Dimensionless Coefficient Research Articles

Численное моделирование и верификация точечного лазерного нагрева нержавеющей стали AISI 316L

The paper considers the laser spot heating process in the AISI 316L stainless steel sample and its three-dimensional mathematical model. It proposes an option in this process numerical simulation by introducing a laser radiation source specified as the super Gaussian distribution with refined and experimentally selected dimensionless coefficients. Boundary conditions of convection and radiative heat transfer, as well as the Marangoni convection on the melting pool free surface, were taken into account. Metal phase transition from solid to the liquid aggregation state was realized within the solidus and liquidus temperature ranges due to effective functions of heat capacity and viscosity. Geometrical characteristics of the melt pools obtained during a number of practical experiments were compared with the data determined by numerical solution. It is shown that the results in both the options quantitatively and qualitatively coincide with the insignificant error. Conclusions are made on the error in the numerical solution.

Kinetic drop friction

Liquid drops sliding on tilted surfaces is an everyday phenomenon and is important for many industrial applications. Still, it is impossible to predict the drop’s sliding velocity. To make a step forward in quantitative understanding, we measured the velocity (U), contact width (w), contact length (L), advancing ({theta }_{{{{{{rm{a}}}}}}}), and receding contact angle ({theta }_{{{{{{rm{r}}}}}}}) of liquid drops sliding down inclined flat surfaces made of different materials. We find the friction force acting on sliding drops of polar and non-polar liquids with viscosities ({eta }) ranging from 10−3 to 1 {{{{{rm{Pa}}}}}}cdot {{{{{rm{s}}}}}} can empirically be described by {F}_{{{{{{rm{f}}}}}}}(U)={F}_{0}+beta weta U for a velocity range up to 0.7 ms−1. The dimensionless friction coefficient (beta ) defined here varies from 20 to 200. It is a material parameter, specific for a liquid/surface combination. While static wetting is fully described by {theta }_{{{{{{rm{a}}}}}}} and {theta }_{{{{{{rm{r}}}}}}}, for dynamic wetting the friction coefficient is additionally necessary.

Redefined interface error, 2D verification and validation for pure solid-gallium phase change modeling by enthalpy-porosity methodology

For simulating phase change process of pure solid gallium, previously published literature contains some key problems, including the inappropriate definition & computation for interface errors, and the unsatisfactory numerical verifications & validations. Herein, the 2D verifications and 2D validations for the enthalpy-porosity modeling of pure gallium melting starting from a vertical end wall have been reported comprehensively. The well-known and classic experimental data presented in literature are used to verify and validate the model. The groundbreaking contributions in this work are that: i) The definition and computational method of the interface-position errors between the numerical and experimental results are revisited and proven carefully; ii) The numerical schemes as well as major parameters of 2D modeling gallium melting are selected with overall interface error <9%. However, these schemes and parameters are not appropriate for the solidification modeling of gallium due to the irregular and non-reproducible interface shapes caused by highly anisotropic properties of solid crystal gallium as experimentally reported in literature; iii) The 2D validations of enthalpy-porosity modeling of gallium melting are investigated in detail, and the maximum interface error is within the limits of ±12%. Moreover, the simulated liquid volume fractions and dimensionless heat transfer coefficients are well correlated in terms of related criteria parameters, and they are compared with correlations available in literature. It is concluded that to solidly validate the modeling of pure metal melting, both the global parameters (e.g., volume-averaged liquid fraction) and the local parameters (e.g., interface position) need to be considered together.

Aerodynamic Investigation on the Artefact “Bird of Saqqara”

Abstract Lost, technical knowledge of ancient cultures is being rediscovered in modern times during archaeological excavations. A presumed example of the innovative power of ancient cultures is the artefact “Bird of Saqqara”. In the context of this paper, the aerodynamic characteristics of the artefact are to be determined by a computational fluid simulation, in order to be able to make a statement about the actual flight suitability and to examine the theses of the pre-astronautics critically. Based on a 3D scan, a CAD model of the artefact is created and then a numerical flow simulation is performed. By varying the angle of attack, the dimensionless coefficients can be represented in corresponding polars. The results show that the artefact has a low maximum glide ratio and thus the glide properties are not sufficient for use as a handglider. The centre of gravity of the artefact is located at the trailing edge of the wing and behind the neutral point. The resulting longitudinal stability does not meet modern specifications. Asymmetric lift distribution in the spanwise direction results in uncontrolled roll. Consequently, the artefact cannot fly a straight path. Within the scope of this work, the connection between the “Bird of Saqqara” and an alleged knowledge of aerodynamics in ancient Egypt could not be confirmed.

Residence time distribution of ultrafine aerosol particles in a tube with transient and parabolic laminar flow

This paper presents a theoretical investigation concerning the residence time distribution (RTD) of ultrafine monodisperse aerosol particles flowing in a circular tube in laminar flow regime. If a fully developed, parabolic flow (PF) velocity profile is assumed for the whole tube length, the convection-diffusion process undergone by the aerosol particles can be described by means of two parameters, the dimensionless particle diffusion coefficient D and the tube aspect ratio a (radius/length). An additional parameter, the Reynolds number Re, must be taken into consideration when the flow develops starting from a given velocity profile at the tube entrance, which we have assumed to be a uniform (plug) flow. The latter situation is referred to as transient flow (TF). The RTD has been determined using two different variations of a Monte Carlo (MC) technique to simulate the particle trajectory within the tube. The difference between the two MC methods is the assumed distribution of Brownian random displacements of the particles; in both cases the distribution had zero mean and variance 2DΔt, but the distribution was uniform in one method and normal in the other. The simulation results obtained with the two methods were almost coincident. In either PF or TF, even for relatively small values of D the aerosol RTD is quite different from that of the fluid where the particles are suspended. In particular, the dimensionless mean particle residence time, which initially decreases with D, soon attains an asymptotic value of 0.65 for D ≥ 0.3 (the mean residence time of the fluid is 1) in PF; a similar asymptotic value is attained for TF but in this case it depends on the particular combination of a and Re considered. The relative influence of axial diffusion on the RTD is insignificant unless the tube ratio a is of the order of 0.5 (tube with a length equal to its diameter).

Совершенствование проточной части десендеров циклонного типа с использованием мультифазного коэффициента относительной скорости движения дискретных частиц

In the oil producing wells with high content of mechanical impurities and free gas, efficiency of the electric centrifugal pump is increased by installing the cyclone-type desenders at its inlet. Desender protects the submersed pump from mechanical impurities entering it by separation and collecting them in a special container. At the same time, the problem of free gas bubbles enlargement is being solved to facilitate their separation into the annulus and thus reduce the free gas content at the pump inlet. Analysis was made of specifics of the formation fluid flow containing mechanical impurities and free gas in the flow path of a cyclone-type separator with the fixed screw. Expressions were derived to determine the dimensionless multiphase coefficient of the discrete particles relative separation rate and of the multiphase similarity criterion. They allow evaluating efficiency of the mechanical impurity separators and developing new highly efficient structures based on the previously created ones. Recommendations are provided for development of the new highly efficient structures.

Design of double-shoulder threaded joints of drilling string elements

Purpose. Development of a method for simulating the screwing torque/moment and researching the design of double-shoulder threaded joints while preserving their geometric parameters. Determination of the optimal length of the additional shoulder pin part for the developed drill collar (DC) of NC50, NC55 type of various standard sizes. Establishing the dependence between the pin part length of the additional shoulder and other geometric parameters of the double-shoulder joint of the DC for further use when developing other standard sizes of similar design threads. Methodology. The development of design and the method for simulating the screwing torque of double-shoulder threaded joints was carried out using the finite element method and parametric modeling. Finding. A method for simulating the screwing torque of threaded joints was proposed and developed, which made it possible to improve the model of their automated design. The optimal lengths of the pin part of the additional shoulder of the developed design of double-shoulder threads of the NC50, NC55 types were determined. For planning threaded joints of similar design with the above-mentioned types of threads, a dimensionless coefficient was derived and its value was calculated. A nomogram was built to determine the length of the joint additional shoulder pin part due to the value of this coefficient. Originality. The model of automated design for double-shoulder threaded joints of drill string parts has been improved. This model preserves their geometric parameters and enables modeling a wide range of standard sizes of similar joints. Practical value. The optimal geometric parameters of the developed structures of double-shoulder threaded joints of the drill string elements were determined. A nomogram was built to determine the length of the additional shoulder pin part of the joint by the value of the dimensionless coefficient.

Cross-Scale Seepage Characteristics of Fractured Horizontal Wells in Tight Gas Reservoirs.

Tight gas reservoirs are rich in microscale pores and fractures. The effect of microscale gas seepage in tight sandstone matrix on gas well productivity cannot be ignored. At present, the effect of microscale gas flow on the well testing model of fractured horizontal wells has not been systematically studied. In this paper, first, the coupling influence mechanism of "multicomponent gas effect-fracture geometry characteristics" is expounded, second, a seepage model coupling the flow in the fracture and the flow in the gas reservoir is established on the fracture wall surface, and third, an unsteady pressure analysis model for fractured horizontal wells in tight gas reservoirs is established. Results show that (a) when the microscale fracture is at a quite small level, the Knudsen diffusion plays a dominant role at a wide range of pressures; (b) the mass transfer rate of multicomponent shale gas through macrofractures increases with increasing CO2 fraction; (c) the unsteady flow process is divided into six stages in turn: microscale diffusion stage, linear flow stage in fractures, linear flow stage between fractures, early radial flow stage in gas reservoirs, linear flow stage in gas reservoirs, and late radial flow stage in gas reservoirs; and (d) with an increase of dimensionless bottom-hole storage coefficient, the second and third stages of flow are gradually covered up.

Rapid evaluation of lateral-torsional buckling of European standard I-section cantilevers

Lateral-torsional buckling (LTB) is the primary failure mode for thin-walled steel members where the cantilever beams experience nonuniform twisting and buckling about their weak axes. Much research exists in the literature, and modern codes have presented simple formulations for calculating of elastic LTB load of simply-supported beams. However, there are limited numbers of treatments for predicting of elastic LTB load of cantilevers, most of which are numerical, because as different from the simply supported beams, the LTB failure mode of the thin-walled cantilevers is much more complicated. The present study aims to develop a simplified equation for calculating the elastic LTB of the cantilevers with the European standard I-section. First, an analytical model considering first-order bending distribution, load height level, and monosymmetry property of the section has been introduced. Then, a simplified formula for cantilevers has been introduced utilizing the analytical model and two dimensionless coefficients called the slenderness and the load case parameters. The presented analytical solutions were verified with the finite element analysis (FEA), and the effects of slenderness and loading positions on the LTB behavior of cantilevers with European standard I-section have been investigated. It is found analytical solutions are quite compatible with FEA, and the proposed equation could be safely used for calculating the elastic LTB of the cantilevers.

Wake flow control of a square cylinder via distributed jets over the rear porous surface

An active control method was used to attenuate the unsteady vortex shedding in the wake of a square cylinder. Distributed jets were applied to the rear porous surface at a Reynolds number of 1.07 × 104. The strength of the jets was measured using the dimensionless jet momentum coefficient CQ. The dynamic mode decomposition, instantaneous vorticity evolution, and time-averaged characteristics, e.g., turbulent kinetic energy, streamlines, velocity profiles and Reynolds stress distributions of the wake flow field were used to analyze the control effects. The results suggest that with increasing CQ, two jet vortices gradually form near the rear cylinder wall and compete with the vortex shedding. Consequently, the vortex shedding pattern became nearly symmetrical, whereas the jet vortices remained asymmetrical. The vortex shedding process was pushed downstream. The fluctuations in the wake, particularly near cylindrical walls, were significantly suppressed. Thus, this scheme was successful, indicating potential for drag reduction and energy efficiency. Better control effects were associated with higher CQ in the present study.

Experimental Study and Numerical Analysis on Windage Power Loss Characteristics of Aviation Spiral Bevel Gear with Oil Injection Lubrication

With the increasing speed of aviation spiral bevel gears, the load-independent windage power losses caused by hydrodynamic have increasingly more influence on gear transmission efficiency. Firstly, a test rig for the windage power loss of spiral bevel gear under oil-jet lubrication is established, and on this basis, a method for measuring windage torque is proposed. Next, the interactive effects of different injection lubrication parameters on the windage power loss were studied by orthogonal experiment, and the formula for calculating the windage loss was obtained by fitting the experimental data. Then, the fluid distribution, velocity field and pressure field around the gear were analysed by using a computational fluid dynamics (CFD) numerical model, and the mechanical and energy characteristics of the gear windage power loss were obtained. Finally, the dimensionless processing of the windage moment was carried out, and the variation of the dimensionless windage moment coefficient with the rotational Reynolds number is obtained. The comparison between the dimensionless windage moment coefficient of experimental data and simulation results shows that the CFD values are in good agreement with the measured data. This study provides experimental and methodological guidance for the calculation of windage power loss and windage reduction design of aviation gear pair under oil injection lubrication.

The Effect of Biot Number on a Generalized Heat Conduction Solution

Abstract Analytical solutions for thermal conduction problems are extremely important, particularly for verification of numerical codes. Temperatures and heat fluxes can be calculated very precisely, normally to eight or ten significant figures, even in situations involving large temperature gradients. It can be convenient to have a general analytical solution for a transient conduction problem in rectangular coordinates. The general solution is based on the principle that the three primary types of boundary conditions (prescribed temperature, prescribed heat flux, and convective) can all be handled using convective boundary conditions. A large convection coefficient closely approximates a prescribed temperature boundary condition and a very low convection coefficient closely approximates an insulated boundary condition. Since a dimensionless solution is used in this research, the effect of various values of dimensionless convection coefficients, or Biot number values, are explored. An understandable concern with a general analytical solution is the effect of the choice of convection coefficients on the precision of the solution, since the primary motivation for using analytical solutions is the precision offered. An investigation is made in this study to determine the effects of the choices of large and small convection coefficients on the precision of the analytical solutions generated by the general convective formulation. Results are provided, in tabular and graphical form, to illustrate the effects of the choices of convection coefficients on the precision of the general analytical solution.

Effect of Sodium Carboxymethyl Cellulose on the Dynamic Wetting Characteristics of the Dust Suppression Droplet Impacting the Coal Surface.

The dynamic wetting behavior of droplets impacting the coal surface directly affects the efficient application of water-based dust suppression materials in coal-related industrial production. In this paper, ultrapure water, Tween-80, and sodium carboxymethyl cellulose are taken as the research objects. Using high-speed photography technology, the spreading, oscillation process, and splash morphology of many kinds of droplets during impacting the coal surface are captured. The effects of viscosity, surface tension, and impact velocity on dynamic wetting characteristics were studied. The results show that with the decrease of surface tension, the retraction and oscillation of droplets are significantly reduced. For the same kind of droplets, the greater the impact velocity, the faster the droplet spread, and the dimensionless maximum spreading coefficient (βmax) and dimensionless steady-state spreading coefficient (βe) of droplets are bigger. With the increase of velocity, the time for different kinds of droplets to reach the βmax increases. At the same impact velocity, βmax and βe of droplets (0.2% Tween-80 + 0.1% sodium carboxymethyl cellulose) are the largest, indicating that adding a small amount of sodium carboxymethyl cellulose can promote droplet spreading. With the increase of sodium carboxymethyl cellulose content, βmax and βe decreased gradually. The results have a great significance to the research, development, and scientific utilization of water-soluble polymer dust inhibitors.

Variation of temperature stratification during and after the human movement in displacement ventilation

Indoor temperature stratification can be weakened or even eliminated by human movement in displacement ventilation (DV). Thus far, the investigations of temperature destratification and stratification recovery during and after indoor human body movement are still very limited. This study investigated the influence of movement velocity (v), movement distance (A), human shoulder breadth (B), indoor heating load (P), and air change rate (ACH) on indoor temperature stratification. The concepts of the dimensionless degree of temperature destratification (φ), time required for temperature destratification (td), and time required for the recovery of temperature stratification (tr) were proposed to evaluate the robustness of such thermal stratification. The Richardson number (Ri) was a suitable dimensionless parameter for assessing the overall effects of influencing factors comprehensively. The results are as follows：(1) For the temperature destratification process during human movement, φ was linearly correlated with Ri number: φ = a × Ri. The symbol a was a dimensionless coefficient determined by boundary conditions. Likewise, there was a positive linear correlation between Ri and td. (2) For the recovery process of temperature stratification after the cessation of human movement, tr was only related to φ and indoor air change rate. tr had a negative relationship with φ when the ACH kept constant. Similarly, tr tended to a constant value when the ACH exceeded 6 h−1 with the constant φ value. This study can guide designers to strengthen the temperature stratified anti-disturbance performance by increasing the supply air volume and supply air temperature in the design stage of DV.

Models of the dynamics of maximal and optimal profits of a manufacturing enterprise implementing technological innovations

The published article presents new mathematical models that describe the dynamics of the development of manufacturing enterprises using innovative technologies. It is shown that the level of use of innovative technologies in an enterprise depends on dimensionless coefficients that describe the diffusion process of introducing technological innovations and affect the increase in output and cost reduction. The dependence of the enterprise's profit on the levels of production and transaction costs has been studied. It has been established that the formation of transaction costs arising from the search and processing of economic information, financing of negotiation procedures, conclusion of contracts with partners, protection of property rights and payment for the opportunistic behavior of employees and management of the enterprise, force the management of the enterprise to maximize not only the profit function, but also the target a transactional utility function that takes into account the redistribution of profits in the interests of the enterprise's management and for the implementation of socially-oriented programs. Dimensionless redistribution coefficients are calculated, which determine the size of the part of the profit that is used for non-production purposes. It is shown that in the presence of transaction costs, the limiting value of the enterprise's profit is not its maximum possible value, but its lower optimal value.

Исследование внутреннего трения натуральной и модифицированной прессованием древесины березы повислой (Betula pendula Roth)

A method is proposed for approximating of the internal friction of wood based on the Boltzmann superposition principle, which describes the complex viscoelastic behavior of the system by a linear combination of components. Prepared samples of natural and modified wood, sawn from the stem part of drooping birch (Betula pendula ROTH) trees growing in the Khlevensky Forestry (52.184130, 39.110463, ASL 157m), were exposed to radial and tangential directions with ultrasound (frequency 24.5 kHz, exposure 0 -20 minutes, step 5 minutes) and pulsed magnetic field (strength - 0.3 T, exposure 0-2 minutes, step 0.5 minutes). Next, the internal friction of the samples was studied on an experimental setup using the logarithmic damping decrement based on free-bending vibrations. The absolute values of the dimensionless viscosity coefficient κ included in the model as the main structural parameter for samples of natural and modified wood were obtained at a significance level of p=0.95: for moisture content from 4.3 to 15; for ultrasound 4.6 to 20; for a pulsed magnetic field from 3.6 to 7.7. The absolute values of the dimensionless scaling factors μ for natural and modified wood samples range from 1.92 to 3.91. The highest approximation value was achieved when testing natural wood samples of silver birch (Betula pendula ROTH): R2=0.98 for the radial direction, the influence of the humidity factor, and R2=0.85 for the tangential direction, the influence of the ultrasonic factor, as well as for a sample of modified wood brand "Destam" in the radial direction R2=0.96, the influence of the factor of the pulsed magnetic field.

ANALYSIS OF EFFICIENCY OF HORIZONTAL WELLS WITH MULTI-STAGE HYDRAULIC FRACTURING ON THE EXAMPLE OF KONDINSKOYE FIELD

In the structure of potential oil reserves in Western Siberia, the share of hard-to-recover reserves (HRR) is growing. At the same time, a significant share of these reserves is concentrated in low-permeability reservoirs. Horizontal wells using multi-stage hydraulic fracturing are the basis of technological solutions used for cost-effective development of low-permeability reservoirs by Russian oil and gas producers [1-4]. Due to the high efficiency of the subsea development systems with MSHF, oil production from such facilities exceeds oil production from traditional reservoirs and accounts for more than 60 % of the total oil production of the Company's fields [5]. The following characteristics are identified as the key parameters of the horizontal section, the number of hydraulic fractures, as well as the specific weight of the injected proppant at the frac stage. The decisions approved as part of the design documents for the development of facilities with TPP indicate a tendency to increase the length of the horizontal hole and the number of frac operations with a decrease in the specific mass of proppant on the port. The article examines the impact of these characteristics on the technological efficiency of wells. The purpose of the work is to assess the feasibility of increasing the technological complexity of HW with multi-stage hydraulic fracturing of the MSHF formation in the form of increasing the number of stages and length of the horizontal hole, as well as the specific mass of proppantane in the example of the AS10/1 Kondinskoye field development target. Within the framework of the study, three types of HW with MSHF were identified, the technological effectiveness of which was assessed in two ways. The first method consisted in comparing the magnitudes of the dimensionless productivity coefficient Jd (d. units) of three different types of wells with a horizontal end in relation to directional wells (FWS with frac) of the environment. Taking into account the similarity of the geological conditions of the neighboring wells, this method made it possible to assess how effectively the completion of the horizontal wells under study was completed. The multiplicity assessment methodology was developed by RN-BashNIPIneft LLC [6]. The second method was to compare the ratio of dimensionless productivity factor to the specific weight of proppant Jd/Mpr _ specific of the identified types of HW with multi-stage hydraulic fracturing (MSHR). This approach made it possible to take into account the effective thickness and permeability of the formation in the well drilling zone, as well as the weight distribution of the injected proppant. The results showed that if the length of the horizontal hole is constant, an increase in the number of frac stages while reducing the proppant weight on the port is impractical. Confirmation was also obtained based on statistical data that there is a relationship between the cumulative fluid withdrawal and the weight of the injected proppant. It has been established that drilling HW with multi-stage hydraulic fracturing of the (MSHF) formation of the most common type (1000 m, 10 stages) is not optimal for the study target: for a length of 1000 m, the maximum number of stages should be limited to 7–8 units per well. Further monitoring and analysis of production wells with horizontal termination is recommended to collect more statistical data and compare them over time.

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ РОБОТИ СУДНОВИХ СТЕРН ПРИ РІЗНИХ РЕЖИМАХ МАНЕВРУВАННЯ

The availability of adequate mathematical models of the ship propulsion system is essential for developing effective ship control systems, building high-quality simulators, and studying the ship’s maneuvering behavior. With the advancement of new computing and information technologies, the mathematical models of the ship propulsion system need to meet higher requirements and cover wider applications. This leads to the need for continuous improvement of mathematical models, especially those of non-inertial forces acting on the ship. This work investigates the influence of the ship’s curvilinear movement on the rudder performance. Mathematical models of the forces and moments acting on the rudder at different values of the local drift angle and the rudder angle are derived. The resultant force on the rudder is decomposed into components due to the rudder lift, drag, normal force, and tangential force. Expressions for the coefficients of rudder hydrodynamic quality, reverse quality, and normal force are obtained. The existing mathematical models of the rudder hydrodynamic coefficients are analyzed and their limitations and applicability are discussed. New mathematical models of the rudder lift and drag coefficients are proposed, which take into account the aspect ratio, relative thickness, and angle of attack of the rudder. The proposed models are validated by comparing them with experimental data for NACA series rudders. t is shown how the lift and drag of the rudder, as well as the components of the resulting force, change for the maximum possible range of changes in the local drift angle and the rudder angle, for different values of the rudder aspect ratio and relative thickness. Keywords: mathematical models, ship rudders, curvilinear movement, longitudinal and transverse components of forces, dimensionless hydrodynamic coefficients.

Numerical simulation of the dynamic wetting of coal dust by spray droplets

The dust particles generated during coal mining and processing are generally removed by spray dust reduction. The dynamic process via which spray droplets wet and wrap coal dust can directly affect the spray dust reduction efficiency. Here, we analyzed the contact wetting and wrapping process of dust particles by droplets under different particle size ratios and different initial droplet velocities. The results show that the larger the particle size ratio θ of the droplets and dust particles, the greater the variation in the dimensionless spreading coefficient. When the particle size ratio is more than 2, the droplets can completely wrap the coal dust particles. If the initial velocity is too small, the droplets will shrink and return to form a single sheet after coming into contact with the coal dust. With increasing velocity, the dimensionless spreading coefficient increases rapidly, and the coal dust is moistened and rapidly wrapped. By experimenting with various spray atomization characteristics, when the spray pressure is 6 MPa，the droplet size distribution in the spray field accounting for the highest proportion is 10 μm. Under the optimized parameters, the settling efficiency of respirable dust at each measuring point of mine return air duct reaches 86.2% on average.

Scaling relations for the geometry of wire-to-airfoil atmospheric ionic thrusters

This work presents a multiparameter experimental investigation on the effects of geometrical parameters on the performance of corona thrusters. A scaling model is presented in order to define physically consistent reference values and dimensionless coefficients that describe the main performance indicators. Airfoil collectors of different thickness and chord are tested in a parallel array configuration at different spacings, gaps and voltages. Direct thrust and electrical measurements are performed and used to determine the dimensionless coefficients. The results identify scaling relations and indicate that collectors with short chord and adequate thickness maximize, within the investigated parameter space, the performance parameters.