Test on a Twin-Screw Compressor

Similar documents
Two-Stage Linear Compressor with Economizer Cycle Where Piston(s) Stroke(s) are Varied to Optimize Energy Efficiency

Gas Vapor Injection on Refrigerant Cycle Using Piston Technology

A Chiller Control Algorithm for Multiple Variablespeed Centrifugal Compressors

Development of Large Capacity CO2 Scroll Compressor

The Estimation Of Compressor Performance Using A Theoretical Analysis Of The Gas Flow Through the Muffler Combined With Valve Motion

Pressure Indication of Twin Screw Compressor

LGWP & HC Refrigerants Solubility Tests Performed in Running Scroll Compressor

Influencing Factors Study of the Variable Speed Scroll Compressor with EVI Technology

Operation of Compressors Through Use of Load Stands

Scroll Compressor Performance With Oil Injection/Separation

Technology issues regarding Blends of Refrigerants Buffalo Research Laboratory

Variable Volume-Ratio and Capacity Control in Twin-Screw Compressors

Research of Variable Volume and Gas Injection DC Inverter Air Conditioning Compressor

Modeling and Testing of an Automobile AC Scroll Compressor, Part II: Model Validation

Application of Computational Fluid Dynamics to Compressor Efficiency Improvement

Development of a High Pressure, Oil Free, Rolling Piston Compressor

Ball Beating Lubrication in Refrigetation Compressors

An Investigation of Liquid Injection in Refrigeration Screw Compressors

Scroll Compressor Operating Envelope Considerations

Tip Seal Behavior in Scroll Compressors

Impact Fatigue on Suction Valve Reed: New Experimental Approach

Linear Compressor Discharge Manifold Design For High Thermal Efficiency

Self-Adjusting Back Pressure Mechanism for Scroll Compressors

CFD Analysis and Experiment Study of the Rotary Two-Stage Inverter Compressor with Vapor Injection

A Twin Screw Combined Compressor And Expander For CO2 Refrigeration Systems

Capacity Modulation of Linear Compressor for Household Refrigerator

Lubrication of Screw Compressor Bearings in the Presence of Refrigerants

Investigation of Suction Process of Scroll Compressors

Valve Losses in Reciprocating Compressors

Experimental Investigation on the Operating Characteristics of a Semi-hermetic Twin Screw Refrigeration Compressor by means of p-v Diagram

Correlation Between the Fluid Structure Interaction Method and Experimental Analysis of Bending Stress of a Variable Capacity Compressor Suction Valve

GLOSSARY OF TERMS. Adiabatic Compression Compression process when all heat of compression is retained in the gas being compressed.

Small Variable Speed Hermetic Reciprocating Compressors for Domestic Refrigerators

Updated Performance and Operating Characteristics of a Novel Rotating Spool Compressor

Centrifugal Compressor Performance Deviations with Various Refrigerants, Impeller Sizes and Shaft Speeds

Single- or Two-Stage Compression

Development of Scroll Compressors for R410A

Linear Compressor Suction Valve Optimization

Evaluation of a Prototype Rotating Spool Compressor in Liquid Flooded Operation

Multifunctional Screw Compressor Rotors

Hermetic Compressor Manifold Analysis With the Use of the Finite Element Method

Development and Experiences with a Hermetic CO2 Compressor

Numerical Simulation for the Internal Flow Analysis of the Linear Compressor with Improved Muffler

HANDBOOK SAFETY DEVICES. Ed SAFETY DEVICES DS-ED 01/ ENG 1

Using PV Diagram Synchronized With the Valve Functioning to Increase the Efficiency on the Reciprocating Hermetic Compressors

COMMERCIAL REFRIGERATION SYSTEMS WITH CO 2 AS REFRIGERANT

Purdue e-pubs. Purdue University. Stephan Lehr Technische Universitaet Dresden. Follow this and additional works at:

Development of a New Mechanism Compressor Named "Helical

Capacity and pressure similar to R-507. Flooded systems. Low temperature (-46.7 C). R22 replacement as long as the condenser has the right size.

Improvement of the Volumetric and Isentropic Efficiency Due to Modifications of the Suction Chamber

ENGINEERING FLUID MECHANICS

Noise Characteristics Of A Check Valve Installed In R22 And R410A Scroll Compressors

Compression Model for Open Reciprocating Compressor Application to Cylinder Wall Cooling Study

Design and Development of a Variable Rotary Compressor

Refrigeration and Air Conditioning Technical leaflet

System Conditions Harmful to Compressors Their Diagnosis and Prevention

Experimental Analysis on Vortex Tube Refrigerator Using Different Conical Valve Angles

Performance and Operating Characteristics of a Novel Rotating Spool Compressor

Troubleshooting Guide. Pg. 1

Incorporating 3D Suction or Discharge Plenum Geometry into a 1D Compressor Simulation Program to Calculate Compressor Pulsations

Efficiency Improvement of Rotary Compressor by Improving the Discharge path through Simulation

Heat Transfer Research on a Special Cryogenic Heat Exchanger-a Neutron Moderator Cell (NMC)

Performance Analysis of Centrifugal Compressor under Multiple Working Conditions Based on Time-weighted Average

Pressure = 15.2 bar TXV. 10K super heat. Pressure = 1.82 bar. Line temp = 8 C. Line temp = 9 C

Heat Pump Connections and Interior Piping

INDIAN INSTITUTE OF TECHNOLOGY ROORKEE NPTEL NPTEL ONLINE CERTIFICATION COURSE. Refrigeration and Air-conditioning

Case 12 Multistage Centrifugal Refrigeration System Halocarbon Refrigerant

Using P-T Analysis As A Service Tool

Soft-optimization test of R-410A alternative refrigerant R-32 in a split condensing unit - Phase II

THE IMPORTANCE OF SUCTION LINES

Comparative Analysis of Two Types of Positive Displacement Compressors for Air Conditioning Applications

Internal Leakage Effects in Sliding Vane, Rotary Compressors

SELECTION CRITERIA FOR SAFETY VALVE

Fundamentals of Compressed Air Systems. Pre-Workshop Assignment

Removing nitrogen. Nitrogen rejection applications can be divided into two categories

Pressure Strength Test Requirements for Hermetic Refrigerant Compressor Housings Using Fatigue Analysis

Impact of imperfect sealing on the flow measurement of natural gas by orifice plates

Blocked Suction Unloading Improves Part Load Efficiency of Semi-Hermetic Reciprocating Compressor

Predicting the Suction Gas Superheating in Reciprocating Compressors

A NEW PROCESS FOR IMPROVED LIQUEFACTION EFFICIENCY

CFD Simulation of the Flow Through Reciprocating Compressor Self-Acting Valves

A centrifugal pump consists of an impeller attached to and rotating with the shaft and a casing that encloses the impeller.

Real Gas Performance Analysis of a Scroll or Rotary Compressor Using Exergy Techniques

PERFORMANCE AND CHARACTERISTICS OF COMPRESSOR/EXPANDER COMBINATION FOR CO 2 CYCLE ABSTRACT

Performance Measurement of Revolving Vane Compressor

Characterization and Performance Testing of Two- Stage Reciprocating Compressors using a Hot-Gas Load Stand with Carbon Dioxide

LP Separator Level Control by Variable Speed and Multi Stage Brine Reinjection Pumps at Kawerau and Nga Awa Purua Geothermal Projects, New Zealand

TESTING AND ANALYZING ON P-V DIAGRAM OF CO 2 ROLLING PISTON EXPANDER

Domain Decomposition Method for 3-Dimensional Simulation of the Piston Cylinder Section of a Hermetic Reciprocating Compressor

Compressors. Basic Classification and design overview

A Balanced View of Reciprocating and Screw Compressor Efficiencies

Seminar 65 Compression Challenges for Low GWP Refrigerants

Vibration-Free Joule-Thomson Cryocoolers for Distributed Microcooling

IRC 2011 All Rights Reserved

1.2 Example 1: A simple hydraulic system

CONTROL VALVE WHAT YOU NEED TO LEARN?

Energy savings in commercial refrigeration equipment: High Pressure control implementation

CORESTA RECOMMENDED METHOD N 6

Analytic and Experimental Techniques for Evaluating Compressor Performance Losses

Single Phase Pressure Drop and Flow Distribution in Brazed Plate Heat Exchangers

Transcription:

Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 1996 Test on a Twin-Screw Compressor C. Ducruet Electricite de France B. Hivet Electricite de France J. Boone Mycom Europe M. Torreilles Quid Refrigeration Follow this and additional works at: https://docs.lib.purdue.edu/icec Ducruet, C.; Hivet, B.; Boone, J.; and Torreilles, M., "Test on a Twin-Screw Compressor" (1996). International Compressor Engineering Conference. Paper 112. https://docs.lib.purdue.edu/icec/112 This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/ Herrick/Events/orderlit.html

TEST ON A TWIN-SCREW COMPRESSOR: COMPARISON BETWEEN TWO COOLING MODES C. DUCRUETl, B. HIVET1, J. BOONE 2, M. TORREILLES 3 lelectricite de France, ADEI Department Centre des Renardieres, BP 1, 7725 Moret-sur-Loing, France Phone (+33) (1) 6 73 65 41 - Fax (+33) (1) 6 73 64 4 2Mycom Europe Leuvensesteenweg 65, 193 Zaventem, Belgium Phone (+32) (2) 757 9 75 - Fax (+32) (2) 757 9 23 squiri Refrigeration 46, route de Bischwiller, BP 155, 6734 Schiltigheim Cedex, France Phone (+33) 88 19 19 - Fax (+33) 88 19 19 49 ABSTRACT An open twin-screw compressor supporting two distinct cooling modes (by external oil cooling or liquid injection into the compressor) has been tested with HCFC 22 and an alkylbenzene lubricant. The test procedure was as specified in the ISO 917 standard (testing of refrigerant compressors). Using both cooling methods, compressor efficiencies for evaporation from - 35 oc to - 5 C, condensation from 3 oc to 47 C, and discharge superheat of 35 K are determined. To conclude the study, compressor cooling needs for different values of discharge superheat and of compressor capacities are analysed. INTRODUCTION When designing or implementing compressors using HCFC 22, full allowance must be made for the phenomenon of refrigerant heating during compression, especially under harsh operating conditions. In many cases, the compressor will require cooling. Rather than cooling the injected lubricant, which is the conventional method for cooling screw compressors, it might be economically advantageous to inject liquid HCFC22. To compare the impact of cooling methods on compressor efficiencies and cooling needs, both cooling modes were tested on the same twin-screw compressor, having a swept volume of 294 ms.h-1. TEST PROCEDURE AND OPERATING CONDITIONS The compressor was implemented on a test installation consisting of a dry-expansion refrigerating system. The refrigerant HCFC 22 was used with an ISO 1 grade alkylbenzene lubricant. To accurately determine compressor efficiencies and ensure results reliability, ISO 917 procedure (testing of refrigerant compressors) was applied to the existing installation and the compressor under test. The preliminary study ofiso 917 standard revealed the following points : reference test conditions are compressor suction pressure, discharge pressure, suction temperature and shaft speed, with tolerances for each values specified. For coolable compressors, the ISO 917 procedure is not sufficient to defme a unique set of test conditions : for a full defmition, discharge temperature or superheating is also to specify. In the present work, we determined compressor efficiencies under refrigerating system conditions (see table 1), at nominal compressor capacity, with discharge superheating of 35 K. We assessed compressor 175

cooling needs at 5 %, 75 % and 1 % compressor capacity, for discharge superheating values between 2 and 4 K (discrete points only). 1.3 bar ( 35 C) Discharge 11.9 bar (3 C) 13.5 bar (35 C) pressure 16.5 bar (43 C) c 18 bar ( 46.7 C} Suction pressure 2bar 3 bar 4 bar (- 25 C) (- 14.6 C) ( 6.5 C) X X X c X X X cv cooled lubricant injection x HCFC 22 liquid injection cvariable capacity v variable discharge superheating suction superheat : 1 K Table 1 : Test conditions Basically, the ISO 917 procedure involves determining the refrigerant mass flow rate through the compressor, which conditions calculation of the other values (volumetric and isentropic efficiencies, refrigerating power and COP). In order to determine this mass flow rate, two distinct methods are necessary ; in our case, flow rates of liquid at expansion valve inlet and of vapour at the discharge of the compressor should not differ by more than 4 %. Both of these values are taken to determine test mass flow rate (average of the two methods). This values must be multiplied by a corrective factor to bring the test point into line with the reference conditions. Here, we have rectified certain inconsistencies in the ISO 917 standard. Efficiencies and accuracy errors were calculated in accordance with ISO 917 defmitions. Isentropic efficiency is defmed as the ratio between isentropic compression power and compressor mechanical power demand. This definition was adopted in all cases, noting that there is no specific reference to compressor cooling in ISO 917. ISO 917 makes no allowance for the fact that, in liquid injection mode, part of the discharge refrigerant flow rate is drawn off for cooling the compressor. To allow for this, we compare the volumic flow rate of liquid HCFC 22 directed to the expansion valve with the flow delivered by the compressor, subtracting the flow of liquid HCFC 22 injected during compression, measured using a volumic flow meter. COMPRESSOR EFFICIENCIES IN LUBRICANT COOLING MODE For compressor standard configuration (external lubricant cooling and nominal capacity), tests covered the five points shown in table 1, plus the point given by suction/discharge pressures of 1. 75/13.5 bar. Figures 1 and 2 summarise results for volumetric efficiency (preferred to mass flowrate) and isentropic efficiency. The volumetric efficiency curve is typical of that found with fixed Vi screw compressors. For pressure ratios from 3 to 13, volumetric efficiency varies widely, from.8 to.57. Volumetric efficiency is highest at pressure ratios approaching manufacturers specified Vi, though there is no maxima value within the studied range. The rate of decrease in volumetric efficiency with pressure ratio is constant at all discharge pressures (2.5 % decrease in efficiency per point increase in pressure ratio). At any given suction pressure, we observe a steeper decline in efficiency (5 % to 8 %) which is as more important as the suction presure increases. At fixed pressure ratio, an increase of 1 bar in suction pressure produces an 11.7 % drop in volumetric efficiency, whereas an increase of 1 bar in discharge pressure produces a 1.5% drop in volumetric efficiency. A wide variation in isentropic efficiency with pressure ratio is also observed : from.67 to.35. However the curves for constant discharge pressures are very close (less than.5 deviation between curves for 11.9 bar and 18 bar). The variation in isentropic efficiency with pressure ratio is more 176

pronounced at constant suction pressure (slope from.4 to.6) than at constant discharge pressure (slope.3). - 1..9,.!...8 =.7 II).6 l"il.5 :s.4.3 II).2.1 1..9 8.8.7 s o.6 II) s l"il.5 a o.4 t::l.3 t.2 +.1 +. +---+---+----+----+------1. +---+----+----+----t----1 Suction and Discharge Pressures: ------ 1.3 bar... -----... 1. 75 bar - - --- 3 bar ----- -------... 4 bar 11.9 biu' 13.5bar A 16.5bar e 18bar 3 5 7 9 11 13 3 5 7 9 11 13 Pressure Ratio (-) Pressure Ratio (-) Figures 1 and 2: Volumetric and Isentropic Efficiencies versus pressure ratio, in lubricant cooling mode IMPACT OF HCFC 22 LIQUID INJECTION ON COMPRESSOR BEHAVIOUR On this compressor, cooling by liquid injection is only usually applied for ammonia. We therefore extended tests using HCFC 22 and this cooling mode to ten points. As compressor cooling is for this method performed by drawing off part of the liquid refrigerant (i.e. part of the discharge flow rate) from the HP receiver, for reinjection into the compressor, it is interesting to analyse the HCFC 22 flow rates throughout the system : the refrigerating power only depends on HCFC 22 mass flow rate, whereas the mechanical power depends on the sum of the suction and injected flow rates (since the injected fluid must be compressed from the intermediary pressure to the discharge pressure). Suction Pressure (bar) /leferencj 1% == tnschargflow Ra.fe) "1% +----t------i---+---i 9% Suction flow Rate = :: 8% s 7% "' 6% " Ill 5% 4% ::: Ill = 'i 3% N 2% N 1% % r:z:.. ::c A L\.. D I!. Injected Tiow Rate! Discharge P:ressllt'e: 11.9 bar 13.5 bar A16.5 bar eisbar Figure 3 shows the part of HCFC 22 discharge flow rate used for refrigeration and the part used for compressor cooling. At low suction pressures, the part of discharge flow rate used for compressor cooling (for a constant discharge superheating of 35 K) rises with high discharge pressure up to 47 %. At high,suction pressures (i.e. lower pressure ratios) 8 % to 9 % of the discharge flow rate is used for refrigeration. Figure 3: HCFC 22 Mass FZow Rates in the test loop 177

We then examine how compressor efficiencies are affected by the different mass flow rates associated with this cooling mode. Figures 4 and 5 show refrigerating COP and refrigerating power curves for liquid injection mode. Tables 2 and 3 compare refrigerating power and COP between both cooling modes, at five identical points. 15 '=II 9 c 1-1 7 II ;s II 5 3-4 Discharge Satul."ated T emperatul."e ; / / / / -3-2 -1 Suction Saturated Temperature (OC) 8 :: 3 11 2.5 ; e 2.s 1-1 1-1 1.5... = 1 s II s.5 Q +-----r---r------- -4-3 -2-1 Suction Saturated Temperature (OC) Figures 4 and 5: Refrigerating Power and COP versus suction saturated temperature, for liquid injection cooling mode Discharge pressure Table 2: Suction Pression 1.3 bar 3bar 4 bar 11.9 bar 92% 97% 16.5 bar 84% 92% 18 bar 96% Refrigerating Power compared to results obtained for lubricant cooling mode (reference 1 %) Suction Pression 1.3 bar 3bar 4bar Discharge 1L9bar 88% 93% pressure 16.5 bar 79% 89% 18bar 92% Table 3 : Refrigerating COP compared to results obtained for lubricant cooling mode (reference 1 %) Under identical compressor operating conditions, as gas suction density and enthalpies are the same for both cooling modes, the refrigerating power is only affected by the difference in suction flow rates, i.e. a decrease from 8 % to 16 % (3 % to 8 %) for an evaporation temperature of - 35 C ( 15 oc) and condensation temperatures from 3 to 43 C. The drop in refrigerating power only becomes significant when suction and discharge saturated temperatures start to diverge. - As for coefficient of performance, it depends directly on the ratio between suction mass flow rate and mechanical power. Under worst conditions (high pressure ratio or large difference between saturating temperatures), we observe a 21% drop in compressor performance with respect to the COP obtained using the usual cooling mode, but only a 6% drop in the most favourable conditions. The drop in COP is higher than drop in refrigerating power because of the increase in mechanical power (3 to 5 %) when liquid injection cooling is considered. COMPRESSOR COOLING NEEDS The ISO 917 test procedures fails to specify whether or not the compressor is cooled and the test report specified by ISO 917 makes no mention of parameters relative to compressor cooling needs. However, the complete study of the compressor is also based on the analyse of these terms. - - 178

So the following parameters are examined : temperature and flow rate of lubricant injected into the compressor (all functions included) ; power required for cooling the compressed gases, calculated at the water side of the external water/lubricant exchanger (for lubricant cooling method only) ; flow rate of refrigerant injected during compression and injection pressure (for HCFC 22 liquid injection method only). Figure 6 shows the oil injection flow rate versus pressure difference at compressor inlet and outlet, for both cooling modes. In lubricant cooling mode, the injected oil flow rate varies linearly with the difference between suction and discharge pressures. In liquid injection mode, the points on the graph show ± 1 dm 3 /h dispersion around an average value. Lubricant flow rates are 15 % to 25 % below the values found previously and, within the compressor range under study, depend primarily on the discharge pressure. This difference in injected oil flow rate behaviour between both cooling modes may be attributable to the pressure difference between discharge and lubricant injection ormces, which is responsible for circulating the lubricant. In both cooling modes, the flow rate of lubricant injected into the compressor remains constant, when discharge superheating or compressor capacity varies. This conflrms the previous conclusions, given the lubricant flow rate as only dependant on pressure difference. 24 2! 22 ; =-- :; o:!; 2 Ql...,... E - ".S!,-- 1 Q " 8 ::..... :! t 16 =-, 14 :: 1:.\ 12 ii: cooled lubricant 1+----+------+----+-- 8 1 12 14 16 18 Compressor Pressure Difference (bar) 5 45 :::. 4 g 35 :;: 3-25.1: Ql..:: 2 o... 15 1 5 Compressor Capacity : 1% Discharge Pressure : O-t--------t---+---- 1 2 3 4 Suction Pressure (bar) 75%.. 5% -------11.9 bar ---- --------- 13.5 bar ----- - ---- 16.5 bar -- - ----- -- 18 bar., Figures 6 and 7: Characterisation of compressor cooling needs for cooled lubricant mode The power required for compressor cooling is examined, for constant discharge superheat of 35 K, by reference to figure 7, which shows the usual behaviour cooling power with suction and discharge pressures : compression cooling need (and thus cooling power) drops as the temperatures of the heat sink and cold source get closer together (i.e. best-case conditions for compressor). The power increase required for compressor cooling is estimated at + 6.9 kw per bar decrease in suction pressure, and + 2. 7 kw per bar increase in discharge pressure. The ratio between cooling power and mechanical power at nominal capacity varies from 3% (for lowest \T between sources: 45 K) to 7% (for highest \ T between sources : 79 K). Thanks to tests at 5% and 75% capacity, it can be concluded that cooling compressor power level is independent of the compressor capacity stage : under the same suction and discharge conditions, compressor cooling needs remain unchanged regardless of compressor power. 179

Tests also confirmed that the compressor cooling power varies with discharge superheating. In lubricant cooling mode at the 4/18 bar point, the compressor cooling power drops from 3 kw to 24 kw as discharge superheating goes from 25 K to 35 K, though the mechanical power required for compressing the HCFC 22 remains the same. The magnitude of heat exchanges between lubricant and refrigerant during compression thus appears to have no effect on the mechanical power, at least over the parameter range covered by our tests. However, this observation would need checking for the case of zero lubricant cooling, i.e. uncontrolled discharge superheating. For a discharge pressure of 11.9 bar, a suction pressure from 1.3 to 3 bar and a discharge superheat of 35 K, oil temperatures vary from 35 oc to 46 oc at the injection orifices. For a discharge pressure of 16.5 bar, temperatures ranged from 42.2 oc to 52.4 C. The highest lubricant injection temperature was observed at the 4 bar/18 point. The injection temperature is important as it determines the viscosity of the lubricant/refrigerant mixture injected into the compressor (to ensure lubrication, leaktightness between screws, etc... ). For a comparison, in liquid injection mode, the injection temperature varies between 58 C and 77 C and only depends on the discharge temperature (i.e. it is only affected by losses in the main lubrication circuit). These temperatures are on average 6 K lower than the discharge temperature. In this last case, owing to the levels of viscosity ranged at the high end of the temperature range, viscosity may become a limiting factor for use of liquid injection cooling mode at discharge pressure greater than 16 bar. In liquid injection mode, the flow rate of the refrigerant injected into the compressor (parameter analysed above) and the intermediary injection pressure, used for sizing the valve of the liquid injection circuit (controlled by means of a bulb at the compressor discharge), were analysed. At nominal capacity, HCFC 22 injected flow rate ranged from 3 to 73 kglh, for pressure difference (discharge minus intermediary pressures) from 7 to 12.5 bar. Though the proportion of mechanical power responsible for compressing the HCFC 22 coming from compressor suction is lower than in external cooling mode, the additional flow of fluid to be conveyed from intermediary pressure to discharge pressure is responsible for an observed increase of 3 % to 5 % in mechanical power. The intermediary injection pressure varies from 3 to 5.8 bar (corresponding to saturating temperatures of. 16 octo 5 C), depending on the compressor cooling needs and thus on the pressure difference at the compressor inlet and outlet. CONCLUSION The efficiencies difference obtained by implementing liquid injection cooling on a compressor that is usually cooled by the lubricant have been analysed. Significant deviations between these two cooling methods, and divergence increased as operating conditions worsened are observed. The results of our investigation should prove useful when selecting compressors cooled by liquid injection. Liquid-injection-cooled compressors have lower performance than lubricant-cooled compressors of the same swept volume, which means they will need a higher swept volume rating to operate under the same evaporation temperature and refrigerating power conditions. However, this performance penalty may be compensated by lower investment and running costs for certain items (simplified auxiliary circuits, no external exchanger, no cooling water). The long-term profitability of adopting this lowerperformance method should be examined case by case. REFERENCES ISO 917 standard, «Testing of refrigerant compressors», 1989, second edition. 18