12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

PREDICTION OF DRAG REDUCTION EFFECT IN TURBULENT PULSATING PIPE FLOWBY MACHINE LEARNING BASED ON EXPERIMENTAL DATA
Takuho Kitta, Akihiko Mitsuishi, Kaoru Iwamoto, and Akira Murata
Department of Mechanical Systems Engineering,Tokyo University of Agriculture and Technology,
2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan,
Corresponding author: iwamotok@cc.tuat.ac.jp

ABSTRACTThe drag reduction effect of pulsation in turbulent pipe
flow was predicted by machine learning based on experimental
data. In the experiment, we measured 2498 types of pulsatingflows generated by randomly setting the way of acceleration,
deceleration, and period. The average drag reduction rate was
19% with a maximum of 39%. A machine learning model
which is suitable for time-series is trained to predict bulk flow
velocity and differential pressure to calculate the drag reduction
rate. The pressure gradient is predicted over a wider range thanthat in the previous study. The correlation coefficients between
the experimental results and prediction results were over 0.9.
The predicted drag reduction ratio was 2.3% lower than theexperimental results on average with an RMSE of 6.3%.

METHOD
Experimental method
A schematic of experimental apparatus is shown in Fig. 1.
It consists mainly of acrylic pipe with inner diameter d = 19.5
mm. The radius of the bend is R = 250 mm. The length of theentrance section is 1000 mm to develop turbulent flow. The
length of the test section is l = 2000 mm, and the differential
pressure Δp between upstream and downstream edges of thetest section is measured by differential pressure gauge(EJX110J, Yokogawa Electric co. ltd). Bulk flow velocity ub
and temperature are measured by an electromagnetic flowmeter(LF410, Toshiba Infrastructure systems & Solution co.) andthermocouple (HTK0226, Hakko Electric co.) respectively
which are installed downstream side of the test section. The
working fluid is water. Gear pumps (TG-30S-PU-EB-KA,
Tsukasa electric co.) are adopted to generate pulsating flow
with rapid flow velocity changes. To make a sufficient flow
rate, a set of the five gear pumps are connected in parallel anddriven synchronously.
By changing the voltage input to the pumps with time, theflow velocity changes, and thus a pulsating flow is generated.
To measure the drag reduction effect of various pulsating flows
with different acceleration and deceleration intensities andpulsation period, the following procedure was conducted togenerate the input voltage waveform to the pumps. Figure 2
shows an example of input voltage waveform to the pumps.
The voltage waveforms were generated using splineinterpolation to smooth out changes in flow velocity andpressure gradient to improve prediction accuracy. In addition,
the fact that the pressure gradient does not change abruptly has
advantages from a practical perspective. First, pulsation period
T is set randomly to 4-20 sec. Second, 3-7 control points at 1-6
V are set. The first and last control points are set to the same
voltage. Third, control points are connected by cubic periodic
spline interpolation. Finally, voltage waveforms were generated
when the following conditions are fully met; all voltage values
were in the range of 1-6V, the maximum voltage gradient wasunder 3 V/s, and the mean voltage corresponds to bulk
Reynolds number Reb = 3400-3800. Voltage to the pumps was
input at 50 ms interval. 2498 types of pulsating flows areinvestigated.
Friction drag is evaluated by friction coefficient Cf which is
calculated as

BACKGROUND AND OBJECTIVE
Skin friction drag reduction by control of turbulent flow isimportant for various fields in terms of saving energy. One of
the effective ways to reduce the skin friction drag is an active
control to accelerate the flow. It has been observed that theaccelerated flow reduces the wall shear stress byrelaminarization (Shuy, 1996; Greenblatt and Moss, 1999). The
drag reduction effect of pulsating flow, which repeats
acceleration and deceleration periodically, has been also
investigated. In an experiment, the skin friction drag inpulsating pipe flow was reduced by 63% compared tocorresponding steady flow (Souma et al., 2009). However, due
to a large degree of freedom for acceleration and deceleration
patterns, pulsation in turbulent pipe flow has not been
optimized.
Machine learning has been introduced in the field of fluid
mechanics to deal with problems involving combinations ofmany parameters. In the latest study, the voltage input to acentrifugal pump was changed with time to generate over 7000
types of pulsating flows in a pipe and the machine learning was
performed by using long short-term memory (LSTM) which issuited to predict time-series data (Kobayashi et al., 2021). As aresult, the time response of the bulk flow velocity and thedifferential pressure to the voltage input to the pump was
predicted and the drag reduction effect was also predicted withhigh accuracy. However, the drag reduction effect of pulsating
flow at high pressure gradients has not been sufficiently
investigated because of the limitation of the pump specification.
The purpose of our study is to develop a predictive modelof the drag reduction effect of pulsation in turbulent pipe flow
over a wide range of pressure gradients. In the present study,
we examined the drag reduction effect of various types of
pulsating flows and performed machine learning based on
experimental data.

(1)

1

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

d = 19.5 mm

Flow

Differential pressure gage

Flow meter1000 mml = 2000 mm

Entrance region

Test section

Thermocouple

Gear pumps

Figure 1. Schematic of experimental apparatus.

Acceleration Deceleration
24

T
ub +

V2

…

Vn

LSTM

LSTM

…

LSTM

LSTM

LSTM

…

LSTM

LSTM

LSTM

…

LSTM

Decoder

ub1
Δp1

ub2
Δp2

ubn
Δpn

OutputV1

20
16

Control point
12

V [V]

Mean voltage
0.06

0

200

400

+

0.02
0.00
-0.02
-0.04

t [s]

Encoder

800

αacc
αdec

+

t

0.04

(p/l)

600

Input

0

200

400

600

800

…
…

+

t

Figure 2. An example of pump voltage.

Figure 3. Examples of changes in bulk
flow velocity and pressure gradient.

where τw is the wall shear stress. Drag reduction rate RD is
defined as

Figure 4. Schematic of network structure.

Machine learning
The sequence-to-sequence model is used for machinelearning which is shown in fig. 4. It is the same model used in
the previous study which has shown to be superior in prediction
accuracy to the multilayer perceptron model (Kobayashi et al.,2021). LSTM which is used in this model is a type of recurrent
neural network that can learn time-series data for long-term
dependence. It consists of an encoder that converts time-series
data into a feature vector and a decoder that converts it into
other time-series data. The encoder has two layers of LSTMs inthe forward direction and backward direction. The decoder has
two layers of LSTMs in the forward direction. In this model,
input data is pump voltage, and output data are time-series dataof flow velocity and differential pressure. In other words, timechanges in flow velocity and differential pressure are predictedfrom pump voltage. Then, the drag reduction rate is calculated
from eq. (1) and eq. (2).
Adamax method is used as an optimizer to update theweights. 1998 cases, that is 80% of all cases, are selected astraining data set randomly. 500 cases, that is 20% of all cases,
are selected as validation data set randomly. Training data set isused to fit the parameters of the model. Validation data set isused for the evaluation of a model fit on the training data set.

(2)

where Cf, Blasius represents a value of the empirical formulaprovided by Blasius. The bracket [ ]T represents the timeaveraged value.
As shown in Fig. 3, the pressure gradient is defined in two
sections, one for acceleration where the velocity increases, andthe other for deceleration where the velocity decreases. The
pressure gradient parameter αacc is defined as(4)

where superscript + represents non-dimensionalization by
friction velocity uτ and kinetic viscosity ν, and subscript acc
represents averaged value during the time where the flow isaccelerated within a period. Relaminarization is found to occur
when α>0.018(Patel and Head, 1968).

RESULTS
The present result of drag reduction effect upon pressure
gradient during acceleration and pulsation period from 2498
types of pulsating flows is shown in Fig. 5(a). The maximum
drag reduction rate is RD = 39% at αacc = 0.11 and T+ = 740.

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

RD [%]

RD [%]
50

10 15 20 25 30 35

0.25

0.25

0.20

0.20

0.15

0.15

acc

acc

0

0.10

5

10 15 20 25 30 35

0.10

0.05

0.05

0.00
500 1000 1500 2000 2500 3000 3500 4000

0.00
500 1000 1500 2000 2500 3000 3500 4000
+

+

T

T

(a)

(b)

Figure 5. Distribution of drag reduction rate upon pressure gradient during acceleration and pulsation period:(a) present results; (b) previous results(Kobayashi et al., 2021).
RD [%]

RD [%]
50

10 15 20 25 30 35

0.25

0.25

0.20

0.20

acc,predacc,exp

0

0.15
0.10

10 15 20 25 30 35

0.15
0.10
0.05

0.05
0.00
500

5

0.00
500

1000 1500 2000 2500 3000 3500

1000 1500 2000 2500 3000 3500++

T predT(a)(b)

Figure 6. Distribution of drag reduction rate upon pressure gradient during acceleration and pulsation period:(a) experiment (validation data); (b) prediction.

Regardless of the pulsation period, little drag reduction effect isachieved when αacc < 0.02. This is due to weak acceleration andlack of relaminarization. Many cases of RD > 30% wereobserved at αacc > 0.05 and 700 < T+ < 1200. The sparsity of the
distribution indicates that just the pulsation period and themean pressure gradient during acceleration are unable todetermine the drag reduction rate. Figure. 5(b) shows theresults of the previous study (Kobayashi et al., 2021). Due tothe quick acceleration of the gear pumps, the maximum valueof αacc is 0.22, which is larger than 0.10 in the previous study.
The overall trend is similar. However, the distributions do notmatch accurately because each pulsating flow has different
combinations of acceleration and deceleration.
Figure 6(a) shows the distribution of the drag reduction rateof validation data. A counterpart of Fig. 6(a) predicted by thepresent machine learning model is depicted in Fig. 6(b).
Prediction results are expressed based on αacc, T+ and RD
predicted from the respective validation data. The overall
trends of drag reduction rate between experimental results andprediction results are similar.

Figure 7 shows a representative example of predicting thetime change of flow velocity and pressure gradient. The
prediction result of bulk flow velocity is close to theexperimental results. The Pressure gradient, which is difficult
to predict due to its low linearity with flow velocity, is also
predicted well. In the validation data, the mean pressure
gradient during acceleration of the validation data is αacc = 0.10,
the pulsation period is T+ = 770, and the drag reduction rate is
RD = 35%. On the other hand, because of errors in the meanvalues of flow velocity and pressure gradient compared to theexperimental results, the prediction results were αacc = 0.09, T+= 830, and RD = 31%.
To evaluate the accuracy of the prediction of flow velocity
and differential pressure, the correlation coefficient R is
calculated from the following equation;(5)3

12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

600

0.5
Expriment (Validation)
Prediction

0.3
0.2
0.1
0.0

Expriment (Validation)
Prediction

400

p [Pa]ub [m/s]

0.4

200
0
-200
-400
-600

0

1

2

3

4

5

6

7

0

1

2

3

4

t [s]

t [s]

(a)

(b)

5

6

7

Figure 7. A representative example of prediction by machine learning: (a) bulk flow velocity; (b) pressure gradient.
40

RD,pred [%]30

Prediction
Ground truth
Approximation

20

10

0

-10
-10

0

10

20

30

40

RD,exp [%]Figure 8. Prediction results of drag reduction rate.

Table 1. Error of each parameter in validation data.
Parameter
Flow velocity
Differential pressure

R
0.992
0.977

Here, X represents either flow velocity or differential pressure,σ represents their standard deviation, and n represents thenumber of data points of each waveform. Coefficient ofvariation CV is calculated based on the following definition;

CV
0.01430.0830for differential pressure in the previous study (Kobayashi et al.,2021). Thus, high prediction accuracy is kept even though therapid change in flow velocity and differential pressure due to
new pumps. On the other hand, a comparison of the respective
CV values shows that the CV of differential pressure is morethan five times larger than the CV of flow velocity. This isbecause differential pressure is nonlinear and more difficult topredict than flow velocity.
Figure 8 shows the relationship between experimental
results and prediction results of drag reduction rate. The solidline represents the case of correct prediction, and the dashedline is the regression line of the prediction results. The overall
trend is predicted. Predicted drag reduction rate was on average
2.3% lower than the experimental results. RMSE of dragreduction rate is also calculated to evaluate the mean variation.
RMSE is calculated based on the following definition;(6)Here, RMSEX represents the root mean square errors of either
flow velocity or differential pressure, and the superscript barmeans averaged value.
Table 1 shows correlation coefficients and coefficient ofvariation between the experimental value and predicted valueof flow velocity and differential pressure. The calculated
correlation coefficients are over 0.9 for both flow velocity anddifferential pressure, confirming high correlation between
experimental results and prediction results. These results arecomparable to the R = 0.991 for flow velocity and R = 0.979(7)

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12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12)
Osaka, Japan (Online), July 19-22, 2022

0.02

0.20

Prediction
Ground truth

Prediction
Ground truthdec,predacc,pred

-0.02

0.16
0.12
0.08

-0.06

-0.10

0.04
0.00
0.00

0.04

0.08

0.12

0.16

-0.14
-0.14

0.20

-0.10

-0.06

-0.02

0.02

dec,expacc,exp

Probability density

Probability density(a)(b)
Figure 9. Prediction of pressure gradient: (a) acceleration; (b) deceleration.

0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.00

0.05

0.10

0.15

0.20

0.14
0.12
0.10
0.08
0.06
0.04
-0.08

acc

-0.06 -0.04

-0.02

0.00

0.02

dec

(a)
(b)
Figure 10. Probability density of pressure gradient: (a) acceleration; (b) deceleration.

As a result, the value of 6.3% is obtained whereas 3.8% is in
the previous study (Kobayashi et al., 2021). This is because
machine learning was performed on more than 7000 data ofpulsating flow with slow acceleration and deceleration, whichmeans little change in flow velocity and differential pressure, inthe previous study. Thus, the increase in the RMSE value may
be related to the large variation in flow velocity and differential
pressure and the number of training data.
Figure 9 shows the predicted pressure gradient during
acceleration and deceleration. In both cases, the error tends toincrease as the absolute value increases. This is due to thedifficulty of predicting waveforms that change more rapidly
and the lack of training data for these waveforms. Figure 10
shows the probability densities of the pressure gradient during
acceleration and deceleration for all measured data. Since there
are few data with large absolute values, there is a possibility to
improve the prediction accuracy by increasing such data.

the previous study. The average drag reduction rate for allcases was 19%.
By performing machine learning, time-series data of flow
velocity and differential pressure were predicted from input
voltage to the pumps. Drag reduction rates which are calculated
from them captured the trend of experimental results. The
predicted drag reduction rate was 2.3% lower than theexperimental results on average with an RMSE of 6.3%.

REFERENCES
Shuy, E.B., 1996, "Wall Shear Stress in Accelerating and
Decelerating Turbulent Pipe Flows", Journal of HydraulicResearch, Vol. 34, pp. 173-183.
Greenblatt, D., Moss, E. A., 1999, "Pipe-Flow Relaminarization by Temporal Acceleration", Physics of Fluids, Vol. 11,
pp. 3478-3481.
Souma, A., Iwamoto, K., Murata, A., 2009, "Experimental
Investigation of Pump Control for Drag Reduction in Pulsating
Turbulent Pipe Flow", Proceedings, 6th International
Symposium on Turbulence and Shear Flow Phenomena, Vol. 2,
pp. 761-765.
Kobayashi, W., Shimura, T., Mitsuishi, A., Iwamoto, K.,
Murata, A., 2021, "Prediction of the Drag Reduction Effect ofPulsating Pipe Flow Based on Machine Learning",
International Journal of Heat and Fluid Flow, Vol. 88, 108783.
Patel, V and Head, M. , 1968, "Reversion of Turbulent toLaminar Flow", Journal of Fluid Mechanics, Vol. 34, No. 2, pp.
371-392.

CONCLUSIONSTo develop a predictive model of the drag reduction effectby machine learning, 2498 types of pulsating flows in a pipewith various periods and acceleration/deceleration were
investigated in the experiment. Using those experimental dataas training data, machine learning based on sequence-tosequence model with LSTM was also performed.
In the experiment, we measured drag reduction rate of RD =39% at αacc = 0.11 and T+ = 740. maximum average pressure
gradient during acceleration of αacc = 022, which is larger than

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