Percent per Degree Rule of Thumb for Refrigeration Cycle Improvement

Transcription

1 7 Percent per Degree Rule of Thumb for Refrigeration Cycle Improvement Steve Doty, PE, CEM ABSTRACT A value of 1-1.5% power reduction per degree Fahrenheit (F) has been used successfully for years to estimate the effects of either lowering condenser temperature or raising evaporator temperature in a mechanical cooling system. This concept shows up in a variety of energy conservation measures, all with the goal of reducing power requirements. Reviewing the underlying science will allow confident use of this rule of thumb and explain the range of values given. The principles involved with this rule of thumb include lift, heat exchanger approach, coefficient of performance, refrigeration cycles, and sources of error. Since the work involves differences, pressure and temperature units do not have to be in absolutes. These terms and a Mollier Diagram (pressure-enthalpy, or p-h) were used to evaluate this rule of thumb. Manufacturer s data is the most accurate source of power reduction from a change in operating conditions because it captures all the various influences in a bottom-line live test. A Mollier (p-h) diagram can be used with before/after system conditions for good results. The rule of thumb can be used for reasonable accuracy, especially when incorporating the baseline lift (system lift before the change is made). Using the traditional 1-1.5% rule of thumb can overstate savings, but is safe at the 1% level. REVIEW OF IMPORTANT TERMS Lift is the difference between the high and low pressure regions a compressor works against. Compressor power is proportional to lift. If all the existing lift is removed, all of the existing work associated with lift is removed. So, 0-100% lift power reduction will follow a 0-100% reduction in lift.

2 8 Energy Engineering Vol. 112, No Note: The compressor has additional power requirements besides lift, such as fluid friction, bearing losses, and motor losses. If all power came from lift, the task would simply be to find the change in lift as a portion of total lift. In a refrigeration cycle, saturated conditions allow interchanging pressure and temperature. For measures that lower condensing temperature or raise evaporating temperature, power reduction can be estimated from temperature difference even though what the compressor really sees is a change in pressure difference. An example of low refrigeration lift is a water-cooled chiller (~40-55F lift). An example of high refrigeration lift is an air-cooled walk-in freezer with a blower coil (~ F lift). Approach is a heat exchanger term that describes how closely the leaving fluid on one side can approach the entering or ambient fluid on the other side of the heat exchanger. Oddly, there are differences in industry definitions of approach what-compared-to-what depends on heat exchanger style but the basic concept is the same. An infinitely large heat exchanger or infinite contact time will produce an approach temperature of zero, but for practical purposes there is always some differential. The value of approach will vary by heat exchanger type, fluid, and sizing. Approaches for liquid heat exchangers are generally lower than for those using air and gas. Turbulent flow (scrubbing at the boundary layer) and higher Reynolds numbers reduce approach; greater surface area or part-load operation reduces approach; longer contact time reduces approach, and fouling increases approach. Examples of using approach to calculate lift: 45F chilled water with 5F approach, and 80F condenser water with 10F approach à (80+10) (45-5) = 50F lift. 55F supply air with a 15F approach, condensing at 95F with a 20F approach à (95+20) (55-15) = 75F lift. (Note the lift advantage using water cooling vs. air cooling for the same 40F heat exchanger leaving fluid temperature).

3 9 Approach values can be derived from manufacturer s data or measured in the field, but will vary depending upon load. This is because heat exchangers become effectively oversized as load decreases. For example, one chiller was found to have a condenser approach of 10F at full load, 7F at 75% load and 4F at 50% load. Coefficient of Performance (COP) is the ratio of output to input energy or power and is unitless since both terms are the same; e.g., Btu output/btu input, and Btus cancel. Applied to refrigeration systems, COP is the ratio of refrigeration output to power input (in same units). This can be measured with the actual machine in service, and can also be derived from the cycle states of a Mollier (p-h) diagram using COP = (h1-h4)/(h2-h1). Compressor power can be derived from COP using kw/ton=3.517/cop. State 1-2 Vapor compression State 2-3 Condenser State 3-4 Liquid expansion State 4-1 Refrigeration effect Chart A compares theoretical results to values of % power reduction predicted by the conventional rule of thumb. The theoretical values consistently fall within the range of 1% and 1.5% power reduction per degree F change. The uncertainty error band becomes larger with larger changes. Estimates of 1.5% per degree F will likely overstate savings. Chart B incorporates baseline lift. The baseline lift is the range of high-to-low refrigeration temperature boundaries, approach included, before a change is made. By first calculating the baseline lift, a single value of % power reduction per degree F is found on the chart. Example: A water cooled chiller system is found making 38F chilled water with 75F condenser water. An efficiency measure would raise water temperature by 7F to 45F. An approach temperature of 3F is assumed for the evaporator and 5F for the condenser. Baseline lift, in temperature terms, is then (75+5) (38-3) = 45F. From Chart B, power reduction would be ~1.1 percent per degree F, or 7.7% power reduction. Chart C shows refrigeration cycle efficiency for equal values of lift at different temperatures not a flat line. Additional error is introduced

4 10 Energy Engineering Vol. 112, No when the rule of thumb is applied equally to measures affecting the low and high temperature regions of the cycle. Refrigeration efficiency is affected somewhat more at lower pressures and will respond differently to a lift change the explanation is beyond the scope of this article but part of it is visible in non-parallel lines shown in Chart C. SOURCES OF ERROR Not incorporating baseline lift. This is the dilemma of working in percentages and is a watch-out for any/all rules of thumb using percentages. For lift-related power, the same one degree F change will make a 10% impact for an original lift of 10F, but only a 1% impact if the original lift is 100F. Not incorporating heat exchanger approach will understate lift. 55F supply air and 95F ambient temperature is incorrectly identified as 40F lift. If both air-cooled heat exchangers have a 20F approach, the true lift would be (95+20) (55-20) = 80F lift. For this example, the error in savings would be ~14% (From Chart B, 1.08% reduction vs. 1.22%). Refrigerant used the Mollier (p-h) diagrams used were for R-717 (ammonia). Different working fluids have different properties. Range of load. At part load, some things get better, some get worse. Seasonally, it s a mix. Machinery type. This affects actual energy use at the meter. Machine losses are not considered in a Mollier (p-h) diagram. SUMMARY The refrigeration rule of thumb 1-1.5% power reduction per degree F of change is useful if taken with a grain of salt. The range given is a catch-all for a number of variables. The most influential variable is lift which is responsible for the majority of refrigeration energy input. Actual machine test data is best for evaluating different conditions. Direct use of the 1-1.5% rule of thumb can overstate savings, so adhering to 1% is suggested. By incorporating baseline lift, a single value of percent

5 11 power change per degree F is available. Other than actual machine testing, each method has unknowns. Experience and good judgment are needed to determine if savings de-rates are appropriate when using any rule of thumb. Chart A Chart A: Rule of Thumb Error Band % Compressor Power Reduction vs. degree F Lift Reduction (No Regard for Baseline Lift) Dotted lines shows actual vs. estimated savings using the 1-1.5% rule of thumb without regard to baseline lift. Uncertainty increases with the size of the change in lift. Mollier (p-h) diagram prediction for power based on COP = (h1-h4) / (h2-h1) Rule of thumb prediction = degrees F change in lift * assumed % per degree F (1% or 1.5%) % power reduction = (P1-P2) / P1

6 12 Energy Engineering Vol. 112, No Chart B Chart B: Modified Rule of Thumb for Single Value of % Compressor Power Reduction power degree F, by Referencing Baseline Lift By first determining baseline lift, the % power per degree F value can be taken directly. Baseline lift = T high T low temperature boundaries of the refrigeration system, including approach values. Mollier (p-h) diagram prediction for power based on COP = (h1-h4) / (h2-h1) % power reduction = (P1-P2) / P1

7 13 Chart C Chart C: Coefficient of Performance vs. Median Cycle Temperature Refrigeration cycle power requirements are more sensitive on the low temperature side than the high temperature side. Measures affecting the low side will have greater benefit, per degree F change, than on the high side. Median temperature = [(Condenser HX fluid + approach) + (Evaporator HX fluid approach)] / 2 (COP) = (h1-h4) / (h2-h1)