillup].

###  III-B Dialogue Manager (DM)

Burt’s dialogue flow guides users to report the OB, EB, and S2Rs. Burt’s
dialogue is multi-modal and capable of suggesting both natural language and
graphical elements, e.g., screenshots, to assist the user through the
reporting process. The DM relies upon the RP engine to assess the quality of
the bug elements reported by end users. There are two main dialogue flows that
Burt navigates: (i) performing quality checks on written bug report elements
(applies to all bug elements), and (ii) automated suggestion of S2Rs (for S2Rs
only).

###  III-C Report Processing Engine (RP)

Burt’s RP Engine consists of three sub-components:

(1) the App Execution Model is a directed graph where nodes represent app
screens and the edges are transitions between screens, triggered by GUI
interactions (e.g., taps or type events) on GUI components (e.g., buttons or
text fields). The graph screens contain the hierarchy of GUI components with
their metadata (e.g., labels) and a screen capture. The graph edges contain
the action type, the interacted GUI component, and a screen capture
highlighting the component. Burt builds the execution model from app usage
data collected automatically, via automated app exploration, or manually (see
section III-D).

(2) the Dialogue Quality Processor performs quality verification of the parsed
OB/EB/S2R descriptions, by mapping them to app states/interactions from the
execution model. A textual description is high-quality if it can be matched to
the model, otherwise, it is low-quality. This definition and Burt’s dialogue
features that prompt users to improve low-quality descriptions aim to reduce
the knowledge gap between reporters and developers. To perform quality
verification, Burt extends the bug description resolution/matching algorithm
from our prior work [9] and performs exploration of the execution model,
driven by the matching of the reported OB/EB/S2Rs and user confirmations
during the bug reporting process.

(3) the S2R Response Predictor determines and suggests to the reporter the
next S2Rs that she may have performed in practice. Burt implements a shortest-
path approach to predict the next S2Rs [6]. Burt determines the paths between
the current graph state and the corresponding OB state, and then, it computes
the likelihood score based on the execution model edge weights, which are
higher for manual app usage [6].

###  III-D Collecting App Execution Data

Burt requires app execution data for building the execution model. This data
encodes sequential interactions made on the app features and comes from two
sources: systematic app exploration via CrashScope [11, 12] and crowdsourced
app usage (e.g., from app users or developers).

CrashScope’s GUI-ripping engine automatically generates app execution data
(app interactions such as taps or type events) by running an app on a mobile
device/emulator and a set of systematic exploration strategies (e.g., top-down
or bottom-up) on the app [11], to uncover as many app screens as possible and
interact with most screen GUI components.

Crowdsourced app usage data complements the automated app usage data [13].
This data can be collected through built-in trace recording app features that
capture app usages “in the wild”, or during in-house GUI-level app testing
performed by developers. Burt provides two tools to assist trace capture: Avt
and TraceReplayer. Avt is a desktop app that allows humans to collect video
recordings and getevent traces from a mobile device/emulator while humans are
using an app. TraceReplayer parses the collected Avt traces (i.e., from
humans) and converts them into the CrashScope data format. In this way, Burt
can read/use this data to augment the app execution model (see details in
Burt’s repository [5]).

###  III-E Burt Implementation

Burt is currently implemented as a web application, using the React Chatbot
Kit [14] and Spring Boot [15]. Burt also provides command-line tools for
CrashScope and TraceReplayer, and the desktop Avt app, along with detailed
documentation on how to use them. Burt’s implementation is tailored for
Android applications, however, its underlying techniques are generic enough to
be easily adapted for other types of software—the App Execution Model Data
Collection is the only platform-specific part.

##  IV Burt’s Evaluation

We conducted an empirical study to evaluate: (1) Burt’s perceived
usefulness/usability (RQ1/RQ2); (2) Burt’s intrinsic accuracy in performing
bug report element quality verification and prediction (RQ3); and (3) the
quality of the bug reports collected with Burt (RQ4).

###  IV-A Methodology

We selected 12 Android bugs (seven crashes, one handled error, and four non-
crashes) from the dataset of our prior work [16]. The bugs come from six
Android apps of different domains: AntennaPod, Time Tracker, GnuCash,
GrowTracker, and Droid Weight. To collect app execution data, we executed
CrashScope on these apps and asked two computer science (CS) students to use
their main features—see our original paper for more details [6]. We recruited
18 participants to report these bugs (each reported three bugs) using Burt
(most had little or no bug-reporting experience) and asked them to evaluate
their experience via a questionnaire (with Likert-scale and open-ended
questions). We analyzed the conversations the reporters had with Burt and
measured how accurate Burt was during the reporting process. We asked
additional 18 participants to report the same bugs with a template-based bug-
reporting system (a.k.a. Itrac) and analyzed the collected bug reports to
measure their quality based on the bug element correctness framework from our
prior work [9]. Itrac resembles existing issue trackers as it implements a web
form with text fields and templates that explicitly ask for the bug
summary/title and the OB/EB/S2Rs.

###  IV-B Results

####  IV-B1 RQ1/RQ2: Burt’s User Experience

The participants evaluated the usefulness of Burt’s main features.

Screen Suggestions: Half of the 18 reporters agreed that the screen
suggestions were useful, and another half (nine reporters) agreed that they
were sometimes useful.

OB/EB/S2R Quality Verification: The reporters had a positive impression on how
often Burt correctly verified the quality of their bug descriptions. Burt was
able to always (sometimes) verify the OB/EB/S2R descriptions of 9/10/11
(9/6/6) reporters (out of 18). Only two/one participant(s) felt that Burt
rarely recognized and verified their EB/S2Rs.

BURT Messages & Questions: 11 of 18 users often understood Burt’s
messages/questions, while 6 reporters understood them sometimes. Only one
reporter rarely understood them.

Panel of Reported S2Rs: Burt’s panel of reported S2Rs was deemed to be useful
by nine participants and somewhat useful by six participants – one reporter
found it somewhat useless.

The reporters also assessed Burt’s overall ease of use. 12 of 18 reporters
indicated Burt was either easy or somewhat easy to use. Four reporters were
neutral, while two reporters expressed that Burt was somewhat difficult to
use.

RQ1/RQ2 Summary: Overall, reporters found Burt’s screen suggestions and S2R
panel useful and Burt is easy to use. Reporters also suggested improvements to
Burt to support additional wording of bug report elements and provide more
accurate suggestions. Improvements are planned for future work to improve Burt
’s ability to recognize additional vocabulary and ways of phrasing the
OB/EB/S2Rs.

####  IV-B2 RQ3: Burt’s Intrinsic Accuracy

We analyzed the 54 conversations with Burt to assess how often Burt was able
to 1) match OB/EB/S2R descriptions to the execution model, and 2) suggest
relevant OB/S2R app screens to the reporters.

OB reporting: Burt matched the OB description to the correct screen in 3 of 54
(5.5%) conversations and multiple screens in 35 of 54 (64.8%) conversations.
In 29 of 35 (80%) conversations, the reporters selected one of the suggested
screens. Overall, Burt correctly matched the users’ OB descriptions in 32 of
54 (59.3%) conversations.

EB reporting: Burt correctly matched the EB against the OB screen in 17 of 32
(53.1%) cases without having to ask the reporter for confirmation. In 6 of 32
(18.8%) cases, Burt needed to ask the users for confirmation. In the remaining
9 cases, Burt struggled to parse the EB description.

S2R reporting: In the 54 conversations, Burt matched 205 of the written S2R
descriptions from the reporters. Burt matched the correct screen in 157 of 205
(76.6%) cases. As for S2R prediction, among 32 conversations with a matched OB
screen, S2R prediction occurred 146 times (mean: 4.6 per conversation). The
reporters selected 1.6 of the 3.9 suggested S2Rs (on avg.) in 91 of 146 cases
(62.3%).

RQ3 Summary: The results confirm the users’ perception on the usefulness of
screen suggestions and ability of performing correct bug element verification,
which indicates that the techniques used in designing Burt’s components are
adequate.

####  IV-B3 RQ4: Bug Report Quality

We compared the quality of the $54\times 2=108$ bug reports, collected with
Itrac and Burt.

S2R Quality: On average, Burt’s reports contain fewer incorrect S2Rs than the
Itrac reports (8.3% vs. 20.4%) and fewer missing S2Rs (19.4% vs. 32%).

OB/EB Quality. Burt and Itrac reports have a comparable number of incorrect EB
descriptions (8 vs. 6 out of 54 reports). However, Burt reports have more
incorrect OB descriptions compared to Itrac reports (16 vs. 8 out of 54
reports).

RQ4 Summary: Burt bug reports have higher-quality S2Rs than Itrac reports, and
comparable EB descriptions. Burt improvements are needed to better collect OB
descriptions.

##  V Most Related Existing Tools

Moran et al. [4, 17] proposed Fusion, a web system that allows the user to
report the S2Rs graphically via dropdown lists of GUI components and actions
(taps, swipes, etc.). Song et al. [18] proposed Bee, a GitHub plugin that
identifies the type of each sentence in bug reports and alerts reporters of
missing OB/EB/S2Rs. Fazzini et al. proposed EBug [19], a mobile app bug
reporting system, similar to Fusion, that suggests possible future S2Rs as
they are written. Shi et al. [20] proposed BugListener, an approach that
identifies bug report dialogs in community live chats and synthesizes bug
reports from them.

Burt has two main advancements over these prior tools: (1) it supports end-
users with little or no bug reporting experience; for example, Fusion was not
specifically designed to end-users, as inexperienced users found it more
difficult to use; and (ii) it offers an interactive interface, supporting
automated suggestions, instant quality verification, and prompts for
information clarification.

##  VI Final Remarks and Future Work

Burt is a web-based chatbot for interactive bug reporting. Unlike existing bug
reporting systems, Burt can guide end-users in reporting essential bug report
elements (i.e., OB, EB, and S2Rs), provide instant feedback about issues, and
produce graphical suggestions of the elements that are likely to be reported
next. Burt can help end-users easily report bugs and provide higher-quality
bug reports. As future work, we plan to integrate Burt with existing issue
trackers.

## acknowledgements

This work is supported in part by the NSF grants: CCF-1955837, CCF-1955853,
CCF-2217733, and CCF-2007246. Any opinions, findings, and conclusions
expressed herein are the authors and do not necessarily reflect those of the
sponsors.

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