Thiết kế và lắp đặt hệ thống đo dao dộng rung trong hầm gió

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Thiết kế và lắp đặt hệ thống đo dao dộng 
rung trong hầm gió 
 Trần Tiến Anh 
 Hoàng Ngọc Lĩnh Nam 
Trường Đại học Bách Khoa, ĐHQG-HCM 
TÓM TẮT: 
Bài báo trình bày các bước thiết kế và 
lắp đặt bộ mô hình đo dao động rung trong 
hầm gió diện tích 1m x 1m. Việc phân tích lý 
thuyết về kết cấu lò xo trong mô hình này 
giúp ta có thể tự thiết kế được một hệ thống 
phù hợp với diện tích hầm gió, tốc độ gió 
cũng như là mô hình cánh khảo sát để thu 
được kết quả như mong muốn. 
Hệ thống này giúp ta quan sát được sự 
dao động của cánh khảo sát bằng mắt 
thường, nhưng để biết được chính xác cánh 
đã dao động lên xuống như thế nào, góc 
xoay cánh ra sao, ta cần đến sự giúp đỡ của 
bộ cảm biến siêu âm Sensick UM30-21-118 
dùng để đo khoảng cách, sẽ được trình bày 
cụ thể hơn trong phần nội dung. 
Đồng thời bài báo cũng trình bày cách 
làm một mô hình cánh đơn giản nhưng bền, 
đẹp với biên dạng cánh NACA 0015 – là mô 
hình cánh sẽ được khảo sát dao động trong 
mô hình trên.Các hiện tượng khí động gây 
ảnh hưởng đến sự dao động của cánh cũng 
được nhắc tới và khắc phục trong phần thiết 
kế cánh. 
Cuối cùng là xử lý các số liệu sau khi đo 
được để thấy sự tương đồng giữa thực 
nghiệm và các lý thuyết của hàng không 
động lực học. 
Từ khóa : hầm gió, đầu cảm biến siêu âm, bộ khuếch đại cảm biến siêu âm, thiết bị đo 
khoảng cách, khí đàn hồi, dao động của cánh.
REFERENCES 
[1]. Wright, J. R. & Cooper, J. E. (2007). 
Introduction to aircraft aeroelasticity and 
loads. England, West Sussex: John Wiley & 
Sons Ltd. 
[2]. Hodges, D. H. & Pierce, G. A. (2011). 
Introduction to structural dynamics and 
aeroelasticity (2nd edition). New York, NY: 
Cambridge University Press. 
[3]. Dowell, E. H. (2004). A modern course in 
aeroelasticity. New York, NY: Kluwer 
Academic Publishers. 
[4]. Buthaud, L. (1998). Cours d’aeroelasticité. 
France, Poitiers: ENSMA. 
[5]. Shubov, M. A. (2006). Flutter phenomenon 
in aeroelasticity and its mathematical 
analysis. Journal of Aerospace 
Engineering. 
[6]. Chen, S. S. (1990). Flow-induced vibration 
of circular cylindrical structures. 
Hemisphere. 
[7]. Blevins, R. D. & Reinhold, V. N. (1990). 
Flow-induced vibration (2nd edition). 
Malabar, FL: Krieger Pub Co. 
[8]. Obayashi, S. (2009). Multidisciplinary 
design optimization of aircraft wing plan 
form on evolutionary algorithms. IEEE 
International Conference on Systems Man 
and Cybernetics 4, 3148-3153. 
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Toward wave-body interaction roblems 
using CIP method: A demonstrating 2 
phase problem 
 Tran Tien Anh 
 Bui Quan Hung 
Ho Chi Minh city University of Technology, VNU-HCM 
(Manuscript Received on July 08th, 2015, Manuscript Revised September 23rd, 2015) 
ABSTRACT: 
CIP (constrained interpolation profile) is 
one of the CFD (computational fluid 
dynamics) methods developed by Japanese 
professor Takashi Yabe. It is used to 
simulate 3 phase problems including air on 
the surface, liquid and structure in solid form. 
To check the validity of CIP theory, 
experiments with different problems have 
been implemented and obtained very 
positive results. This proves the correctness 
of the CIP method. 
Based on the need of simulation of wave 
structure interaction (water wave with float of 
seaplanes, wing in ground effect crafts, 
piers, drilling, casing ships...), this paper 
applies the theory of CIP method to find the 
answer to the problem of 2D simulation via a 
obstacle. Objectives to do are understanding 
the physics, finding out the differential 
equations describing the phenomenon, then 
proceeding discrete, setting up algorithms 
and finding out solution of the equations. 
This paper uses Matlab software to write 
programs and displays the results. 
Key words: numerical algorithm, constrained interpolation profile, free surface problem, 
fluid structure interaction, multiphase flows, governing equations. 
1. INTRODUCTION 
1.1.Objectives 
It is very important to know interaction of 
water waves on structures (body and float of 
seaplanes, flying boats, piers, drilling, casing 
ships...). The main objective of this paper is to 
establish a numerical prediction way for how 
water waves impact to a solid body. 
Purpose of this paper includes constructing 
algorithms and computational simulation 
modules, calculating the fluid forces acting on 
the structure (lift, drag, torque) and processing 
and displaying calculated results. 
Figure 1. Two phases flow (initial frame). 
1.2. Missions 
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CIP is a CFD method developed by a 
Japanese professor [1]. CIP is used to simulate 3-
phase environments consisting of air over the 
surface, liquid and a structure. The problem can 
be understood simply as follows: 
- Using equations to describe the movement 
of water waves. 
- Discretizing mathematical equations to 
establish algorithms programmed on the 
computer to find the answer. 
- Using the programming language to 
calculate an explanation of the equations. 
- Using graphics software to display the 
results of the problem found in graphs image. 
Software used in this paper is Matlab. 
2. GOVERNING EQUATIONS [1] 
From the basic conservation equations: 
2 up p iu Cit x xi i
 
  
 (1) 
Where 
t is the time variable; 
xi (i =1,2) are the coordinates of a Cartesian 
coordinate system; 
ρ is the mass density; 
ui (i=1,2) are the velocity components; 
fi (i=1,2) are due to the gravityorce. 
 2 1 / 3p Sij ij ij ij    (2) 
where: 
σij is the total stress 
p is the pressure; 
μ is the dynamic viscosity coefficient; 
δij is the Kronecker delta function; 
1
2
uu jiSij x xj i

 
 (3) 
Kronecker delta function: 
0 if i j
1 if i = jij

C is sound speed. 
In order to identify which part is the air, the 
water or the solid body, density functions 
φm (m=1, 2, 3) is introduced: 
 1, ,, ,
0, otherwise
x y mx y tm 
 
where Ωm : domain occupied by the liquid, 
gas and solid phase, respectively. 
These functions satisfy: 
0m muit xi
  
 
 (4)
Figure 2. Density function ϕm (m=1,2,3) for 
multiphase problems with 0≤ ϕm ≤ 1 and 
ϕ1 + ϕ2 + ϕ3 = 1 in the computational cells. 
3. CIP METHOD 
3.1. Principle of CIP Method [2] 
CIP method has some advantages over other 
methods with respect to the treatment of 
advection terms. In this section, the principle of 
CIP method is explained. Figure 3 shows the 
principle of CIP method. Here, a one-
dimensional advection equation is used to 
simplify the explanation of CIP method. As 
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mentioned in the previous section, a one-
dimensional advection equation is described as 
below, 
0
f f
u
t x
 
  (5) 
The approximate solution of the above equation 
is given as: 
 , ,f x t t f x u t ti i  
Where xi is the coordinates of calculation 
grid. The above equation indicates that a specific 
profile of f at time t + t is obtained by shifting 
the profile at time t with a distance u∆t as shown 
in Figure 3(a). In the numerical simulation, 
however, only the values at grid points can be 
obtained, as shown in Figure 3(b). If we eliminate 
the dashed line shown in Figure 3 (a), it is 
difficult to imagine the original profile and is 
naturally to retrieve the original profile depicted 
by solid line in (c). This process is called as the 
first order upwind scheme [3]. On the other hand, 
the use of quadratic interpolation, which is called 
as Lax-Wendroff scheme [4] or Leith scheme [5], 
suffers from overshooting. 
Figure 3. The principle of CIP method: (a) solid line 
is initial profile and dashed line is an exact solution 
after advection, whose solution (b) at discretized 
points, (c) when (b) is linearly interpolated, and (d) In 
CIP [6] 
In CIP method, a spatial profile within each 
cell is interpolated by a cubic polynomial. 
Differentiating equation (5) with a spatial 
variable x gives: 
g g u
u g
t x x
  
   (6) 
By this equation the time evolution of f and 
g can be traced on the basis of Equation (5). If g 
propagates in the way shown by the arrows in 
Figure 3(d), the profile looks smoother that is 
more precise. It is not difficult to imagine that by 
this treatment, the solution becomes much closer 
to the original profile. If two values of f and g are 
given at two grid points, the profile between the 
points can be described by a cubic polynomial: 
 3 2F x ax bx cx d 
The profile at n+1 step can be obtained by 
shifting the profile with u∆t, 
 1nf F x u t 
 1 F x u tng
x
 
 (7) 
3.2. Separation of Equations 
The governing equations of the fluid and the 
density function is: 
0
0 2 1 1
0 30
00 2
0
0
ui
xi
pu u S S fj j ij ij kk ju x xi j ip pt xi uim m C
xi
 

 
 
           
 (8) 
This equation is separated into three parts 
Advection phase: 
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0
0
0
0
u uj juit xp pi
m m
 
 
 (9) 
Non-advection phase 1: 
0
2 1
3
0
0
u S S fj ij ij jkkx jt p
m



 
 

(10) 
Non-advection phase 2: 
1
2
0
ui
xi
p
u j xit p
uiCm
xi



 
 



 (11)
Instead of calculating 
1n nf f (n is 
time step) directly from Equation (7), 
intermediate value of 
*f and **f are 
provided, and *nf f using Equation (9), 
* **f f using Equation (10), ** 1nf f 
using Equation (11) are calculated. 
After obtained components of velocity, 
density, pressure, function of density; spatial 
derivatives of these components, ,
f f
x y
 
 
, 
can be calculated. 
This procedure can be summarized as Table 1. 
Table 3. Procedure of separation solution 
Figure 4. Computational grid distributions 
Figure 5. Computational procedures 
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4. NUMERICAL SIMULATION 
4.1. Problem Statement 
Two-dimensional water interacting with a 
solid body is considered in this section. The fluid 
is assumed to be incompressible and inviscid. 
Temperature variations are neglected. The 
problem is described in Figure 6. 
2-phase problem is the first step, the base 
premise to write programs for 3-phase problem 
and absolutely no experimental verification` [5]. 
Figure 6. Two phases flow (initial frame) 
In which, 
U0 is inlet velocity. 
Computational domain is presented by two 
points P1 and P2. 
Obstacle is presented by two points P3 and 
P4, as shown in Figure 6. 
4.2. Boundary Grid Structure 
Boundary grid structure is shown in Figure 
7, 8 and 9. 
Figure 7. Boundary grid structure (left-bottom) 
nx nx+2
ny
Figure 8. Boundary grid structure (right-top) 
Figure 9. Boundary grid structure (obstacle) 
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4.3. Boundary Conditions 
Inlet boundary condition: 
2,3: 2 0u Uny 
02,3: 2v ny 
Outlet boundary condition: 
2nx 2,3: 2 nx 1,3: 2 nx,3: 2u u uny ny ny 
nx 3,3: 1 nx 2,3: 1v vny ny 
Bottom wall boundary condition: 
 2:nx 2,2 2:nx 2,3u u 
02:nx 3,2v 
Top wall boundary condition: 
2:nx 2,ny 3 2:nx 2,ny 2u u 
02:nx 3,ny 2v 
Condition for obstacle 
0Iob1:Iob2,Job1 1:Job2u 
Iob1 1,Job1 1:Job2 1 Iob1,Job1 1:Job2 1v v 
Iob2,Job1 1:Job2 1 Iob2 1,Job1 1:Job2 1v v 
0Iob1 1:Iob2,Job1:Job2v 
Iob1 1:Iob2 1,Job1 1 Iob1 1:Iob2 1,Job1u u 
Iob1 1:Iob2 1,Job2 Iob1 1:Iob2 1,Job2 1u u 
4.4. Boundary Condition for Poisson's 
Equation 
Inlet boundary condition: 
2,3: 2 3,3: 2p pny ny 
Bottom wall boundary condition: 
2: 2,2 2:nx 2,3p pnx 
Top wall boundary condition: 
2: 2, 3 2:nx 2, 2p pnx ny ny 
5. RESULTS 
The computing Matlab program was 
developed to perform this problem. In this 
program: 
Computational domain (m): P1(x1,y1) and 
P2(x2,y2). 
Obstacle position (m): P3(x3,y3) and 
P4(x4,y4). 
Coordinate of obstacle: P3(Iob1, Job1) and 
P4(Iob2, Job2). 
Number of mesh in two axis x, y are: nx and 
ny respectively. 
The size of a small grid is : h (h = x= y) . 
Time step : dt. 
Number of time step: nt 
Inlet velocity: U0. 
With: 
U0 =10 (m/s), dt=0.002 
x1=0, y1=0, 
x2=0.02, y2=0.01, 
x3=0.45*x2, y3=0.1*y2; 
x4=0.6*x2, y4=0.65*y2; 
The velocity vector fields, u-velocity 
contour, v-velocity contour, pressure contour are 
presented in Fig. 10-13. 
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Figure 10. Velocity vector field (h=0.0002, nt=100) 
Figure 11. u-velocity contour (h=0.0002, nt=100) 
Figure 12. v-velocity contour (h=0.0002, nt=100) 
6. CONCLUSIONS 
This paper presented an applicable method 
for simulating the wave body interaction 
problems. This method is cip (constrained 
interpolation profile). Throughout the research, 
we obtained some results as follows: from the 
physical phenomena, in particular here is the 
flow through an object in three phase 
environments (solid, liquid, gas). Then, we 
proceed to discretize these mathematical 
equations to create an algorithm and used 
computer to find the solution. This study uses 
matlab software as a tool for programming and 
presenting the results as graphs. 
This paper has built a solver for two 
dimensional flows in a two phase (liquid, solid) 
environment. These results can be used to 
develop a three phase flow (liquid, air, and solid) 
[5]. 
Due to limited on the basis of information 
technology, mathematical knowledge, and fluid 
dynamic, this paper stops at the simulation of two 
phases flow problems and much remains 
unresolved, specifically error analysis and 
validation by experimental results. 
In order to develop this work, it is necessary 
to analyze more simulations cases and invest 
more time. That is the future work. This method 
can be developed successfully to find the answer 
of three phase flow problem [6]. 
Acknowledgements: This work was 
supported by the research grant of AUN/SEED-
Net (JICA) over a total period of 2 years for 
Collaborative Research with Industry (CRI) 
project (Project No. HCMUT-CRI-1501). 
Figure 13. Pressure contour (h=0.0002, nt=100) 
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Bài toán tương tác giữa sóng nước và 
kết cấu sử dụng phương pháp CIP-Bài 
toán minh hoạ tính cho hai pha. 
 Trần Tiến Anh 
 Bùi Quan Hùng 
Trường Đại học Bách Khoa, ĐHQG-HCM - ttienanh@yahoo.com 
TÓM TẮT 
Phương pháp CIP (Constrained 
Interpolation Profile) là một trong những 
phương pháp tính toán mô phỏng động lực 
học lưu chất (CFD) được phát triển bởi giáo 
sư người Nhật, Takashi Yabe. Nó được sử 
dụng để mô phỏng bài toán ba pha bao gồm 
không khí trên bề mặt, chất lỏng và kết cấu 
ở dạng rắn. Để kiểm tra tính chính xác của 
lý thuyết CIP, nhiều thí nghiệm với các bài 
toán khác nhau đã được thực hiện và thu 
được kết quả rất khả quan. Điều này chứng 
minh tính đúng đắn của phương pháp CIP. 
Căn cứ vào nhu cầu mô phỏng tương tác 
giữa sóng nước và kết cấu (sóng nước và 
phao của thủy phi cơ, thuyền bay, trụ bến 
tàu, giàn khoan, vỏ tàu ...), bài báo này áp 
dụng các lý thuyết của phương pháp CIP để 
tìm lời giải cho vấn đề của mô phỏng 2D của 
sóng nước qua một vật thể. Mục tiêu nghiên 
cứu là để hiểu biết rõ hơn về vật lý, tìm ra 
các phương trình vi phân mô tả hiện tượng 
này, sau đó tiến hành rời rạc hoá, thiết lập 
các thuật toán và tìm ra lời giải của phương 
trình. Bài viết này sử dụng phần mềm Matlab 
để viết các module chương trình và hiển thị 
kết quả. 
Từ khóa: giải thuật tính toán số, đường biên dạng nội suy, bài toán mặt thoáng, tương tác 
lưu chất và kết cấu, dòng nhiều pha, phương trình động lực học lưu chất. 
REFERENCES 
 Takashi Yabe, Feng Xiao, Takayuki Utsumi 
(2001). The constrained interpolation 
profile method for multiphase analysis. 
Journal of Computational Physics 169, pp. 
556–593. 
 Kashiwaghi, M., Hu, C., Miyake, R. & Zhu. 
T. (2008). A CIP-based cartesian grid 
method for nonlinear wave-body 
interactions. Nippon Kaiji Kyokai. 
 Washino, K., Tan, H. S., Salman, A.D. & 
Hounslow, M.J. (2011). Direct numerical 
simulation of solid–liquid–gas three-phase 
flow: Fluid–solid interaction. Powder 
Technology 206, pp. 161–169. 
 Kishev, Z. R., Hu, C. & Kashiwagi, M. 
(2006). Numerical simulation of violent 
sloshing by a CIP-based method. Journal of 
Marine Science and Technology, Vol 11., 
pp. 111–122. 
 Shiraishi, K. & Matsuoka, T. (2008). Wave 
propagation simulation using the CIP 
method of characteristic equations. 
Communications in Computational Physics, 
Vol. 3, pp. 121-135. 
 Xiao, F. & Ikebata, A. (2003). An effcient 
method for capturing free boundaries in 
multi-fuid simulations. International 
Journal for Numerical Methods in Fluids, 
pp. 187–210.