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Engineering, Technology & Applied Science Research Vol. 9, No. 1, 2019, 3705-3710 3705  
  

www.etasr.com Manafpour & Ebrahimnezhadian: Investigating the Effect of Ramp Geometry on the Flow … 

 

Investigating the Effect of Ramp Geometry on the 

Flow Characteristics Around Under Pressure Tunnel 

Aerator Using OpenFoam Open Source Software 
 

Mohammad Manafpour 

Department of Civil Engineering 

Urmia University 

Urmia, Iran 

m.manafpour@urmia.ac.ir 

Hamzeh Ebrahimnezhadian 

Department of Civil Engineering 

Urmia University 

Urmia, Iran 

h.ebrahimnezhadian@urmia.ac.ir 
 

 

Abstract—The flow around the ramp embedded in a pressurized 

tunnel is divided into various zones downstream of the ramp, 

including the cavity and the main zone of flow above the shear 

layer. Ramp angle and height are parameters that affect the flow 

characteristics such as cavity length, velocity, and pressure 

coefficient immediately downstream of the ramp. In this study, 

OpenFOAM open source software and RNG K-ε turbulence 

model were used to simulate the flow around the under pressure 

tunnel ramp. In order to investigate the effect of the ramp 

geometry on the flow in various relative air discharges 0<β<10, 

the range of height and the angle of the ramp as 5<θ<20 and 

0.1<tr/d<0.4 were developed and simulated. The correlation 

coefficient between the numerical and experimental results for 

the relative cavity length is in the range of 0.9377≤ R
2
≤ 0.9722 

that indicates proper agreement between results. The result of 

the research shows that in both cases of fixed height of ramp and 

increasing ramp angle, and fixed angle of the ramp and 

increasing ramp height, the values of the cavity length and 

maximum turbulence intensity increase, and the minimum 

pressure values at the cavity zone bed are decreased. But in both 

cases, the sensitivity of the three mentioned parameters is higher 

than the ramp height increment. 

Keywords-aerator ramp; pressurized tunnel; RNG K-ε 

turbulence model; OpenFOAM; cavity length 

I. INTRODUCTION  

Aeration is known as the most efficient and economical 
method for prevention of cavitation in high-speed flows over 
chute spillways [1, 2]. With 8% air near the concrete surface 
the damage of cavitation attack is completely prevented [3, 4]. 
Surface aeration takes place in spillways but in this way usually 
not enough air is introduced near the concrete surface [5]. 
Therefore, forced aeration of flow is recommended [6]. 
Aerators, which locally create an air cavity at the lower 
boundary of the flow, have been found to be an effective and 
cheap way of promoting air entrainment into the flow. Aerators 
cause the flow to separate from the surface of the spillway and 
form a nappe. Flow behavior on aerator ramps in Figure 1 
shows the complex interaction between flow turbulent 
structures, the phenomenon of cavitation, the behavior of the 
jet in the atmosphere, the air entering the jet, as well as the 

propagation of bubbles in the downstream of ramps. Air will be 
entrained along the lower surface as well as along the upper 
surface of the nappe [7]. The entrainment on the lower surface 
introduces air bubbles near the bed of the spillway for some 
distance downstream [8, 9].  

 

 
Fig. 1.  Flow region over typical aerator. 

In under pressure flow upon ramp aerator embedded in the 
tunnel floor (Figure 2), immediately downstream of the ramp, 
the flow is two-phased and disturbed. There is no surface 
aeration and it is divided into the various zones immediately 
downstream of the ramp, including the cavity zone and the 
main zone of flow above the shear layer. As flow separates 
from the trailing edge of the ramp, the lower layers accelerate 
and small intense eddies form on the lower surface of the nappe 
which roughens the air-water interface. As turbulence 
overcomes surface tension, this air will be entrained into the 
flow. On the other hand, the pressure distribution in the nappe 
rapidly adjusts itself to near atmospheric conditions, the slip 
velocity of air bubbles falls and the air bubbles are diffused by 
turbulence deeper into the core of the nappe. Further 
downstream, more and more air will be entrained into the flow 
[10]. Turbulence plays an important rule here, and higher 
turbulence levels cause more air entrainment [5, 11].  

The introduction of forced air, especially from the bottom 
of the jet, will increase air concentration near the surface of the 
concrete. Aeration in spillways and under pressure tunnels is 
usually carried out by aeration systems and by using ramp, 
groove, and steps. The most common type of aeration can be 
seen in Figure 3. Bringing air to the bottom of the jet is carried 

Corresponding author: Mohammad Manafpour



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out by a duct from the floor. In this way, the flow is completely 
aerated and despite this air near the floor, the damage caused 
by cavitation is prevented [12]. 

 

 

Fig. 2.  Flow pattern upon under pressure tunnel ramp. 

Proper recognition of the two-phase flow pattern in under 
pressure tunnel spillways with and without aeration system is 
among the studied topics, but because of the complexity of 
two-phase flows, there is still a need for more studies in this 
field. Many research works have been conducted to find the 
relationship between the inflows of air through aerators. 
Relative air discharge (β), which is defined as the ratio of air to 
water discharge, is a function of cavity length, Froude number 
and cavity subpressure. In 1990, a mathematical model based 
on Galzoo's work in 1984 was presented [13]. This model 
computed the cavity length as well as the airflow and cavity 
subpressure. Based on this model, cavity length directly 
affected airflow. Authors in [4] studied and compared VOF and 
mixture methods during a series of experimental and numerical 
studies with three-dimensional simulation of aerated flow 
downstream of ramp aerator in a tunnel under pressure. 
Comparing numerical and experimental results indicated that 
both methods calculated accurately free water surface and 
cavity length. Air concentration inside the water and the 
average values of pressure downstream the aerator from the 
mixture model have less error than the experimental results. 
Authors in [14] examined the effects of flow regime 
downstream of aerator on entering the air into the flow and 
preventing damage of cavitation. The results of the experiments 
showed that the conversion of flow regimes downstream of 
aerator to each other depends on aerodynamic parameters such 
as ramp angle, ramp height and slope of tunnel floor. Authors 
in [15] compared laboratory performance of two types of 
aerator in two different designs. It was found that for tunnel 
spillways, the shape and size of aerator require special design 
and tunnel spillways can be protected from cavitation by 
applying a plan of aerator that increases cavity zone length, air 
inflow, and the air concentration near the floor. 

Authors in [16] carried out laboratory studies on measuring 
the pressure fluctuations in downstream of the aerator located 
in a circular tunnel and studied aerator performance with 
different geometries. It was found that the use of aerator with 
small heights for air supply in tunnel duct is more suitable than 
aerator with high heights from a hydrodynamic point of view. 
Authors in [17] studied the effect of geometric and hydraulic 
parameters on pressure, cavity length and relative air discharge 
in the flow around the ramp embedded at the end of the tunnel. 
It was found that by increasing the relative cross-section of the 
air inflow, which leads to an increase in the amount of air 
entering the flow, the cavity length downstream of the ramp 
and the aeration coefficient of the flow increase. The average 
cavity pressure also increases significantly with increasing air 

inflow. Authors in [18] experimented in the effect of air 
injection on the wall pressure in the near field of deflectors 
placed in a duct. Various quantities of air have been injected 
just downstream of the ramps to form stationary air cavities. 
The variation of cavity length has been studied as a function of 
the ratio of the volume of air flow to the water discharge. This 
study showed how air injection affects the wall pressure field. 

The effects of aerator ramp geometry on the flow 
characteristics have been studied, but the effective factor 
between ramp height and angle is not determined on the flow 
characteristics. Hence, in this study, the flow near the aerator 
ramp embedded in a under pressure flow in various relative air 
discharges 0<β<10, angle 5<θ<20 and height 0.1<tr/d<0.4 was 
developed and simulated, by the use of an open-source 
numerical model and appropriate turbulence model. The effect 
of the angle and ramp height on the characteristics of the flow, 
the minimum values of the pressure at the cavity zone bed, and 
the maximum turbulent intensity are determined immediately 
downstream of the ramp. 

II. MATERIALS AND METHODS 

A. Experimental Setup 

The details of the experimental arrangement are presented 
in Figure 3. The experimental model consists of a horizontal 
pressurized duct with a square cross section that ramps of 
perspex of triangular cross section were glued to the duct 
bottom. Four ramps were used. Two heights of tr/d=0.1 and 0.2 
were used, where tr is the height of the ramp and d is the height 
of the duct. For each value of tr/d test, two slopes of 5

0
 and 10

0
 

were used. Water supply to the duct housing the ramps was 
from a constant head tank located on the roof of the laboratory. 
A 0.1m wide and height duct was used with a tank upstream to 
achieve the desired flow velocities. The modeled aerator 
consisted of a ramp. Dimensions of the aerator are given in 
Table I. The aerator was installed 1m downstream of the 
channel entrance to allow the turbulent boundary layer to 
develop completely. A Pitot tube was employed to measure 
flow velocity. Air was introduced through nine 10mm diameter 
holes placed at regular intervals immediately downstream of 
the ramps [19]. 

TABLE I.  CHARACTERISTICS OF THE STUDIED RAMPS 

tr/d Ramp angle (θ) Ramp length Lr (mm) Ramp height tr (mm) Ramp 

0.1 5 113.4 10 A 

0.1 10 56.7 10 B 

0.2 5 226.8 20 C 

0.2 10 113.4 20 D 
 

B. Numerical Model 

OpenFoam software was used to simulate the flow around 
the aerator ramp embedded in a under pressure duct. 

C. OpenFOAM 

The widely known CFD-toolbox “OpenFOAM” (Open 
Field Operation and Manipulation) is a well-designed C++ 
library that allows numerical simulation of various engineering 
applications. Through its object-orientated structure it is very 
flexible and can be adjusted to very specific problems. Since 



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the code is open source, code analysis and manipulation are 
possible. With its specific data types for describing the PDEs 
and the usage of operator overloading, OpenFOAM allows 
formulating equations in a way that resembles the 
mathematical formulation. In contrary to most CFD programs, 
OpenFOAM is not delivered with a graphical user interface for 
performing pre- and post-processing of the simulations [20]. 

 

 

Fig. 3.  Experimental apparatus. 

The most important difference between OpenFOAM and 
other computational fluid dynamics commercial software is 
that in OpenFOAM to create a model in each subcategory, the 
user must choose a proper solver to project physics. Therefore, 
one of the difficulties of OpenFOAM is the choice of 
proportional solver. The flow around the under pressure tunnel 
ramp aerator has a two-phase nature. Multiphase flow 
modeling is performed using three views: 1) volume of fluid, 2) 
Eulerian-Lagrangian, and 3) Eulerian-Eulerian. In 
OpenFOAM, to analyze multiphase flow problems, various 
solvers are foreseen. The choice of a suitable solver is the most 
important part of the simulation in OpenFOAM. A number of 
multiphase solvers in the OpenFOAM are InterFoam, 
bubbleFoam, twoPhaseEulerFoam and multiPhaseEulerFoam. 
In this study, due to the two-phase nature of the flow and the 
importance of mixing the two phases, the Eulerian-Eulerian 
approach and a solver that has the basis of the 
twoPhaseEulerFoam solver were used. Necessary development 
in the solver to increase efficiency in the discussion of the two-
phase mixing simulations has been done. OpenFoam was used 
to simulate the flow around the aerator ramp embedded in a 
under pressure duct. 

D. Geometry, Meshing and Boundary Conditions  

In order to construct the geometry of the numerical model, 
a code was written in Fortran. By applying the input data such 
as the ramp angle and height, the distance to the ramp entrance 
and the distance from the end of the ramp, the information 
necessary for constructing geometry from the Fortran code was 
extracted and transferred to the BlockMesh environment inside 
the OpenFOAM. Regarding the dimensions of the study area 
and air bubble diameter, a geometry grid of the numerical 
model with dimensions of 2mm was prepared. The meshing of 
the numerical model is shown in Figure 4. 

 
Fig. 4.  Numerical model meshing. 

Sensitivity analysis of the numerical model was measured 
relative to the mesh size, and it was found that using a smaller 
cell size did not affect the accuracy of the calculations. The 
boundary conditions in the present study include: 1) water 
inlet: mass flow rate, 2) air inlet: mass flow rate, and 3) outlet: 
pressure outlet and for all duct walls, a wall boundary condition 
was used. 

III. RESULTS AND DISCUSSION 

In order to evaluate the performance of a numerical model 
in the simulation of two-phase flow around an aerator ramp 
embedded in under pressure duct bed for 4 types of ramps that 
are presented in Table I, numerical and experimental results 
were compared. The flow near the aerator ramp embedded in a 
under pressure flow in various values of relative air discharge 

β, 0≤β≤10, angle θ, 5
o
≤θ≤20

o
, and height tr, 0.1≤tr/d≤0.4 were 

simulated until the effect of θ and tr on the characteristics of the 
flow, such as the cavity length (LC), the minimum values of the 
pressure at the cavity zone bed (CPmin) and maximum turbulent 
intensity (T.I.max) were determined immediately downstream of 
the ramp. 

A. Verification of Numerical Results 

1) Cavity Length (Lc) 

After the passing flow through the aerator ramp, in addition 
to the main zone, cavity zone is formed: two regions are 
separated by a shear layer between them (Figure 5). In Figure 
6, the comparison between the relative cavity lengths 
calculated by the numerical model using the two-equation 
turbulence model RNG K-ε and experimental results for cavity 
formed immediately downstream of four different ramps in the 
various relative values of β are shown in which LC and tr are 
the length of the cavity zone and ramp height respectively. 
According to Figure 6, the two-dimensional numerical model 
in all ramps estimates a cavity length less than the experimental 
model. The correlation coefficient between the relative cavity 
length of the numerical and experimental models for forced 
relative air discharge 2%, 4%, 6% and 8% was 0.9729, 0.9371, 
0.946 and 0.966 respectively, which suggests an acceptable 
simulation of the flow by the numerical model. Results for 2% 
and 8% relative air discharge are presented. 

 

Fig. 5.  Cavity in the under pressure duct due to forced air injection. 

2) Flow Velocity 

The comparison of average velocity distribution profiles 
between numerical and experimental results for ramp D 
(tr/d=0.2, θ=10

o
, β=2%) is displayed in Figure 8, where Z is the 

distance from the end of the ramp and U is the average velocity 
of the flow equal to 4.1 m/s. The adaptation of numerical and 
experimental results suggests the proper accuracy of the 
numerical model in simulating the flow velocity field near the 
aerator ramp. According to Figure 8, the velocity in the 
direction of flow at the end of the ramp due to the existence of 



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the ramp and the decrease of the duct cross section reaches its 
maximum value. 

 

 
Fig. 6.  Comparison of the cavity length generated by the numerical model, 
the experimental results, and their correlation. 

 

 

Fig. 7.  Flow velocity profiles for ramp D (tr/d=0.2, θ=10
o
), in section (Z/tr: 

a=-28, b=-0.2, c=2.1, d=6.7, e=15.7). 

3) Pressure Coefficient 

The dimensionless parameter of pressure coefficient (Cp) is 
defined as the static pressure ratio to the dynamic pressure. In 
this research, the pressure coefficient is obtained from the 
relationship CP=P-Po/0.5ρU

2
 where P is the static pressure of 

the floor at the desired point, Po is the static pressure at the 
reference point located at the upstream of the ramp, ρ is the 
water density and U is the average flow velocity. Figure 8 
shows the variation of the pressure coefficient in the duct floor 
relative to the distance from the downstream of ramp. The 
correlation coefficient between the numerical and experimental 
results for pressure coefficient of the ramp B (tr/d=0.1, θ=10

o
) 

and forced relative air discharges (β=2%,4%,6%,8%) is in the 
range of 0.7163<R

2
<0.9167 which emphasizes the accuracy of 

the numerical model in simulating the flow field. 

 

 

Fig. 8.  Changes in the pressure coefficient in the duct floor relative to the 

distance from the end of the ramp A (tr/d=0.1, θ=5
o
) and (β=2%, 8%). 

B. Effect of Ramp Angle and Height on Cavity Length  

To investigate the effect of the angle and height of ramp on 
the flow characteristics near the aerator ramp embedded in an 

under pressure flow in various β, various values of θ 

(5
o
≤θ≤ 20

o
) and tr (0.1≤ tr/d≤ 0.4) were simulated. The 

variation process of cavity length in aeration to flow is the 
same as the variations in the length of recirculation zone of the 
flow in a non-aeration state. Figure 9(a)-(b) shows the effect of 

increasing tr relative to the fixed θ=5
o
 and the effect of 

increasing θ relative to the fixed tr/d=0.1  for various β. 
According to Figure 9, increased intensity of cavity length (Lc) 

 in increased tr/d is more than the increase of θ. This suggests 
greater sensitivity of cavity length to the increase of the ramp's 
relative height. The cavity length increases with increment of 

relative air discharge (β ) in both cases. 

 

 
(a) 

 
(b) 

Fig. 9.  Changes in cavity length: (a) Ramp height increase relative to 

fixed ramp angle 5
o
, b) ramp angle increase relative to fixed ramp height 

(tr/d=0.1). 

In Figure 10, variations in the relative air discharges 
coefficient of flow are presented as a function of cavity length 
for different ramps. The changes in this function are very close 
in both quantitative and qualitative terms for ramps of the same 
height. In other words, the effect of the ramp angle on the 
aeration coefficient through the relative cavity length is very 
low (comparing ramp A with B and C with D). While the effect 
of ramp height on this relationship is high (ramp A comparison 
with C and B with D). 



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Fig. 10.  Air discharges coefficient variation relative to cavity length for 
different ramps. 

C. Effect of Ramp Angle on Minimum Pressure Coefficient of 

the Cavity Zone Bed  

The effect of increasing relative height and ramp angle on 
CPmin follows [17] which showed that with increasing ramp 
height and angle, the local pressure in the whole tunnel, 
decreases. The effect of increasing relative height and ramp 
angle on CPmin at the cavity zone created at the downstream of 
the ramp is shown in Figure 12. CPmin values in both cases are 
reduced and the impact intensity of the CPmin of the ramp height 
(tr/d) is far greater than ramp angle. Therefore, the sensitivity of 
the minimum pressure coefficient to increasing ramp height is 
higher than the ramp angle’s. Also, by increasing the relative 
air discharge to the flow, the minimum pressure coefficient 
value increases, indicating the effect of flow aeration on 
localized pressure increase over the entire duct. 

 

 
(a) 

 
(b) 

Fig. 11.  Minimum floor pressure of cavity zone variations: a) Increasing 

ramp height for fixed ramp angle 5
o
, b) increasing ramp angle for fixed ramps 

height (tr/d=0.1). 

D. Effect of Ramp Angle on Minimum Turbulence Intensity of 

the Flow  

The changes in turbulence intensity due to the increase in 
relative height and ramp angle in different relative air 
discharges follow the qualitative process of Figure 12. With 
increasing ramp angle and height, turbulence intensity 
increases. Figure 12 illustrates the effect of increasing height 
and ramp angle on the maximum turbulence intensity at the 
downstream of the ramp. Results indicate that increasing angle 
and relative height of the ramp increase the turbulence intensity 
with the difference that the increase in maximum turbulence 
rate due to ramp height (tr/d) is higher than the ramp angle 
increase. Also, maximum turbulence intensity was reduced due 
to an increase in the air flow rate (β). 

 

 
(a) 

 
(b) 

Fig. 12.  Maximum turbulence intensity variation: a) Increasing ramp height 

for fixed ramp angle 5
o
, b) increasing ramp angle for fixed ramp height 

(tr/d=0.1) 

IV. CONCLUSIONS 

This study on the flow field near the aerator ramp of a 
tunnel under pressure with OpenFOAM produced the following 
results: The correlation between numerical and experimental 
results for relative cavity length and relative air discharge of  
2%, 4%, 6% and 8%, was 0.9722, 0.9371, 0.946 and 0.966 
respectively, which indicates proper agreement between 
numerical and experimental results and the superiority of the 
TwoPhaseEulerFoam solver in the simulation of two phase 
flow. In both cases of fixed ramp height and increasing ramp 
angle and fixed ramp angle and increasing ramp height, the 
values of the cavity length and maximum turbulence intensity 
increase, and the minimum pressure values at the cavity zone 
bed are reduced. However, with increasing ramp height at fixed 
ramp angle, the intensity of the increase in the cavity length, 
maximum turbulence intensity and the reduction of the 
minimum pressure at the cavity zone bed are greater indicating 
higher sensitivity to ramp height. By increasing the forced 
relative air discharge β, minimum pressure coefficient value is 
increased and maximum turbulence intensity is reduced. 

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