energies Communication Measurement Uncertainty Estimation for Laser Doppler Anemometer Karolina Weremijewicz 1 and Andrzej Gajewski 2,* 1 Students’ Scientific Society “Heat Engineer”, Faculty of Civil Engineering and Environmental Sciences, Bialystok University of Technology, Wiejska Street 45 A, 15-351 Białystok, Poland; [email protected] 2 Department of HVAC Engineering, Faculty of Civil Engineering and Environmental Sciences, Bialystok University of Technology, Wiejska Street 45 A, 15-351 Białystok, Poland * Correspondence: [email protected]; Tel.: +48-797-995-923 Abstract: Twenty percent of global electricity supplied to the buildings is used for preventing air temperature increase; its consumption for this prevention will triple by 2050 up to China’s present needs. Heat removed from the thermal power plants may drive cold generation in the absorption devices where mass and heat transfer are two-phase phenomena; hence liquid film break-up into the rivulets is extensively investigated, which needs knowledge of the velocity profiles. Laminar flow in a pipe is used in the preliminary study, velocity profile of developed flow is used as a benchmark. The study account writes the applied apparatus with their calibration procedure, and the uncertainty estimation algorithm. The calibration regression line with the slope close to one and a high Pearson’s coefficient value is the final outcome. Therefore, the apparatus may be applied in the principal research. Keywords: liquid film break down; rivulet; velocity profile; laminar flow; surface tension Citation: Weremijewicz, K.; Gajewski, A. Measurement Uncertainty Estimation for Laser Doppler Anemometer. Energies 2021, 1. Introduction 14, 3847. https://doi.org/10.3390/ Crisis in cold generation approaches the world’s economy, for the air conditioners and en14133847 electric fans working against air temperature increase need nearly 20% of the total electrical energy used in buildings in the world. Electricity demands for these purposes is forecasted Academic Editor: Adrian Ilinca to triple by 2050, which would equal China’s present usage [1]. These demands reach the winter and summer peaks. Figure1 shows the former in December and January and the Received: 26 May 2021 latter in July and August; these seasonal peaks concern total energy production and its part Accepted: 23 June 2021 generated in thermal power plants, from fossil fuels combustion, or radioactive decay [2]. Published: 25 June 2021 Thermal power plants, in accordance with the second law of thermodynamics, need to remove heat to a heat sink which can be either surface water or a district heating system. Publisher’s Note: MDPI stays neutral However, in summer time, these systems supply heat only for generating domestic hot with regard to jurisdictional claims in water, which may be insufficient; this insufficiency might be overcome with cold produc- published maps and institutional affil- iations. tion, in the absorption refrigeration systems, from the removed heat temperatures of at least 80 ◦C[3]. In other words, the absorption refrigeration system might utilize heat that is removed from the thermal power plant during electricity generation. Absorption refrigeration systems might alternate from the traditional ones if they are equipped with compact and high-performance heat and mass exchangers [4]. A low usage of the ab- Copyright: © 2021 by the authors. sorption refrigeration systems stems from high ratio between the volume and the cooling Licensee MDPI, Basel, Switzerland. capacity [5]. For this reason, they are also experimentally studied [6,7]. An absorption This article is an open access article refrigerator uses two fluids, which change phases, and concentration flowing through the distributed under the terms and conditions of the Creative Commons absorber, generator, evaporator, and condenser [8,9]. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Energies 2021, 14, 3847. https://doi.org/10.3390/en14133847 https://www.mdpi.com/journal/energies Energies 2021, 14, 3847 2 of 11 Energies 2021, 14, 3847 2 of 11 1800 1600 1400 1200 1000 800 600 400 Electrical energy production[TWh] 200 0 Thermal power plants Total production Figure 1. A report of International Energy Agency [2] into monthly electricity production. Figure 1. A report of International Energy Agency [2] into monthly electricity production. The change of phase or concentration occurs due to heat and mass transfer in thin liquidThe layers, change which of phase flow or down concentration a solid surface occurs (cf. due Figure to heat 3 in and [4]). mass Firstly, transfer these in layers thin liquidwere investigatedlayers, which because flow down of the a burnoutsolid surface in the (cf. steam Figure boilers 3 in or[4]). distillatory Firstly, these equipment. layers wereHartley investigated and Murgatroyd because [10of ]the investigated burnout in liquid the steam film breakboilers away or distillatory into the rivulets equipment. using Hartleytwo approaches: and Murgatroyd the first [10] one investigated is mechanical liquid equilibrium film break in away the highest into the point rivulets of the using dry twopatch, approaches: which results the first in the one force is mechanical balance in thisequilibrium point named in the stagnation highest point point; of the the other dry patch,method which employs results energy in the minimization, force balance assuming in this point the sum named of kinetic stagnation energy point; across the a other plane methodand the employs surface energy energy approaches minimization, minimum. assuming Bankoff the sum [11] balancedof kineticflow energy rates across and energiesa plane andof the the film surface and energy rivulets approaches at the critical minimum. film thickness; Bankoff it[11] was balanced assumed flow that rates a segment and ener- of giescircle of asthe a film cross-section and rivulets of theat the rivulet, critical and film the thickness; velocity it profiles was assumed in film, that and a in segment each slice of circleof the as rivulet, a cross-section are the same. of the Mikielewicz rivulet, and andthe velocity Moszynski profiles [12,13 in] appliedfilm, and minimization in each slice of of theenergy rivulet, extended are the bysame. surface Mikielewicz energy of and the Mo solid-gasszynski interface.[12,13] applied A common minimization feature of of en- the ergyinvestigations extended by presented surface energy above, inof the this soli paragraph,d-gas interface. is assumed A common laminar feature velocity of the profile in- vestigationsderived by Nusseltpresented (1916) above, (cf. in Madejski this paragraph, [14]); additionally, is assumed Hartley laminar and velocity Murgatroyd profile [de-10] rivedassumed by Nusselt a linear (1916) laminar (cf. profile Madejski for film, [14]); motivated additionally, by surface Hartley shear and only Murgatroyd or a von Karman[10] as- sumeduniversal a linear velocity laminar profile profile for turbulent for film, flow.motivated by surface shear only or a von Karman universalEl-Genk velocity and Saberprofile [15 for] continued turbulent researchflow. into film breakdown, applying the energetic approach;El-Genk their and analysis Saber [15] includes continued a two-dimensional research into film velocity breakdown, profile applying solved using the ener- Ritz geticmethod. approach; Perazzo their and analysis Gratton [includes16] derived a two-dimensional another two-dimensional velocity velocityprofile profile,solved whichusing Ritzis solved method. in closed Perazzo form, and forGratton both the[16] rivulet derived and another film, flowingtwo-dimensional along a vertical velocity plate; profile, the whichcontact is anglesolved was in closed assumed form, to be for either both perpendicularthe rivulet and to film, the flowing plate for along the rivulet a vertical or parallel plate; thefor contact the film. angle While was Tanasijczuk assumed etto al.be [ 17either] derived perpendicular a two-dimensional to the plate velocity for the profile rivulet for or a parallelrivulet pendingfor the film. from While a horizontal Tanasijczuk plate. et al. [17] derived a two-dimensional velocity pro- file forAtaki a rivulet and pending Bart [18] from applied a horizontal a velocity plate. profile for a gravity driven rivulet along an inclined plate in the analysis of their experiments. Another assumption was the static contact angle value 56◦. Energies 2021, 14, 3847 3 of 11 Charogiannis et al. [19] experimentally determined laminar velocity profile for a gravity driven rivulet along an inclined plate for a Reynolds number less than 5.9 and Kapitza number equal to 1.4 following its definition: s Ka = (1) r(g sin an4)1/3 where s is surface tension, g is gravitational acceleration, a is an inclination of film to the horizon, and n is kinematic viscosity; they also obtain a profile for wavy flow forced with frequencies 2 and 6 Hz, when the Reynolds number was about 5.2. The very familiar configurations of the absorbers, applied in the absorption cooling systems, consists of the horizontal tubes, which are covered with falling liquid film; this film is an absorbent solution that, flowing across the tubes, absorbs the vapor of a re- frigerant [4]. The flow divides into three regimes: falling-film flowing around the tubes, droplet-formation flow that occurs on, and in, the vicinity of the lowest tube generatrix, and the droplet-fall flow that appears between two tubes; these regimes exist for LiBr/water [20] and aqueous alkaline nitrate solution [4]. When the absorbent