ES_StmNzl and ES_StmPipe Program Test Results

1. Introduction
2. Test Results of ES_StmNzl
3. Test Results of ES_StmPipe
	3.1. Superheated and Saturated Steam
	3.2 Flashing Saturated Water
4. Conclusion

1. Introduction (TOC)

ES_StmNzl and ES_StmPipe are the computer programs developed by ENGSoft Inc. for the compressible flow analysis of steam of nozzle and pipe respectively, using steam table, the basic equations of flow dynamics and the speed of current desktop computers. In order to prove the effectiveness of the programs, the outputs of the program runs have been compared with the data of several reference papers and presented here.

Through the comparison, the programs has been proved as effective for the compressible flow analysis of steam regardless of the conditions of steam. Since the program outputs had not been proved by actual experimental test, the term of "effective" has been used. Meanwhile, ENGSoft Inc. is proud in that the program run outputs are well in line with the measurements performed in a actual cascade heater drain system and presented in Ref. NO. 2, anyway.

For algorithm of ES_StmNzl and ES_StmPipe programs, please refer to "Compressible Flow Analysis of Steam" page, Clause 5.

2. Test Results of ES_StmNzl (TOC)

For the test of ES_StmNzl, the sample calculation of Ref. No. 4 has been used.

The sample calculation of Ref. No. 4 calculates the nozzle areas for safety valves using Napier equation, and correction factors for superheat degree and back pressure are applied to compensate the characteristics of steam. Furthermore, a correction factor is used additionally for high pressure dry saturation steam above 1500 psig pressure to compensate the expansion through wet steam region.

Three sample calculations are presented in Ref. No. 4, and the comparison table with ES_StmNzl outputs are as below.

Description		Dry Saturated		Superheated		HP Dry Saturated
Inlet pressure(P1), psia		262.2		599.9		3039.7
Inlet temperature(T1), oF		405.18		750.0		697.31
Inlet specific volume(v1), ft3/lb		1.759876		1.132059		0.08106365
Inlet enthalpy(H1), Btu/lb		1201.61		1380.41		1010.70
Inlet entropy(S1), Btu/lb-R		1.52293		1.612524		1.153103
Inlet quality(x1)		1.0		Superheated		1.0

Discharge pressure(P3), psia		14.7		14.7		14.7
Mass flow rate(W), lb/hr		21500		108500		88000

		Ref4	ES	Ref4	ES	Ref4	ES
Critical pressure(P2*), psia			152.35		327.19		1938.77
Nozzle throat steam condition;
-	Pressure(P2), psia		152.35		327.19		1938.77
-	Mach no.(M2)		1.0		1.0		1.0
-	Velocity(Vel2), ft/sec		1499.7		1890.81		1046.34
-	Temperature(T2), oF		359.66		592.74		631.41
-	Specific volume(v2), ft3/lb		2.840672		1.814024		0.141703
-	Enthalpy(H2), Btu/lb		1156.71		1309.05		988.85
-	Entropy(S2), Btu/lb-R		1.52293		1.612524		1.153103
-	Quality(x2)		0.956		Superheated		0.678

Mass flow rate per unit area(W/A), lb/hr/inch2			13198.45		26058.24		184600.00
Nozzle throat area, inch2		1.64	1.629	4.285	4.164	0.503	0.477

Calculating for Ideal Gas		k = 1.13		k = 1.3		k = 1.01
Critical pressure(P2*), psia		151.67		327.38		1836.79
Nozzle throat pressure(P2), psia		151.67		327.38		1836.79
Mass flow rate per unit area(W/A), lb/hr/inch2		13182.76		26142.66		200642.1
Nozzle throat area, inch2		1.631		4.15		0.439

where, Ref4 : Ref. No. 4 / ES : ES_StmNzl

The outputs of ES_StmNzle show always larger nozzle throat area than Ref. No. 4 data, and the deviation is within 5%. The calculation method of Ref. No. 4 is same with ASME Section VIII, Division 1, UG-131, and so it is assumed that the equations of Ref. No. 4 have been devised to have some margin in nozzle area selection. Therefore, we may say that program ES_StmNzle is effective program for steam nozzle analysis.

The maximum deviation exists at high pressure dry saturated steam above 1500 psig pressure, for which a additional correction factor is applied in Ref. No. 4 method. It is understandable from the output of ES_StmNzl that the high pressure dry saturated steam expanding through nozzle go through wet steam region which deviates maximum from ideal gas characteristics so that a additional correction factor is applied.

The maximum deviation of high pressure dry saturated steam is also proved from the ideal gas analysis results that even with the minimum isentropic exponent of 1.01 the nozzle throat area is far from the actual value, while the results of other steam conditions are in line with the actual values when selecting appropriate isentropic exponents.

3. Test Results of ES_StmPipe (TOC)

3.1. Superheated and Saturated Steam

For the test of ES_StmPipe for superheated and saturated steam, the sample calculation of Ref. No. 1 has been used.

The sample calculation of Ref. No. 1 analyzes the safety vent stack by the method described below.

- Flow analysis is based on Fanno Line equation derived for ideal gas.

- Sonic velocity is calculated using ideal gas equation, and several experimental equations is used for steam enthalpy, pressure and specific volume.

- For isentropic exponents, 1.3 is used for superheated steam and 1.13 for saturated steam.

The comparison table between Appendix B data of Ref. No. 1 and ES_StmPipe output is as below.

3.1.1 Superheated Steam

< Common Data >
Pipe inlet pressure(P0), psia	: 1214.7
Pipe inlet temperature(T0), oF	: 900
Pipe inlet specific volume(v0), ft3/lb	: 0.6168261
Pipe inlet enthalpy(H0), Btu/lb	: 1440.343
Pipe inlet entropy(S0), Btu/lb-R	: 1.586636
Pipe discharge pressure(P3), psia	: 14.7 psia
Mass flow rate(W), lb/hr	: 67630 lb/hr
Isentropic exponent used in Ref. No. 1(k)	: 1.3

Pipe ND	6 in.		8 in.		10 in.
Pipe cross-sectional area(A), sq. in.	28.891		50.027		78.855
Pipe resistance coefficient(K)	3.58516		2.50796		2.01956

	Ref1	ES	Ref1	ES	Ref1	ES
Critical pressure(P2*), psia	30.79	31.14	17.78	18.68	11.28	11.57
Pipe exit steam condition
Pressure(P2), psia	30.79	31.14	17.78	18.68	14.7	14.7
Mach no.(M2)	1.0	1.0	1.0	1.0	0.787	0.78
Velocity(Vel2), ft/sec	1982.5	1990.74	1982.5	1935.06	1600.8	1621.65
Temperature(T2), oF		655.54		663.04		708.15
Specific volume(v2), ft3/lb	21.17	21.25	36.66	35.741	46.66	47.344
Enthalpy(H2), Btu/lb		1361.23		1365.6		1387.85
Entropy(S2), Btu/lb-R		1.915313		1.975341		2.02123

Pipe inlet steam condition
Pressure(P1), psia	92.14	92.59	47.15	47.39	27.93	28.46
Mach no.(M1)		0.35	0.4	0.41	0.427	0.42
Velocity(Vel1), ft/sec	747.71	756.53	839.62	843.97	896.37	890.29
Temperature(T1), oF		797.89		788.56		783.69
Specific volume(v1), ft3/lb	7.99	8.031	15.53	15.645	26.13	25.959
Enthalpy(H1), Btu/lb		1428.92		1426.12		1424.52
Entropy(S1), Btu/lb-R		1.852949		1.924215		1.97883

where, Ref1 : Ref. No. 1 / ES : ES_StmPipe

From the table above, we know that ES_StmPipe outputs are well in line with the Ref. No. 1 data.

3.1.2 Dry Saturated Steam

< Common Data >
Pipe inlet pressure(P0), psia	: 1214.7
Pipe inlet temperature(T0), oF	: Dry saturated
Pipe inlet specific volume(v0), ft3/lb	: 0.3573578
Pipe inlet enthalpy(H0), Btu/lb	: 1184.15
Pipe inlet entropy(S0), Btu/lb-R	: 1.366749
Pipe discharge pressure(P3), psia	: 14.7 psia
Mass flow rate(W), lb/hr	: 83490 lb/hr
Isentropic exponent used in Ref. No. 1(k)	: 1.13

Pipe ND	6 in.		8 in.
Pipe cross-sectional area(A), sq. in.	28.891		50.027
Pipe resistance coefficient(K)	1.04567		0.73149

	Ref1	ES	Ref1	ES
Critical pressure(P2*), psia	33.18	31.73	19.16	18.09
Pipe exit steam condition
Pressure(P2), psia	33.18	31.73	19.16	18.09
Mach no.(M2)	1.0	1.0	1.0	1.0
Velocity(Vel2), ft/sec	1453.27	1471.88	1438.91	1449.71
Temperature(T2), oF		253.56		222.67
Specific volume(v2), ft3/lb	12.57	12.705	21.55	21.787
Enthalpy(H2), Btu/lb		1140.91		1144.2
Entropy(S2), Btu/lb-R		1.660897		1.72221
Quality(x2)		0.974		0.987

Pipe inlet steam condition
Pressure(P1), psia	63.19	60.85	33.52	31.77
Mach no.(M1)	0.537	0.54	0.589	0.55
Velocity(Vel1), ft/sec	797.89	812.64	857.08	883.01
Temperature(T1), oF		293.62		260.22
Specific volume(v1), ft3/lb	6.90	7.0274	12.84	13.167
Enthalpy(H1), Btu/lb		1170.97		1168.59
Entropy(S1), Btu/lb-R		1.63368		1.69961
Quality(x1)		0.992		Superheated

where, Ref1 : Ref. No. 1 / ES : ES_StmPipe

Deviation between two sources is bigger than that of superheated steam. That is likely because the saturated steam characteristic is deviated from ideal gas more than superheated steam. Particularly it should be noted that the pipe inlet steam of 8 in. ND pipe is superheated steam while the stagnated pipe inlet steam is dry-saturated.

Considering other test results, ENGSoft Inc. wants to say that the output of ES_StmPipe is more close to the actual value of steam rather than Ref. No. 1.

3.2 Flashing Saturated Water (TOC)

Saturated water is found in feed water heater drain lines and condensate drain lines of steam turbine, in which the saturated water is flashed along the pipe by pressure drop and the flow becomes two phase compressible flow. In case of superheated or saturated steam, the Fanno Line equation for ideal gas is applicable. However, in case of two phase flow, the application of Fanno Line equation is difficult. In this concern, there are many papers which handles the heater drain line analysis subject including Ref. No. 2 and 3.

In conclusion, the outputs of ES_StmPipe show very satisfactory results as it is without any additional corrections when comparing with various data as described below.

3.2.1 Comparison with Actual Test Data in Ref. No. 2

Ref. No. 2 presents the actual test data of cascade heater drain lines of Connors Creek Power Plant of U.S.A. Test was done for three individual heater drain lines and herein the test data of the first drain line have been used for comparison with the output of ES_StmPipe. According to Ref. No. 2, the test was done for 30 minutes for four loads using the method described below.

- Mass flow rates are not measured values, but calculated values by heat balancing method around heaters.

- The high pressure feed water saturation pressure was got from steam table by the temperature measured.

- The discharge pressure is the measured value in low pressure feed water heater.

- The pipe exit pressure is the saturation pressure got from steam table by the temperature measured at the pipe exit.

- The decision for choked flow was done by comparing the pipe exit pressure and the discharge pressure. Since the discharge pressures were higher than the pipe exit pressures for all case, choked flow for all cases was assured.

- The pipe inlet below means the level control device exit and the pipe exit pressure was the saturation pressure got from steam table by the temperature measured at the location.

- The accuracy of thermocouples used for measurement was +- 1 oF.

The comparison table between the outputs of ES_StmPipe and the actual test data of Ref. No. 2 is as below.

< Common Data >
Pipe ND and Schedule	: 4 in. Sch. 40
Pipe ID(D), in.	: 4.025
Pipe cross-sectional area(A), sq. in.	: 12.7175
Equivalent length of pipe(L), ft	: 58
Pipe friction factor(f)	: 0.017
Pipe resistance coefficient(K)	: 2.93963

Load	Load 1		Load 2
Mass flow rate(W), lb/sec	18.22		13.05
High pressure feed water heater drain condition
Saturation pressure(P0), psia	37.0		29.8
Saturation temperature(T0), oF	262.57		249.95
Saturated water specific volume(v0), ft3/lb	0.0171106		0.0170055
Saturated water enthalpy(H0), Btu/lb	231.378		218.539
Saturated water entropy(S0), Btu/lb-R	0.3855437		0.3676441

Discharge pressure(P3), psia	8.0		6.5

	Ref2	ES	Ref2	ES
Critical pressure(P2*), psia	18.2	18.1	13.2	12.72
Pipe exit flashed water condition
Pressure(P2), psia	18.2	18.1	13.2	12.72
Mach no.(M2)	1.0	1.0		1.0
Velocity(Vel2), ft/sec		190.85		204.8
Temperature(T2), oF	223	222.7	207	204.8
Specific volume(v2), ft3/lb		0.92459		1.42404
Enthalpy(H2), Btu/lb		230.65		217.66
Entropy(S2), Btu/lb-R		0.38623		0.36863
Quality(x2)		0.041		0.046

Pipe inlet flashed water condition
Pressure(P1), psia	27.0	29.56	20.0	21.72
Mach no.(M1)		0.56		0.54
Velocity(Vel1), ft/sec		43.78		53.47
Temperature(T1), oF		249.48		232.38
Specific volume(v1), ft3/lb		0.21243		0.36128
Enthalpy(H1), Btu/lb		231.34		218.48
Entropy(S1), Btu/lb-R		0.3857		0.36792
Quality(x1)		0.014		0.019

Load	Load 3		Load 4
Mass flow rate(W), lb/sec	10.25		7.29
High pressure feed water heater drain condition
Saturation water pressure(P0), psia	23.9		18.2
Saturation water temperature(T0), oF	237.59		222.98
Saturation water specific volume(v0), ft3/lb	0.0169072		0.0167972
Saturation water enthalpy(H0), Btu/lb	206.006		191.241
Saturation water entropy(S0), Btu/lb-R	0.3498513		0.3284782

Discharge pressure(P3), psia	6.5		3.8

	Ref2	ES	Ref2	ES
Critical pressure(P2*), psia	10.6	10.21	6.7	7.6
Pipe exit flashed water condition
Pressure(P2), psia	10.6	10.21	6.7	7.6
Mach no.(M2)		1.0		1.0
Velocity(Vel2), ft/sec		247.17		285.09
Temperature(T2), oF	195	194.21	175	180.5
Specific volume(v2), ft3/lb		2.12857		3.4518
Enthalpy(H2), Btu/lb		217.32		216.92
Entropy(S2), Btu/lb-R		0.369349		0.370764
Quality(x2)		0.056		0.069

Pipe inlet flashed water condition
Pressure(P1), psia	15.0	18.59	10.7	14.53
Mach no.(M1)		0.51		0.49
Velocity(Vel1), ft/sec		69.37		90.65
Temperature(T1), oF		224.1		211.42
Specific volume(v1), ft3/lb		0.599		1.09899
Enthalpy(H1), Btu/lb		218.44		218.38
Entropy(S1), Btu/lb-R		0.368265		0.36908
Quality(x1)		0.027		0.04

where, Ref2 : Ref. No. 2 / ES : ES_StmPipe

The pipe exit conditions are well in line, but the pipe inlet conditions have considerable deviations. The deviations are likely from the margins of equivalent lengths which may be given consciously or unconsciously by Author of Ref. No. 2.

3.2.2 Comparison with the Sample Calculation of Ref. No. 3

The analysis method of Ref. No. 3 is to improve the method of Ref. No. 2 which takes too much times. The followings briefly describes the method of Ref. No. 3.

- Basically the Fanno Line equation for ideal gas is used for compressible pipe analysis.

- For calculation of sonic velocity, the basic equation of Vc = dP / dRo is used instead of the equation for ideal gas.

- For isentropic exponent for use in Fanno Line equation, a pseudo isentropic exponent calculated from sonic velocity equation is used.

- Process of pipe flow is interpreted as a isentropic process.

The comparison table between the output of ES_StmPipe and the sample calculation data of Appendix B of Ref. No. 3 is as below.

< Case : Cascade Heater Drain >

< Common Data >
High pressure feedwater heater drain condition
-	Pressure(P0), psia	: 11.2
-	Temperature(T0), oF	: 198.61
-	Specific volume(v0), ft3/lb	: 0.0166276
-	Enthalpy(H0), Btu/lb	: 166.69
-	Entropy(S0), Btu/lb-R	: 0.2918849

Discharge pressure(P3), psia		: 8.0
Mass flow rate(W), lb/sec		: 30.69

Pipe ND	6 in.		8 in.
Pipe cross-sectional area(A), sq. ft.	0.2006		0.3474
Pipe resistance coefficient(K)	3.55		2.52

	Ref3	ES	Ref3	ES
Critical pressure(P2*), psia	9.0	10.14	6.2	6.4
Pipe exit flashed water condition
Pressure(P2), psia	9.0	10.14	8.0	8.0
Mach no.(M2)	1.0	1.0	0.69	0.77
Velocity(Vel2), ft/sec		30.63		67.96
Temperature(T2), oF		193.86		182.85
Specific volume(v2), ft3/lb		0.200246		0.770093
Enthalpy(H2), Btu/lb		166.67		166.6
Entropy(S2), Btu/lb-R		0.291893		0.292059
Quality(x2)		0.005		0.016

Pipe inlet flashed water condition
Pressure(P1), psia	10.9	> P0	9.6	9.79
Mach no.(M1)	0.66		0.55	0.6
Velocity(Vel1), ft/sec				24.11
Temperature(T1), oF				192.2
Specific volume(v1), ft3/lb				0.272786
Enthalpy(H1), Btu/lb				166.68
Entropy(S1), Btu/lb-R				0.291927
Quality(x1)				0.007

where, Ref3 : Ref. No. 3 / ES : ES_StmPipe

In the sample calculation of Ref. No. 3, the pipe inlet pressure of 6 in. ND pipe had been calculated and then the 6 in. ND pipe was judged as not-acceptable because the pipe inlet pressure(P1 = 10.9 psia) was higher than the maximum back pressure required by the level control valve(Pcv = 10.6 psia). However, the ES_StmPipe run shows that there is no pressure in the pressure range below the high pressure heater pressure(P0) which satisfies the equation of motion, as seen in the captured figure of ES_StmPipe run as below.

The result that 6 in. ND pipe is not acceptable is same, but the judgement basis is different. If unfortunately the calculation of Ref. No. 3 resulted in 10.5 psia for the pipe inlet pressure of 6 in. ND Pipe by a little bit lower mass flow rate or a little bit higher high pressure heater pressure, then 6 in ND pipe would be judged as acceptable even though the equation of motion was not satisfied.

Meantime, the maximum back pressure of level control valve, Pcv, is the critical pressure when the control valve is assumed as a nozzle. While Ref. No. 3 uses a experimental equation for Pcv calculation, the same critical pressure can be got from ES_StmNzl program run.

Anyway, it is seen from the table that the outputs of ES_StmPipe are well in line with the data of Ref. No. 3, especially in 8 in. ND pipe.

< Case : Heater Emergency Dump >

< Common Data >
High pressure feedwater heater drain condition
-	Pressure(P0), psia	: 41.0
-	Temperature(T0), oF	: 268.74
-	Specific volume(v0), ft3/lb	: 0.0171638
-	Enthalpy(H0), Btu/lb	: 237.66
-	Entropy(S0), Btu/lb-R	: 0.3941941

Discharge pressure(P3), psia		: 1.0
Mass flow rate(W), lb/sec		: 33.75

Pipe ND	4 in.		6 in.
Pipe cross-sectional area(A), sq. ft.	0.0884		0.2006
Pipe resistance coefficient(K)	6.8		4.2

	Ref3	ES	Ref3	ES
Critical pressure(P2*), psia	30.0	31.59	15.0	15.33
Pipe exit flashed water condition
Pressure(P2), psia	30.0	31.59	15.0	15.33
Mach no.(M2)	1.0	1.0	1.0	1.0
Velocity(Vel2), ft/sec		88.85		244.63
Temperature(T2), oF		253.31		214.15
Specific volume(v2), ft3/lb		0.232714		1.454885
Enthalpy(H2), Btu/lb		237.51		236.47
Entropy(S2), Btu/lb-R		0.394255		0.395704
Quality(x2)		0.016		0.056

Pipe inlet flashed water condition
Pressure(P1), psia	52.5 > P0	> P0	28.5	29.16
Mach no.(M1)	0.43		0.45	0.48
Velocity(Vel1), ft/sec				53.96
Temperature(T1), oF				248.7
Specific volume(v1), ft3/lb				0.320021
Enthalpy(H1), Btu/lb				237.6
Entropy(S1), Btu/lb-R				0.394566
Quality(x1)				0.021

where, Ref3 : Ref. No. 3 / ES : ES_StmPipe

In this case, the result of Ref. No. 3 for 4 in. ND pipe shows also the pipe inlet pressure is higher than the pressure P0, as the output of ES_StmPipe is.

Anyway, this table also shows that the outputs of ES_StmPipe are well in line with the data of Ref. No. 3.

4. Conclusion (TOC)

Efforts up to date have been given to the hand calculations of the complicate analysis of steam and flashed water. Therefore, the papers published for this purpose always use the Fanno Line equation for ideal gas, which is the only equation for compressible flow for engineers to solve by hand calculation. And then they use specific methods depending on the steam conditions and furthermore various experimental equations.

However, now the speed of desktop computers available to every engineers are excellent enough to perform a few hundreds of iterations in a few seconds. Therefore, the compressible flow of steam can be easily solved by try-and error method using the basic flow equations with steam table by computer programming, and ES_StmNzl and ES_StmPipe are the programs.

According to the test results of ES_StmNzl and ES_StmPipe above, the analysis method developed by ENGSoft Inc. is effective and acceptable, and it was found that the key codes of ES_StmNzl and ES_StmPipe have no major bugs.

References : (TOC)

1. Analysis of Power Plant Safety and Relief Valve Vent Stacks by G.S. Liao, Bechtel Power Corp., Transactions of the ASME, 1974

2. The Flow of a Flashing Mixture of Water and Steam Through Pipes by M.W. Benjamin and J.G. Miller, Detroit Edison Co., Transcations of the ASME, 1942

3. Analytical Approach for Determination of Steam/Water Flow Capability in Power Plant Drain Systems by G.S. Liao and J.K. Larson, Bechtel Power Corp., ASME Publication 76-WA/Pwr-4, 1976

4. Crosby Pressure Relief Valves Engineering Handbook, Crosby Gage & Valve Company, March 1986