Ehime University Institutional Repository

福田, 隆

矢野, 美由紀

金枡, 栄佳

Japanese

一流女子ビーチバレーボール選手のスパイク踏切動作に関する分析

山川, 廣司

Religion in the Mycenaean Age (2) : Focusing on the Palace Sanctuary

山本, 與志隆

Der Standpunkt der Hermeneutik und Phaenomenologie gegen das wissenschaftliche Denken

若江, 賢三

Sikou (司冦) in the Criminal Law of Qin and Han Dynasty

斎藤, 司

刑事被収容者処遇法と逮捕留置 (故南充彦教授追悼号)

山口, 正隆

日野, 幹雄

畑田, 佳男

大福, 学

野中, 浩一

129
工学ジャーナル　第 8 巻
2009 年 3 月
Annual Journal of Eng.,
Ehime Univ., VIII, Mar., 2009
 
 
Improving Accuracy of Wave Hindcasts in Coastal Waters with the Aid of 
Data from Measurements-Based Sea Wind Distribution 
 
 
 
 
Masataka YAMAGUCHI , Mikio HINO , Yoshio HATADA ,                     
Manabu OHFUKU  and Hirokazu NONAKA  
 
A long-term wave hindcast system using a backward ray tracing model on a nested grid with very high space 
resolution of 100 m is applied for evaluating its accuracy in the computation of wave climate conditions at each 
of the 11 coastal measurement stations in the Kanto Sea Area consisting of Tokyo Bay and the surrounding sea 
areas. Two kinds of wind data sets are employed. One is the NCEP/NCAR (NCEP) reanalysis winds in which 
parametric typhoon model-based winds are embedded. The other is the measurements-based wind data in the 
Kanto Sea Area added to the aforementioned winds. Detailed comparisons with the wave measurements show 
that the wave computation using the NCEP winds aided by measurement-based winds yields a major 
improvement in accuracy, particularly for wave height over that using the NCEP/NCAR winds alone in a local 
wind-generated waves-dominant area and that it becomes less effective to the improvement of accuracy with 
increasingly higher waves generated in an open sea. 
 
Key Words long-term wave hindcasts, NCEP/NCAR reanalysis winds, measured winds, backward ray tracing 
model, Tokyo bay and its surrounding sea areas, coastal waters 
 
 
ECMWF European Centre for Medium-range Weather Forecasts NCEP/NCAR National Center for 
Environment Prediction/National Center for Atmospheric Research /
                                                           
*  
Engineering for Production and Environment, Graduate School of Science and Engineering, Ehime University 
**  
Department of Civil and Environmental Engineering Faculty of Engineering Ehime University 
20 9 10  
130
1990 2000
[1] [3]
[4] [5]
[6]
[7] [9]  
NCEP/NCAR
NCEP
NCEP
 
 
  NCEP/NCAR 10 m NCEP
1.9
1948 2007 12 31 60 NCEP
NCEP
1948 1957 NCEP
1958 NCEP  
  NCEP
80 km 36 35
NCEP [10]
/
980 hPa
NCEP
80 km
NCEP  
 
  22 1979 2004 26
131
NCEP
[11]
11
1.25
37
[11] 2 
km
[9]  
  
1 22
V1 V11
W1 W11
NCEP
NCEP
 
 
  [12]
WAM
0.04 1 Hz 23 0 360 10
37 5 km
1 km 0.1 km
0.1 km
 
  2 km
80 km NCEP
80 km NCEP
30
W1 W11 11
25 50 75 100 12511
25
0 25km
N
grid
121x126
x=2km
j (y)
i(
x)
50
75
100
1
14
13
2
3
68
7
9
11
12
15
16
22
21
20
19
18
NCEP1
V9
V10
V11
NCEP2 NCEP3
NCEP4
V8
V6
V7
V5
V2
V4
V1
V35
10
4
17
W1
W2
W3
W4
W5W6
W7
W8
W9
W10
W11
 
Fig. 1 Location of input wind data points and wave measurement 
stations. 
132
NCEP
NCEP
2004
1980 30
1979
2004 26  
W1 1983 2004 15 m
W2 1994 2004 10 m
W3 1991 2004 29 m
W4 1992 2004 22 m
W5 1972 1990 23 m W6
1979 2004 20 m W7 1979
2004 48 m W8 1979 2004
51 m W9 1998 2004
23 m W10 2000 2004 30 m
W11 2001 2004 48 m
1991
 
 
  Hs Ts 1980
NCEP NCEP+OW NCEP
NCEP
H T
H T
a0H a0T
11
NCEP
NCEP
2004
H T a0H a0T
1,000 H
1 j (y )
i(
x)
grid
673x673
x=5km
0 800 km
1
200
400
600
200 400 600
200 40011
200
0 10km
N
734 x 539
x = 100m
j ( y )
i(
x
)
600
400
10
Chiba obs. tower(W2)
Tokyo 
to–hyo
(W1) h=20m
Daini–kaiho
  (W3)
Ashikajima
  (W4)
Hamakanaya
  (W5)
40
50 100 15011
50
0 25km
h=500m
Ngrid
231x181
x=1km
j(y)
i(
x)
500
100 200
50
150
50
200
200
20
10100m grid
 
Fig. 2 Nested domain for wave hindcasting. 
 
0 1 2 3 4 5
0
1
2
3
4
5
Hs obs  m
Hamakanaya  1980
p=0.1%
H=0.834
H=0.26m
a0 H=1.012
H
s 
ca
l  
m
5
0.5
2
1
NCEP+
 OW
0 5 10 15 20
0
5
10
15
20
Ts obs  s
Hamakanaya  1980
p=0.1%
T=0.576
a0 T=0.954
T=1.19s
10
2
0.5
Ts
 c
al
  s
5
1 NCEP+
 OW
0 1 2 3 4 5
0
1
2
3
4
5
Hs obs  m
Hamakanaya  1980
p=0.1%
H=0.557
H=0.37m
a0 H=0.774
H
s 
ca
l  
m
5
0.52
1
NCEP
0 5 10 15 20
0
5
10
15
20
Ts obs  s
Hamakanaya  1980
p=0.1%
T=0.525
a0 T=0.900
T=1.26s
10
2
0.5
Ts
 c
al
  s
5
1 NCEP
 
Fig. 3 Scatter diagram between hindcasts and measurements for 
wave height and wave period and contourline plots. 
133
T 100 1
1
1979 1990 1980  
H
H a0H 1
T T
a0T 1 1
 
1
W
T T
a0T 1
 
Table 1 Error statistics of wave height and wave period over one year at 11 stations. 
 
obs. st. 
(index) 
No. H 
×10
3 
 H
×10
2
a0H 
×10
3 
 T 
×10
3 
T 
×10
2
a0T 
×10
3 
obs. st. 
(index) 
No. H
10
3
 
 H 
10
2 
a0H 
10
3 
 T 
10
3 
T 
10
2 
a0T 
10
3 
Tokyo  890 11 1000 496 57 972 Habu  786 52 1009 570 135 966
to-hyo  360 22 628 256 57 902 (W7)  741 57 942 549 145 978
(W1)  530 -11  240 0   45 -5  21 -10 
Chiba  912 10 884  Irou-  783 63 1048 714 128 976
tower  607 19 701  zaki  701 71 952 667 142 986
(W2)  305 -9   (W8)  82 -8  47 -14 
Daini-  792 12 883 404 70 897 Omae-  812 44 988 730 140 961
kaiho  567 18 1000 474 73 855 zaki  784 46 944 692 153 996
(W3)  225 -6  -70 -3 (W9)  18 -2  38 -13  
Ashika-  803 29 1073 723 135 926 Kunou  841 35 954 765 134 958
jima  669 35 904 702 150 940 (W10)  812 39 938 745 143 964
(W4)  134 -6  21 -15   29 -4  20 -9 
Hama-  834 26 1012 576 119 954 Tagono-  784 41 962 756 147 972
kanaya  557 37 774 525 126 900 ura  734 46 923 753 151 972
(W5)  277 -11  51 -7 (W11)  50 -5  3 -4 
Hira-  792 38 1138 679 151 992 H m T s 
tsuka  682 42 1025 630 166 999 NCEP winds + Obs. winds 
(W6)  110 -4  49 -15 NCEP winds = -  
 
134
NCEP
NCEP
50 km 25 km
[13] [14]
2 0 0
 
 
  
[9]
NCEP
1979 1990 12
1979 2004 26  
  
H
H a0H 1 H a0H
 
Table 2 Season-separated error statistics of wave height and wave period over a whole measurement period at Hamakanaya 
and Habu. 
 
obs. st. No. Dec.~Feb. (Win.) Mar.~May (Spr.) June~Aug. (Sum.) Sept.~Nov. (Aut.) 
(period) H   H  H a0H H  H a0H H  H a0H H  H a0H 
 T    T T a0T  T T a0T  T T a0T  T T a0T 
Hama- H 864 23 895 882 22 1090 842  27 1119 864 22 1050 
kanaya   549 39 654 687 30 887 708  26 1018 640  30 822 
(1979-1990)   315 -16 195 -8 134  1 224  -8  
 T 493 122 906 576 115 977 610 136 959 550  132 911 
 437 132 821 565 113 935 634 132 941 555  132 876 
 56 -10 11 2 -24 4  -5  0  
Habu H 707 66 735 729 52 943 802 42 1052 774  49 944 
(1979-2004)   612  79 637 697 56 895 795 43 1007 748  53 904 
   95 -13 32 -4   7 -1  26  -4  
 T 453 140 975 508 117 997 567 126 954 580 136 988 
 437 157 963 477 125 1014 581 122 972 540 145 1000 
 16 -17 31 -8 -14 4 40 -9  
H m T s H T 103 H T 102 a0H a0T 103 = -  
 
135
0
1
2
3
4
80 82 84 86 88 90
0
4
8
12
16
0 1 2 3
0
1
2
3
(Hs3)=0.725
a0(Hs3)=
    1.071
Hs3 obs  m
H
s3
 c
al
  m
Hamakanaya 
NCEP+OW
0 1 2 3
0
1
2
3
(Hs3)=0.347
a0(Hs3)=0.862
Hs3 obs  m
H
s3
 c
al
  m
Hamakanaya 
NCEP
0 5 10 15
0
5
10
15
(Ts3)=0.820
a0(Ts3)=
    0.953
Ts3 obs  s
Ts
3 
ca
l  
s Hamakanaya
NCEP+OW
0 5 10 15
0
5
10
15
(Ts3)=0.785
a0(Ts3)=
    0.892
Ts3 obs  s
Ts
3 
ca
l  
s Hamakanaya
NCEP
Hamakanaya '79 –'90
year
obs.
H
s3
 m Hs3
Ts
3 
 s
Ts3
NCEP+OW
NCEP
 
Fig. 5 Variation of monthly-averaged wave statistics and correlation diagrams of 
hindcast- and measurement-based wave statistics at Hamakanaya and 
Habu (a). 
W
T a0T
T
a0H
 
  1/3 Hs3 Ts3
NCEP
12 2
4 8
 
1/3
Hs3 Ts3
NCEP
0
4
8
12
0
2
4
6
obs.
Hamakanaya '79–'90
Month
Ts3
Hs3
H
s3
  m
Ts
3 
 s
NCEP+OW
NCEP
12 2 4 6 8 10
0
4
8
12
0
2
4
6
obs.
Habu '79–'04
Month
Ts3
Hs3H
s3
  m
Ts
3 
 s
NCEP+OW
NCEP
12 2 4 6 8 10
Fig. 4 Comparison of wave statistics averaged over each month of a whole 
measurement period at Hamakanaya and Habu. 
136
1/3
Hs3 1/3
Ts3
Hs3
Ts3
(Hs3) a0(Hs3)
(Ts3) a0(Ts3)
45  
1/10 1/3 Hs10 Ts10 Hs3 Ts3 sH sT
NCEP
a0( sH ) 1
(Ts10)
 
Table 3 Error statistics of monthly-averaged wave height and wave period over a whole measurement period at Hamakanaya 
and Habu. 
 
obs. st. No. 10sH  3sH  sH  10sT  3sT  sT  
(period)   ( ) a0 ( )  ( ) a0 ( )  ( ) a0 ( )  ( ) a0 ( )  ( ) a0 ( )  ( ) a0 ( )
Hama-  774 1024 725 1071 645 1136 774 941 820 953 772 977
kanaya  414 792 347 862 444 989 789 889 785 892 726 934
(1979-1990)  360  378 201 -15 35  46 
Habu  779 989 681 976 414 921 646 962 671 975 673 994
(1979-2004)  746 951 597 922 348 863 629 978 645 990 664 1003
  33  84 66 17 26  9 
 (  ) 103 a0 (  ) 103 = -  
 
0
1
2
3
4
80 82 84 86 88 90 92 94 96 98
0
4
8
12
16
0 1 2 3 4 5
0
1
2
3
4
5
(Hs3)=0.681
a0(Hs3)=
    0.976
Hs3 obs  m
H
s3
 c
al
  m
Habu
NCEP
+OW
0 1 2 3 4 5
0
1
2
3
4
5
(Hs3)=0.597
a0(Hs3)=
0.922
Hs3 obs  m
H
s3
 c
al
  m
Habu
NCEP
0 5 10 15
0
5
10
15
(Ts3)=0.671
a0(Ts3)=
    0.975
Ts3 obs  s
Ts
3 
ca
l  
s Habu
NCEP
+OW
0 5 10 15
0
5
10
15
(Ts3)=0.645
a0(Ts3)=
    0.990
Ts3 obs  s
Ts
3 
ca
l  
s Habu
NCEP
Habu ' 79 –'04
year
obs.
H
s3
 m
Hs3
Ts
3 
 s
Ts3
NCEP+OW
NCEP
40 2
Fig. 5 Variation of monthly-averaged wave statistics and correlation diagrams of 
hindcast- and measurement-based wave statistics at Hamakanaya and Habu (b).
137
Hs10 Hs3 sH Ts10 Ts3 sT
me. sd. NCEP
 
 
  
 
NCEP
 
 
 
   
NOWPHAS
 
    
[1]  
49 pp.201-205 2002. 
Table 4 Mean and standard deviation of monthly-averaged wave height and wave period over a whole measurement period 
at Hamakanaya and Habu. 
 
obs. st. No. 10sH (cm) 3sH (cm) sH (cm) 10sT (s)×102 3sT  (s)×102 sT  (s)×102 
(period)  me. sd. me. sd. me. sd. me. sd. me. sd. me. sd. 
Hama- 151 34 105 20 66 10 715 108 601 80 468 49 
kanaya 118 34 86 14 58 9 670 132 559 100 447 54 
(1979-1990) obs. 145 36 96 22 57 10 752 127 628 84 478 47 
Habu 278 64 212 40 139 25 960 94 869 67 743 50 
(1979-2004) 267 69 200 45 130 28 976 98 882 73 749 59 
  obs. 279 58 216 37 149 22 992 115 887 86 746 57 
me. : mean,  sd. : standard deviation 
 
138
[2] 
51 pp.1266-1270 2004  
[3] 
22 pp.121-126 2006  
[4] 23 pp.138-149
1992  
[5] 
40 pp.166-170 1993  
[6]  28
pp.168-172 1981  
[7]   
53 pp.116-120 2006. 
[8]  
54 pp.106-110 2007. 
[9]  
52 pp.1351-1356 2008. 
[10]  
52 pp.141-145 2005  
[11]  
10 pp.65-78 1985  
[12] 
381 / -7 pp.151-160 1987  
[13] Soares, C. G., Weisse, R., Carretero, J. C. and E. Aluarez : A 40 years hindcast of wind, sea level and waves 
in European Waters, Proc. OMAE 2002, 21st Int. Conf. on Offshore Mech. and Arc. Eng., 2002. 
[14]  ERA40
54 pp.141-145 2007. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 


Improving Accuracy of Wave Hindcasts in Coastal Waters with the Aid of Data from Measurements-Based Sea Wind Distribution

花山, 洋一

牧野, 友彦

西, 陽平

木村, 正樹

24
工学ジャーナル　第 8 巻
2009 年 3 月
Annual Journal of Eng.,
Ehime Univ., VIII, Mar., 2009
Ar CO2 CO2 -Ar
Behaviors of sound velocity in high pressure Ar, CO2 and CO2-Ar gases under 
super critical state 
Yoichi HANAYAMA*,** Tomohiko MAKINO* Yohei NISHI* and Masaki KIMURA**,***  
 
  Abstract: Sound velocities were measured in Ar, CO2 and CO2-Ar gases under super critical region. For Ar, the 
transition curve was obtained from velocity analysis between 333 to 473 K. This curve was discussed relating 
with the critical point of argon. For CO2, the transition curve was obtained from velocity analysis between 300 to 
350 K. For sound velocities in CO2-Ar, the transition curves were obtained and discussed. For CO2-Ar, the phase 
separation was observed by optical method at temperature between 295 to 299 K under the critical temperature, 
and at pressure up to 9.3 MPa over the critical pressure of CO2. 
Key words  Sound velocity, Super critical state, Argon, Carbon dioxide, High pressure 
 
2
Libenberg He[1], Ar[2] 1 GPa Kortbeek He[3], Ne[4], Ar[5]
1GPa He[6], Ne[6], Ar[7]
He 3 GPa Ne 3.7 GPa
                                                                   
*    3  
*    Department of Mechanical Engineering, Ehime University, Matsuyama, Japan 
**   3  
**   Geodynamics Research Center Ehime University, Matsuyama, Japan 
***  3  
***  Department of Materials Engineering, Ehime University, Matsuyama, Japan 
  20  10  31  
25
CO2-Ar
CO2
304.2 K, 7.38 MPa
Ar 150.9 K, 5.0 MPa
2
[8] ,[9] Streett He-Ar[10] 1 GPa
He-Xe[11], He-Kr[12] He-Ar[13], 
Ne-Ar[14] 1 GPa 2 GPa
CO2
CO2-He[15] CO2-Ar
S
Cp CV T
V p u   
TS
T
V
p
p
u
C
C 2
[6] [6] [15]
6-17 MHz LiNbO3 L
T 1 2L u   
T
Lu 2
17 MHz Ar
 
600 K
6 mm 10 mm
26
Ar, CO2 Ar, CO2 CO2-Ar
2
Ar 45 100 MPa
Table 1 Sound velocities u in Ar measured for each pressures p between 44 to 100 MPa as a function of 
temperature T.  
p(MPa) = 100.1 90.0 80.3 69.9 
T , K u , m/s T , K u , m/s T , K u , m/s T , K u , m/s 
314.4  727.28  303.0  698.99 299.8  658.59 300.3  617.40  
350.3  707.67  332.8  681.18 326.4  643.92 306.6  613.61  
368.4  700.56  350.8  673.36 342.6  637.56 327.4  603.99  
389.0  694.42  365.3  668.51 363.6  631.46 343.8  598.84  
410.6  689.89  379.2  664.88 378.4  628.67 361.1  595.30  
425.0  687.83  393.5  662.26 397.0  627.90 370.0  594.05  
443.8  686.08  406.5  660.13 401.0  627.51 377.8  593.33  
454.3  685.70  422.2  658.63 408.6  626.85 390.6  592.58  
465.2  685.35  433.8  657.85 416.1  626.54 400.8  593.38  
475.9  685.39  444.9  657.51 424.5  626.34 413.5  593.53  
487.9  685.64  457.6  657.55 433.7  626.35 426.7  594.25  
498.5  686.10  469.1  658.06 442.0  626.55 438.3  595.12  
510.1  686.71  481.5  658.59 452.0  627.04 448.3  596.13  
522.1  687.54  493.9  659.43 464.5  627.73 458.4  597.40  
533.6  688.53  506.0  660.56 473.9  628.77 469.9  599.12  
550.0  690.26  521.6  662.33 480.1  628.90 483.0  601.05  
570.4  692.60  538.5  664.54 507.9  632.55 491.7  602.53  
* continued 
p(MPa) = 58.9 54.0 49.1 44.1 
T , K u , m/s T , K u , m/s T , K u , m/s T , K  u , m/s
302.5  565.73  302.4  543.76  303.3 520.24  301.9  493.21  
322.8  558.24  323.2  537.00  323.1 514.47  309.0  491.79  
332.3  555.82  332.2  535.01  333.4 512.92  323.3  490.36  
342.6  553.99  342.0  533.53  342.6 512.42  332.9  489.88  
353.2  552.57  348.1  532.96  352.9 512.22  342.9  490.51  
362.3  551.82  353.1  532.47  361.2 512.40  353.0  491.05  
373.1  551.35  361.6  532.20  374.6 513.24  361.8  492.12  
382.2  551.41  373.6  532.23  382.9 514.06  375.1  493.85  
392.7  551.51  382.5  532.56  392.1 515.16  383.1  495.25  
402.9  552.49  393.2  533.31  401.3 516.34  392.4  496.89  
421.4  554.01  402.6  534.26    401.8  498.71  
437.1  556.31  411.8  535.50      
27
0.2 mm LiNbO3 17 
MHz Table 
1 Fig.1
Fig.2 44, 59, 100 MPa
44 MPa 0.01 100 MPa
0.02 m/s/K
Fig.3 
(Liquid like)
p T u 
 MPa  K m/s 
100.1  473.1  685.2  
90.3  455.4  657.5  
80.4  430.5  626.5  
69.9  399.5  592.9  
58.9  383.3  551.0  
54.0  370.2  532.1  
49.1  355.3  512.3  
44.1  333.6  490.4  
300 400 500400
500
600
700
100 MPa
 90
 80
 70
 59
 54 
 49
 44
Temperature T  (K)
V
el
oc
ity
 u
  (
m
/s
)
Fig. 1. Sound velocities in Ar at pressures between 44 
to 100 MPa for as a function of temperature. 
Table 2 Relation of p-T given by 
minimum value of sound velocity u for 
temperature change. 
Fig.3. Minimum value of sound velocities 
for temperature change at each pressure. 
300 400 500400
500
600
700
800
V
el
oc
ity
  u
m
in
  (
m
/s)
Temperature  T  (K)
300 350 400 450485
490
495
500
Temperature  T  (K)
V
el
oc
ity
  u
  (
m
/s
)
44 M Pa
300 350 400 450545
550
555
560
Temperature  T  (K)
V
el
oc
ity
  u
  (
m
/s
)
59 MPa
400 450 500 550680
685
690
695
Temperature  T  (K)
V
el
oc
ity
  u
  (
m
/s
)
100 MPa
Fig.2. Detail of the change of velocity for temperature in Ar at pressures of 44, 59, 100 MPa, 
respectively, 
28
CO2 7.5 50 MPa Table 3
Fig.4
Table 4 CO2
Table 3 Sound velocities u of CO2 at each pressures p between 7.5 to 50.0 MPa as a function of temperature T. 
p(MPa) = 7.5 8.0 9.0 10.0 12.5 15.0 50.0 
T u T u T u T u T u T u T u 
K m/s K m/s K m/s K m/s K m/s K m/s K m/s
288.8 421.9 288.8 429.5 294.3 385.9 288.8 488.3 291.9 498.0 294.2 513.0 296.7 837.1 
291.7 387.9 291.4 395.6 297.1 350.5 298.6 383.2 296.8 453.7 298.4 491.5 309.3 783.4 
294.5 345.5 293.7 362.8 300.2 325.4 304.0 324.5 302.0 410.4 304.0 451.6 329.0 717.4 
296.6 299.8 296.3 317.9 302.0 281.8 308.7 258.7 306.4 370.3 308.4 423.6 348.4 638.6 
298.4 205.6 299.7 238.2 303.5 244.1 314.4 233.3 311.3 328.9 313.6 380.1 364.8 588.5 
299.7 192.5 301.5 200.9 306.4 217.3 320.1 231.8 313.9 304.7 318.0 355.4 372.8 570.6 
308.7 205.4 304.3 199.2 309.7 216.2 325.0 234.5 316.5 288.4 321.1 335.5   
315.4 222.6 307.9 201.3 313.1 215.9 329.7 237.3 319.3 273.7 324.0 321.6   
318.0 219.6 309.7 206.1 315.7 220.1 335.7 241.3 321.9 264.6 328.7 302.4   
322.2 221.7 313.4 218.2 318.5 221.9 340.4 245.5 324.5 260.0 332.6 289.8   
  318.0 218.8 320.6 226.9 344.8 251.0 327.6 256.8 336.7 285.4   
  320.1 219.7 326.1 233.1 350.1 255.9 330.2 253.4 339.4 276.5   
  332.3 232.0 330.5 241.5 356.1 256.5 332.3 252.6 342.8 276.5   
    335.4 244.7 362.1 256.9 334.7 252.7 347.2 275.0   
    341.2 244.8   342.5 254.6 351.1 276.0   
    345.6 248.5   351.1 260.1 355.6 275.8   
 
 
 
 
 
 
p T 
MPa K 
7.5  299.7  
8.0  304.3  
9.0  313.1  
10.0  317.1  
12.5  334.2  
15.0  349.0  
50.0   
300 320 340 360100
200
300
400
500
15 MPa
12.5
10
9
8
7.5
Temperature  T  (K)
V
el
oc
ity
  u
  (
m
/s
)
Table 4 The temperature T obtained from 
the minimum value of velocity in CO2 at 
each pressure p. 
Fig 4. Sound velocities in CO2 at each 
pressure as a function of temperature.
29
CO2-Ar 10 50 MPa
Table 5 2.5%Ar
10 15 MPa 15 MPa 350 K
 
  5%Ar  
 
Table 5 Sound velocities u in CO2-Ar for several mixtures measured on each pressures between 10 to 50 MPa as 
a function of temperature T.
2.5 5 7 10 13 20 40 50 
T u T u T u T u T u T u T u T u 
K m/s K m/s K m/s K m/s K m/s K m/s K m/s K m/s
1) 10 MPa             
299.1  385.0  308.7  253.7 302.8  271.9  303.3 223.7 301.2 208.7       
306.9  276.0  313.1  223.4 307.7  226.1  308.2 209.4 303.2 211.0       
311.5  250.2  317.8  211.8 310.0  218.2  313.4 214.8 307.6 218.5       
314.4  230.9  324.0  218.3 313.1  217.5  319.1 222.3 318.2 242.9       
317.0  224.4  330.0  225.4 318.5  222.2  323.5 227.7 313.6 260.0       
  336.2  229.9 334.1  236.0  343.3 247.3         
2) 12.5 MPa             
298.4  457.8  307.4  361.6 301.7  368.5  303.5 327.6 302.5 267.4 300.6 236.3     
307.7  379.0  314.9  311.3 310.0  308.8  313.4 269.1 308.1 251.8 312.5 242.8     
312.1  346.7  323.2  267.2 320.4  257.7  318.0 255.2 313.3 250.5 323.4 250.1     
315.7  317.1  328.2  253.9 323.7  252.5  323.7 250.0 319.5 252.1 333.1 257.8     
321.7  277.2  332.6  250.3 329.7  249.7  333.9 249.5 323.9 254.1 344.0 264.7     
325.0  266.1  345.1  248.4 334.9  251.2  342.8 254.0 334.6 256.0       
329.5  257.4  353.0  249.0 356.4  263.9  353.7 257.1 354.2 265.9       
3) 15 MPa             
297.6  525.7  303.3  478.0 302.2  425.6  300.4 410.6 296.5 375.2 294.5 295.0 298.6  264.9    
312.8  404.5  318.3  362.0 312.6  357.8  313.6 332.8 313.8 290.7 303.5 278.4 308.6  268.8    
324.3  331.8  323.2  333.3 322.7  307.2  318.5 311.4 319.5 281.7 312.5 272.6 313.3  271.2    
328.9  310.5  328.9  307.1 328.4  290.0  323.5 294.3 323.4 278.7 323.4 272.8 323.7  276.8    
334.4  295.1  332.1  294.0 333.4  282.3  334.1 283.3 333.8 276.3 332.8 273.2 334.4  282.5    
339.9  284.0  344.1  283.3 346.4  274.4  343.8 282.5 343.8 279.5 344.8 274.6 344.8  288.7    
353.2  273.7  354.3  281.1 356.1  274.8  356.4 276.9 354.0 284.1 363.9 282.4 353.7  291.0    
4) 30 MPa             
299.9  659.3  302.8  624.5 300.7  609.0  302.8 593.0 299.6 563.2   296.8  430.6  297.3 434.9 
303.8  643.0  314.4  575.9 315.4  547.8  313.1 539.8 313.3 509.7   315.2  400.4  314.3 414.8 
315.9  580.8  326.1  534.7 325.0  512.9  324.0 502.4 323.4 475.6   324.3  390.2  323.2 408.1 
324.3  548.1  333.4  506.9 333.4  476.4  333.9 471.3 334.1 448.2   334.4  381.8  333.8 400.8 
332.3  517.0  343.0  470.8 343.8  447.9  343.0 448.4 343.5 426.9   354.3  373.9  343.2 396.7 
344.3  468.3  353.0  448.1   353.2 425.1 354.2 409.6   382.4  373.3  353.2 394.7 
5) 50 MPa             
298.6  814.4  302.8  785.8 301.2  765.4  301.2 750.2 295.7 740.4   296.8  612.8  295.0 593.7 
313.4  763.1  315.7  741.3 317.5  712.2  313.6 704.5 314.6 682.2   303.3  598.6  313.6 568.6 
325.6  719.6  324.0  706.0 326.9  683.3  323.7 673.9 324.2 650.5   323.5  560.5  323.2 552.4 
334.4  685.7  346.7  640.3 334.7  659.9  343.3 621.6 343.5 597.7   344.3  530.7  343.8 527.8 
345.6  652.9  357.4  614.6 345.9  631.5  354.5 594.7 354.0 574.6   374.3  510.1  353.7 518.6 
30
10 MPa  12.5 15MPa  344, 349K
7%Ar  10, 12.5 MPa 
15 MPa  348 K 10% Ar, 13%Ar
20%Ar 12.5 MPa 15.0MPa
40%Ar 50 Ar  30 MPa
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig.5 a), b), c) 10, 12.5, 15 MPa 
Ar
Table 6  
Fig.6 Ar5%
CO2100%
Ar
p x  ,  Ar% 
MPa 2.5 5 7 10 13 20 40 50 
10  319.2  311.7 308.2 301.2    
12.5  344.8  329.6 328.3 314.1    
15 352.2  349.2  347.6 337.9 335.8 332.4   
30       364.4  357.3 
280 300 320 340 3605
10
15
CO2 100%
Ar  5 %
Ar  7
Ar 10
Ar 13
L-G phase eq.
Temperature  T  (K)
Pr
es
su
re
  p
  (
M
Pa
)
Fig.6. Temperatures obtained from the 
minimum value of velocity in CO2-Ar at 
each pressure. 
300 320 340 360200
300
400
 2.5 % Ar
 5
 7
10
13
Temperature  T  (K)
V
el
oc
ity
  u
  (
m
/s
)
300 320 340 360200
300
400
 2.5 % Ar
 5
 7
10
13
Temperature  T  (K)
V
el
oc
ity
  u
  (
m
/s
)
300 320 340 360200
300
400
 2.5 % Ar
 5
 7
10
13
Temperature  T  (K)
V
el
oc
ity
  u
  (
m
/s
)
a). 10MPa                             b) 12.5 MPa                    c) 15 MPa 
Fig.5. Sound velocities in CO2-Ar mixtures for each Ar concentrations as a function of temperature. 
Table 6 Temperatures T (K) obtained from the minimum value of velocity in CO2-Ar mixtures having 
concentration x between 2.5 to 50%Ar, at each pressure p. 
31
CO2-Ar 2
3
a) 2
b
c) 
Ar 5, 9, 13% CO2-Ar
Table 7 
ig.7
a)
c)
b)
Fig.7
a) c)
 
Table 8 CO2
Ar
Ar CO2
x (Ar%) = 5 9 13 
p T p T p T 
MPa K MPa K MPa K
a) p : increasing 
6.4 294.9 6.5 292.2 8.4 294.8
7.0 298.2 7.1 295.0 7.7 292.9
7.7 300.5 7.5 297.6 9.2 292.9
8.3 303.6   7.5 292.0
    8.1 294.1
b) p :decreasing 
8.3 297.4 8.3 298.6 9.2 292.2
8.3 299.3 8.5 298.4   
8.2 295.2     
c) T: decreasing 
8.2 301.2 8.4 297.3 8.5 294.2
7.3 297.7 8.6 295.2 9.1 293.3
7.8 300.0 8.4 292.2 8.4 294.5
    9.0 294.5
    9.3 292.0
x p T 
Ar% MPa K 
5 7.7  299.4  
9 8.1  298.0  
13 8.4  294.6  
Table 7 Temperature T and pressure p of the phase 
separetion in CO2-Ar mixture having 5, 9 and 13 
percent Ar concentration x obtained by optical 
method. 
Table 8 The pressure p and 
temperature T limiting value of the 
phase separation curve in Fig.7 for 
each concentration x. 
Fig.7. Pressure and temperature 
diagram of phase separation in CO2-Ar 
obtained by optical method. 
5 6 7 8 9 10290
300
310
Pressure p (MPa)
Te
m
pe
ra
tu
re
 T
  (
K
)
Ar 5%
     9
    13
32
Ar
1300 MPa
Michels et al.[16] 2.5
Liebenberg et al.[2]
Kortbeek et al.[5] 100 MPa 2.01
1000 MPa 1.36
Fig.8 50 MPa 100 MPa
400 K
Ar
CO2 
Ar 330
473 K CO2 300 350 K
CO2-Ar
CO2
50%Ar 100%Ar
 CO2-Ar 2
CO2
L)- (G) CO2 CO2-He[15]
(G) CO2-Ar
 
 
Ar 300 K
45 MPa 2.3 2.0 400 K
Ar, CO2 CO2-Ar
Fig.8. Heat capacity ratio of argon obtained 
from this study at temperature of 300 and 
400 K as a function of pressure. 
0 50 1001.5
2
2.5
3
300 K
400
270 K(Michels)
295 K(Liebenberg)
Pressure  p  (MPa)
H
ea
t c
ap
ac
ity
 ra
tio
  
0 100 200 300 400 5000
20
40
60
80
100
Temperature T    (K)
Pr
es
su
re
  p
   
 (M
Pa
) 100 % Ar
 50 % Ar 
 13 % Ar
100 % CO2 
CO2 L-G eq.line 
Ar L-G eq. line
Fig. 9. Temperature-pressure relation in super 
critical state obtained from this study. 
33
Ar 330 473 K CO2 300 350 K
CO2-Ar
CO2
CO2-Ar 2 CO2
L-G
[1]  R.L. Mills, D.H. Liebenberg and J.C. Bronson: Equation of state and melting properties of 4He from 
measurements to 20 kbar, Phys. Rev. B, 21, pp.5137-5148, 1980. 
[2]  D.H. Liebenberg, R.L. Mills and J.C. Bronson: High-pressure apparatus for simultaneous adiabatic and 
isothermal compressibility measurements: Data on argon to 13 kbar, J. Appl. Phys., 45, pp.741-747, 1974. 
[3]  P.J. Kortbeek, J.J. van de Ridder, S.N. Biswas and J.A. Schouten: Measurement of compressibility and 
sound velocity of helium up to 1 GPa, Intern. J. Therm., 9, pp.425-438, 1988. 
[4]  P.J. Kortbeek, S.N. Biswas and J.A. Schouten: Measurement of compressibility and sound velocity of neon 
up to 1 GPa, Intern. J. Therm., 9, pp.803-812, 1988. 
[5]  S.N. Biswas, N.J. Trappeniers, P.J. Kortbeek and C.A. tenSeldam: Apparatus for the measurement of 
compressibility isotherms of gases up to 10 kbar: Experimental data for argon at 298.15 K, Rev. Sci. Instrum., 59, 
pp.470-476, 1988. 
[6]  Y. Hanayama, M. Kimura and T. Nishitake: Measurements of ultrasound velocity in condensed helium and 
neon gases: Rev. High Press. Sci. Technol., 7, pp.1177-1179, 1998. 
[7]  T. Nishitake and Y. Hanayama: Velocity of ultrasound wave in helium, argon and nitrogen gases at high 
pressure, J. Phys. Soc. Japan, 39, pp.1065-1067, 1975. 
[8]  G.M. Schneider: High-pressure investigations of fluid mixtures review and recent results, J. Supercritical 
Fluids, 13, pp.5-14, 1998.   
[9]  J.A. Schouten: What is different in mixtures? From critical point to high pressures, Inter. J. 
Thermodynamics, 22, pp.23-40, 2001. 
[10]  W.B. Streett and A.L. Erickson: Phase equilibria in gas mixtures at high pressures: Implications for 
planetary structures, Phys. Earth Planet. Interiors, 5, pp.357-366, 1972. 
[11]  Y. Hanayama: Velocity of ultrasound wave in mixed gases at high pressure, J. Phys. Soc. Japan, 46, 
pp.328-333, 1979. 
[12]  M. Kimura, Y. Hanayama and T. Nishitake: Measurement of ultrasound velocity in gases under high 
pressures up to 3.5 GPa, Jap. J. Appl. Phys., 26, pp.1366-1377, 1987.  
[13]  Y. Hanayama and M. Kimura  Sound velocities in helium-argon mixed gases, Sci. Tech. High Press., 1, 
pp.372-375, 2000. 
[14] M. Kimura, Y. Hanayama and N. Nishioka: Measurements of sound velocities and freezing pressures in 
neon-argon mixed gases, Rev. High Press. Sci. Technol., 7, pp.1213-1215, 1998. 
[15]     CO2-He 2
18, pp.395-403, 1999. 
[16]  A. Michels, J.M. Levelt and G.J. Wolkers: Physica, 24, pp.769-794, 1958. 


Behaviors of sound velocity in high pressure Ar, CO_2 and CO_2-Ar gases under super critical state

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