Cold Capacity

Solenoid valve manufacturers determine the performance of products with a standardized set of measures. However, these do not necessarily directly correlate to customer industries. For example, one of the most vital statistics of a solenoid valve to the manufacturer is Cv rating, or the flowrate the valve can handle. This measure can tell a solenoid valve manufacturer a tremendous amount about the valve’s capabilities and the applications for which it is a good fit.

On the other hand, for a user concerned with a refrigeration application, Cv is quite meaningless. The measure of greatest importance in this scenario is the valve’s refrigeration capacity, measured in tons or kilowatts. Yet, because solenoid valves are used across so many industries, this number may not even be specified by the manufacturer.

Early Research & Findings
Research began in the 1960s to develop a simplified, low-cost means of determining the refrigeration capacity of solenoid valves. Recently, the American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHRAE, www.ashrae.org) issued Standard 158.1-2004 to address the need for refrigeration capacity statements for solenoid valves.

The foundation for ASHRAE Standard 158.1-2004 can be traced to research sponsored by the Air-Conditioning and Refrigeration Institute (ARI, www.ari.org). The research was conducted from 1963-1966 at Purdue University’s Herrick Laboratories (www.ecn.purdue.edu/Herrick/). It focused on the flow characteristics of solenoid valves in an attempt to establish a standard code for rating refrigeration capacity in HVACR (heating, ventilation, air-conditioning, and refrigeration) systems. The goal of this study was to develop a simple, reliable method of predicting the flow of refrigerant though a solenoid valve as a function of pressure drop. It also sought to develop an easy means of experimental testing for refrigeration capacity using air or water as the working fluid. After three years, the researchers determined that flow could indeed be predicted for the common refrigerant R12 using water flow correlation.

These seminal results were eventually worked into ARI Standard 760-69, titled "Solenoid Valves for Liquid Flow." ARI then charged the same laboratory with additional research in 1967, with a goal of extending its findings to refrigerants R22 and R502, as well as to compressible (or gaseous) flow through solenoid valves. Several important findings were made:
• Water flow testing could be accurately used to predict flow for liquid refrigerants.
• Water flow correlation is not accurate for high gas flowrates due to the compressibility effects on the gas as it flows through the solenoid valve.
• Flow could be predicted for vapor refrigerants using water flow correlation along with a compressibility correction (flow coefficient plotted against acoustic ratio).

As a corollary, the research also proved that an earlier equation for gas flow (FCI Standard 62-1) did not produce accurate calculations for compressible flows. This equation assumed incompressible flow through the valve using average pressure and a density based on the ideal gas law. Research findings negated this method, as compressibility effects were determined to be essential to the calculation. ARI again included Herrick’s study results in its next revision of its Standard 760, titled "Solenoid Valves for Use with Volatile Refrigerants."

ASHRAE began work on its own standard in 1997. The goal of this research was to develop a conclusive set of methods for the measurement of compressible and incompressible flows through solenoid valves for the purpose of determining refrigeration capacity. Further, the standard aimed to outline prescribed testing procedures. The standard was publicly reviewed in April 2003; it was accepted in January 2004.

ASHRAE Standard 158.1
ASHRAE Standard 158.1 is titled "Methods of Testing Capacity of Refrigerant Solenoid Valves." It is designed to prescribe "a method of testing the capacity of refrigerant solenoid valves for use in refrigerating systems."

The first test set forth by the standard determines the flow curve for water. A water flow system is outlined by the standard and a total of nine flow measurements are made at preselected conditions, five of which are at sequentially increasing pressure drops and four at sequentially decreasing pressure drops (or vice versa). For the valve under test, the standard specifies that users first measure water flow (GPM), pressure drop (PSIG), and water temperature (Fahrenheit). Next, users must plot the flow (w) in lb/m versus sqrt (density x pressure drop). The flow coefficient, C1, is defined by the slope of the least-squares curve fit. This relationship can be expressed as:

Good engineering practice suggests adding the equation and the value of C1 on the curve, along with other pertinent information for the valve under test. The plotted curve, a spreadsheet, or a programmable calculator can be used afterward to determine the flow values at other flow conditions. This method is very similar to determining the flow coefficient, Cv, for incompressible flow where:

Q is flow in GPM and SG is the specific gravity of the fluid compared to water. The water data can also be used to determine the incompressible flow coefficient, Cv, to determine the flowrate for solenoid valves used for secondary coolant applications. However, the Cv method may over-predict flow for pilot-operated solenoid valves near the minimum operating pressure differential point. To determine the flow coefficient for air, measure airflow (CFM), upstream pressure (PSIA), pressure drop (PSIG), and air temperature (Fahrenheit) for the valve under test. An airflow system is defined for the vapor flow capacity test in the standard. Upstream pressure is held constant while downstream pressure is adjusted to give the desired pressure drop across the test valve. For ΔP/P1 < 0.1 or AR < 0.07, plot the air data using the same method as for water. This curve will be used later for determining suction line and low pressure drop discharge line capacity. The slope of the curve or the C1 coefficient may be different for air compared to water due to Reynolds number effects. For ΔP/P1 ≥ 0.1 or AR ≥ 0.07, plot

versus

, where w is in lb/m and k = 1.4 for air. Use engineering judgment to fit the best straight line through the data. The curve must decrease linearly. The compressible flow coefficient can be defined by

, where C1 is the incompressible flow coefficient, and the slope, m, is based on judgment. According to accepted flowmeter theory, C approaches C1 as AR goes to zero. Good engineering practice suggests adding the curve fit equation and the values of C1 and m on the curve, along with other pertinent information for the valve under test. The plotted curve, a spreadsheet, or a programmable calculator can be used afterward to determine the flow values at other flow conditions. This method is very similar to ANSI/ISA Standard S75.02 for control valve capacity, which uses a curve of YCv vs. ΔP/P1. The ISA compressible flow coefficient curve sets YCv as the incompressible value at ΔP/P1 = 0. The ISA method creates a second flow coefficient, XT, to describe the slope of the curve, which is highly dependent on the flow geometry of the valve under test. The slope, m, of the ASHRAE curve can be considered as the second flow coefficient for the ASHRAE method. These figures for refrigerant mass flowrate of liquid or vapor can be converted to a measurement of refrigeration capacity in tons by taking into account the refrigerant properties of enthalpy, density, and the gas specific heat ratio (k). This measure is the one that is most meaningful to HVACR users. Published Capacity Ratings Capacity calculations (or sizing) for refrigeration solenoid valves are provided by valve manufacturers as a means of reference for potential customers. These ratings are based on standards set forth by ARI 760-2001. Appendix A of this standard currently mandates the calculation of the figures as well as method of testing. Capacity in tons is calculated based on the equation:

, where hg is enthalpy at saturation vapor at 40 F and hf is enthalpy at saturated liquid at 100 F. ARI will revise ARI Standard 760 to require ASHRAE Standard 158.1 as the method of test for capacity. The liquid line capacity nominal rating point is defined as a three PSIG pressure drop for refrigerant R22, at 1 F saturation pressure change, 40 F evaporator temperature, 10 F superheat, and 101 F condenser temperature. Other pressure drops, such as one, two, or five PSIG, can be used; likewise, ratings can be determined based on the use of other refrigerants. The suction line capacity nominal rating point for R22 can be defined at an evaporator temperature of 40 F plus 25 F of superheat, and one PSIG pressure drop. Other refrigerants or different evaporator temperatures, such as 20, zero, -20, or –40 F, can also be used. Discharge line capacity nominal ratings are based on a two PSIG pressure drop for R22, plus isentropic compression from 40 F evaporator temperature plus 25 F of superheat, to 101 F condenser temperature, plus an additional 50 F from isentropic compression. Again, one can apply different pressure drops (5, 10, 25, 50, or 100 PSIG) and other refrigerants. The nominal ratings and extended capacity tables are meant to provide potential buyers with a frame of reference for a refrigeration solenoid valve purchase. Tests simulate standard conditions and monitor the valves’ capacities. However, they are not meant to substitute for the consultation of a refrigeration solenoid valve manufacturer. Trained specialists are better equipped to specify the correct valve while taking into account the intricacies of HVACR applications. Examples Finding refrigerant capacity for liquid: Step One: Find the liquid mass flowrate for the refrigerant using the water flow correlation developed for the valve, C1, at the specified flow conditions (T, P1, and ΔP). • Refrigerant: R-22 • Liquid Temperature: 100 F • Evaporator Temperature: 40 F • Inlet Pressure: 211 PSIA • Outlet Pressure: 208 PSIA • Pressure drop, ΔP = 3 PSIG • Density, ρ = 71.06 LB/FT^3 • (ρΔP)^1/2 = 14.6 • C1 = 3.29 • Cv = 2.93 • Refrigerant flow, w = 48.0 LB/MIN Step Two: Find the refrigerant enthalpy values for the specified flow conditions. • Enthalpy of saturated liquid, hf = 39.5 BTU/LB • Enthalpy of saturated vapor, hg = 108.3 BTU/LB Step Three: Calculate refrigerant capacity in tons. • Capacity, Rc = 3300 • BTU/MIN = 16.5 Ton Finding the refrigerant capacity for vapor: Step One: Find the vapor mass flowrate for the refrigerant using the vapor flow correlation developed for the valve, C1 and m, at the specified flow conditions (T, P, and ΔP). • Refrigerant: R-22 • Liquid Temperature: 100 F • Evaporator Temperature: 40 F • Superheat: 25 F • Inlet Pressure: 211 PSIA • Inlet Temperature: 202 F (=152+50) • Outlet Pressure: 161 PSIA • Pressure drop, ΔP = 50 PSIG • Density, ρ = 2.89 LB/FT^3 • (ρΔP)^1/2 = 12.0 • ΔP/P = 0.24 (Use the compressible flow coefficient curve since ΔP/P > 0.1) • k = 1.245 • AR = ΔP/(Pk) =0.19 • C1=3.29 • m=1.85 • C = 2.94 • Refrigerant flow, w = C(ρΔP)^1/2 = 35.3 LB/MIN Step Two: Find the refrigerant enthalpy values for the specified flow conditions. • Enthalpy of saturated liquid, hf = 39.5 BTU/LB • Enthalpy of saturated vapor, hg = 108.3 BTU/LB Step Three: Calculate refrigeration capacity in tons. • Capacity, Rc = 2430 BTU/MIN = 12.2 Ton

ASHRAE Standard 158.1-2004 prescribes a method of testing the capacity of refrigerant solenoid valves for use in refrigerating systems. It does this by listing and defining the terms used for testing liquid or vapor refrigerants and by specifying procedures, apparatus and instrumentation that will produce accurate capacity data. The standard is currently available on the ASHRAE Web site at www.ashrae.org. Members price is $14.00, nonmembers $18.00.

New ASHRAE Standard 158.1 builds on years of research to offer solenoid valve manufacturers and HVACR engineers the ability to accurately and reliably determine refrigeration capacity of solenoid valves. It also outlines affordable testing procedures, so any new refrigeration solenoid valve can be evaluated before introduction without significantly adding to product development costs. This method can also be applied to solenoid valves used for secondary coolant applications, ball valves, globe valves, needle valves, check valves, or other flow control devices used with refrigerants.

About the Author
Charles Bald has been a senior design engineer with Parker Fluid Control Division for the last five years and is currently working on a flow test standard for solenoid valves. He earned a bachelor’s degree in Mechanical Engineering from Syracuse University and a master’s degree in Mechanical Engineering from Rensselaer Polytechnic Institute’s Hartford Graduate Center. Mr. Bald has 15 years of industry experience in such areas as thermal and flow analysis, centrifugal compressor design, and refrigeration systems. He is a member of ASHRAE and serves on the technical committees for SPC 158P and TC 8.8. Mr. Bald can be reached at [email protected] or 860 827-2300.

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