Invariant factors as limit of singular values of a matrix

The paper concerns a result in linear algebra motivated by ideas from tropical geometry. Let $A(t)$ be an $n \times n$ matrix whose entries are Laurent series in $t$. We show that, as $t \to 0$, logarithms of singular values of $A(t)$ approach the invariant factors of $A(t)$. This leads us to suggest logarithms of singular values of an $n \times n$ complex matrix as an analogue of the logarithm map on $(\mathbb{C}^*)^n$ for the matrix group $GL(n, \mathbb{C})$.Comment: 6 page

Experimental study of R450A drop-in performance in an R134a small capacity refrigeration unit

The Kigali amendment to the Montreal Protocol has highlighted the hydrofluorocarbons (HFCs) phase out as a priority to reduce the future global mean temperature increase. R134a is the most abundant HFC in the atmosphere and therefore it must be substituted using environmentally benign alternatives. In the short term, blends of HFCs and hydrofluoroolefins can replace R134a. This paper experimentally evaluates R450A (GWP of 547), a non-flammable mixture of R1234ze(E) and R134a, in an R134a small capacity refrigeration system. The controlled experimental conditions cover evaporating temperatures from −15 to 12.5 °C and condensing temperature of 25, 30 and 35 °C (36 tests in total for each refrigerant). The experimental results showed that with only a thermostatic expansion valve adjustment the average R450A cooling capacity and COP are 9.9% and 2.9% lower than those measured using R134a. Besides, the observed compressor discharge temperature values of R450A are not greater than that of R134a

Recent investigations in HFCs substitution with lower GWP synthetic alternatives: Focus on energetic performance and environmental impact

egulation (EU) No. 517/2014 (F-gas Regulation) controls the use of HFCs in several applications. This paper reviews the recent investigations performed because of F-gas Regulation, with focus on lower global warming potential (GWP) synthetic alternatives. The GWP limit and the date of prohibition have an influence on the studies found for each application. The major relevance of the studies has been observed on mobile air conditioners for pure hydrofluoroolefins (HFOs), possibly caused by the earlier control. Additionally, a great number of studies have been found for stationary refrigeration systems using several mixtures and residential air conditioners using R32. An important number of articles investigate synthetic alternatives for domestic refrigerators given the flammability barriers for hydrocarbons in some countries. Despite higher GWP allowance on cascade supermarket systems, few articles are available on this topic. Given the extent of the current studies and the rate of new refrigerant developments, an increase in studies using the new synthetic mixture is expected in the coming year

R450A and R513A as lower GWP mixtures for high ambient temperature countries: Experimental comparison with R134a

In recognition of the impact of the refrigeration sector on climate change, global commitments are achieved to replace hydrofluorocarbon substances with more planet-friendly alternatives. In this regard, countries with high ambient temperatures (HAT) face additional problems in identifying suitable alternatives due to the impact of such temperatures on energy performance in vapor compression systems. This paper presents an experimental analysis using R134a and two lower global warming potential (GWP) mixtures in a small capacity vapor compression refrigeration system for HAT environments. The range of evaporating and condensing conditions was selected to simulate a refrigeration system working at HAT conditions. The experimental operating results show that although R450A values are acceptable, R513A shows better adaptation to the refrigeration system in terms of pressure ratio, discharge temperature, and mass flow rate. Then, attending to experimental energetic results, R450A energy performance (quantified by COP) and cooling capacity are lower than R513A and R134a. TEWI analysis of a small refrigeration unit shows CO2 equivalent emission saving when using R450A in the different condensation conditions. However, taking into account the variation of cooling capacity, R513A system results in the lowest TEWI when normalizing per unit of delivered cooling capacity

Retrofit of lower GWP alternative R449A into an existing R404A indirect supermarket refrigeration system

R404A is going to be phased out from most of the commercial refrigeration systems due to its high GWP value of 3943. R449A (GWP of 1282) has been proposed to replace R404A with only minor system modifications in supermarkets. This paper presents the measurements of a light retrofit replacement of R404A using R449A in a medium temperature indirect refrigeration system (secondary fluid temperature at the evaporator outlet between −9 and −4 °C). It has been demonstrated that with a slight expansion device adjustment and 4% increase of refrigerant charge, R449A can be used in this refrigeration system designed for R404A because of its suitable thermodynamic properties and acceptable maximum discharge temperature. At a secondary fluid temperature at condenser inlet of 30 °C, the COP of R449A nearly matches that of R404A (both were between 1.9 and 2.2), despite having approximately 13% lower cooling capacity. As a conclusion, attending to the GWP reduction and similar energy performance, it was demonstrated using the TEWI methodology that the use of the recently developed refrigerant R449A in these applications can reduce the total CO2 equivalent emissions of an indirect supermarket refrigeration system designed for R404A refrigerant.This research is funded by the Swedish Refrigeration Cooperation Foundation, KYS (project “Utvärdering av en potentiell R404A-ersättare – fältprov med R449A”) and Swedish Energy Agency (EFFSYS Expand P08) with the support of Bosch Thermoteknik AB, Danfoss Värmepumpar AB, Nibe AB, Nowab, Energi & Kylanalys AB and Svenska Kyltekniska Föreningen

Refrigerant R32 as lower GWP working fluid in residential air conditioning systems in Europe and the USA

Because air conditioning and heat pump systems contribute greatly to greenhouse gas emissions, equipment with both lower global warming potential (GWP) working fluids and a higher level of performance should be used. R32 (difluoromethane) has been proposed to substitute R410A, particularly in residential air conditioning (RAC) systems. This study collected the most relevant and recent researches into R32 as a refrigerant so as to assess its viability in RAC systems in both Europe and the USA, as compared to R410A and other lower GWP RAC alternatives. The R32 value of GWP is 677, which is below the F-gas regulation limit in RAC equipment (750). According to ASHRAE standard 34, R32 is less flammable than hydrocarbons, and the amount of charge permitted for R32 is above the necessary level in RAC equipment. It can be concluded that R32 has significantly good heat transfer characteristics and a level of performance that make it acceptable at low condensing temperatures, thereby avoiding overly high compressor discharge temperatures. Its performance is very similar to that of R410A across the entire operating range, and it is therefore believed that R32 will be utilized in RAC systems in the remaining countries that prioritize lower GWP fluids but are less strict in their security regulations. To replace R410A under extreme conditions, some system modifications can be conducted, or R32 mixtures with hydrofluoroolefins (HFOs) can be used. Such mixtures achieve a lower performance than R32, but are acceptable replacements when considering their lower GWP compared to that of R32, and similar level of flammability. Finally, other (R32-based) alternative mixtures have also been developed and their behaviours studied under a wide range of operating conditions.The authors thankfully acknowledge the Spanish Ministry of Education, Culture, and Sport for supporting this work through “Becas y Contratos de Formación de Profesorado Universitario del Programa Nacional de Formación de Recursos Humanos de Investigación del ejercicio 2012 (Grant number FPU12/02841)” and “Ayudas complementarias para beneficiarios de ayudas (FPU): Estancias Breves. Convocatoria 2015 (Grant number EST15/00154)”. The authors are also grateful to the Swedish Energy Agency for supporting this study under the “EFFSYS EXPAND P08” research program

Using ANNs to approach to the energy performance for a small refrigeration system working with R134a and two alternative lower GWP mixtures

In this paper, an artificial neural network application to model a small refrigeration system is presented. The main objective of this study is an energy comparison of three refrigerants: R134a, R450A and R513A. The application of the artificial neural network was designed to model individually three typical energy parameters: the cooling capacity, the power consumption and the coefficient of performance, as a function of the evaporating temperature and the condensing temperature. Each model was validated using a technique called cross-validation, producing minimum relative errors of for the cooling capacity and the coefficient of performance, while 0.05 for the power consumption. Based on the appropriate validation results, computer simulations were performed to build 3D color surfaces. After inspecting these 3D color surfaces, it was concluded that R450A presented a slightly lower cooling capacity than R134a, actually a 10% reduction in the cooling capacity was estimated. Similar results were observed for the power consumption, that is, R450A had about 10% less power consumption than the other two refrigerants. On the other hand, it was observed that R134a and R513A presented very similar energy behaviors. With respect the COP, it was concluded that all three refrigerants showed a very similar behavior. After the analysis performed with the artificial neural networks and the use of 3D surface color, it was concluded that R450A and R513A are appropriate refrigerants to replace R134a in the short term in applications at medium evaporating temperature

Experimental assessment of R134a and its lower GWP alternative R513A

Lower GWP refrigerants are essential to mitigate the impact of refrigeration systems on climate change. HFO/HFC mixtures are currently considered to replace HFCs in refrigeration and air conditioning systems. The aim of this paper is to present the main operating and performance differences between R513A (GWP of 573) and R134a (GWP of 1300), the most used refrigerants for medium evaporation temperature refrigeration systems and mobile air conditioners. To perform the experimental comparison, 36 tests are carried out with each refrigerant at evaporating temperatures between −15 and 12.5°C and condensing temperatures between 25 and 35°C. The conclusion of the experimental comparison is that R513A can substitute R134a with only a thermostatic expansion valve adjustment, achieving better performance and higher cooling capacity. The discharge temperature of R513A is always lower than that of R134a.The authors thankfully acknowledge the Ministry of Education, Culture and Sports, Spain for supporting this work through “Becas y Contratos de Formación de Profesorado Universitario del Programa Nacional de Formación de Recursos Humanos de Investigación del ejercicio 2012 (Grant number FPU12/02841)” and “Ayudas complementarias para beneficiarios de ayudas (FPU): Estancias Breves. Convocatoria 2015 (Grant number EST15/00154)”. This research is also done within the Effsys Expand P08 project that is funded by the Swedish Refrigeration Cooperation Foundation, KYS and Swedish Energy Agency with the support of Bosch Thermoteknik AB, Danfoss Värmepumpar AB, Nibe AB, Nowab, Svensk Energi & Kylanalys AB and Svenska Kyltekniska Föreningen

Design of an environmentally friendly refrigeration laboratory based on cooling capacity calculation for graduate students

Lower global warming potential (GWP) refrigerants must be used in refrigeration education to integrate the environmentally responsible engineering principles in class. However, most of the refrigeration educational laboratories are still using hydrofluorocarbons (HFCs) as working fluids, which are considered as greenhouse gases. This paper shows the procedure to adapt the new refrigerant R513A in a refrigeration system used for a cooling capacity educational laboratory. First, the paper describes the organization of the laboratory session, and the characteristics of the different methods of cooling capacity calculation taught to the master’s degree students. Then, the benefits of including new sensors in the experimental setup to obtain more accurate results are explained. Later, accurate new graphics and an equation to calculate the R513A cooling capacity are provided. Finally, the educational aspects worked with the students in this session, and each cooling capacity method are assessed. The procedure explained in this paper can be used as a guide for introducing lower GWP refrigerants in similar educational refrigeration laboratories