Experimental investigation of energy dissipation in the multi-cylinder Couette-Taylor system with independently rotating cylinders

Applied Energy 251 (2019) 113362

Contents lists available at ScienceDirect

Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Experimental investigation of energy dissipation in the multi-cylinder Couette-Taylor system with independently rotating cylinders

T

⁎

A.F. Serov, A.D. Nazarov , V.N. Mamonov, V.I. Terekhov Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia

H I GH L IG H T S

generator for direct conversion of the wind energy into heat is studied experimentally. • AThisnewgenerator is a multi-cylinder Taylor-Couette system with independently rotating cylinders. • The limits of dissipation are determined depending on the rotational speed and viscosity. • The high specific values ofenergy heat production of about 1 MW/m are obtained. • 3

A R T I C LE I N FO

A B S T R A C T

Keywords: Heat generator Rotating cylinders Couette-Taylor flows Conversion energy Wind Energy dissipation

The paper presents the results of an experimental study of the process of dissipative heating of fluid in a multicylinder Couette-Taylor system with independently rotating smooth cylinders. The task was set to solve the problem of direct conversion of wind energy into heat. The flow regimes and generation of heat energy at relatively low cylinder revolutions F < 5 Hz were studied. This range corresponds to velocities of cylinder rotation, achieved by the wind turbine at moderate wind load. Rotation of only one cylinder with the braked second cylinder and their counter-rotation are considered. The second regime can be successfully implemented in the schemes of kinetic wind energy conversion without additional mechanical transmissions and reduction gears from two wind wheels. Water-glycerine solutions in a wide range of changes in their viscosity were used as a working fluid. It is shown that the specific thermal power released in the heat generator can be about 1 MW/ m3, and this indicates the competitiveness of such devices among the designs of renewable energy resources.

1. Introduction

turbine activation depending on the braking moments are described in [2]. Some of the most popular methods for controlling wind generators in the regime of constant rotational velocities are compared in [3], where the ways to improve characteristics for each method are also presented. The wind turbines of a variable rotational speed are considered in [4] as a future trend in wind energy conversion in contrast to traditional fixed-speed wind turbines. The main technical parameters of existing designs of wind generators and effective methods of network management are summarized in [5]. At the same time, an important practical issue is the possibility of direct conversion of mechanical wind energy into heat. Exploratory studies of the most economical heat sources for fluid heating at utilization of mechanical energy led to the idea of using the dissipative properties of fluid, which characterize its ability to interact with both the surfaces of solids and internal fluid layers, to produce heat. The wind-driven heat generators can be effectively used not only as

The rising cost of energy resources used for heat supply issues a challenge for the consumers to find the cheaper heat sources. The task of cost-effective heating of fluid, used as a coolant in the systems of water heating and hot water supply, has been and remains relevant regardless of the way how these processes are implemented, heating system design, and heat sources. Wind power engineering is really important among the alternative energy sources, and a large number of works are devoted to the study of this problem. We note only some of the key reviews and monographs, which cover a wide range of problems of wind energy utilization. A detailed review of the modern state of the systems and technologies for wind energy conversion with a focus on existing efficient methods for controlling wind power generators is given in [1]. Wind resource assessments, site selection for the model, including the effects of wind

⁎

Corresponding author. E-mail address: [email protected] (A.D. Nazarov).

https://doi.org/10.1016/j.apenergy.2019.113362 Received 23 July 2018; Received in revised form 19 February 2019; Accepted 16 May 2019 Available online 03 June 2019 0306-2619/ © 2019 Published by Elsevier Ltd.

Applied Energy 251 (2019) 113362

A.F. Serov, et al.

Nomenclature

Rei

Reynolds number of inner cylinder for the case of single equivalent gap ReΣ Reynolds number for single equivalent gap, derived by relative rotational speed of the outer and inner cylinders and current viscosity of working fluid (ReΣ)20 Reynolds number for single equivalent gap, derived by relative rotational speed of the outer and inner cylinders and current viscosity of working fluid at temperature of 20 °C t, °C working fluid temperature V, m3 volume of working fluid in ring gaps of heat generator δef, m width of equivalent single gap ν, m2/s kinematic viscosity of working fluid ν20 kinematic viscosity of working fluid at temperature of 20 °C ΩUp, 1/s rotational speed of the upper “rotor” ΩD, 1/s rotational speed of the lower “rotor” ΩΣ, 1/s relative rotational speed of “rotors” Ωo, 1/s rotational speed of outer cylinder for equivalent single gap Ωi, 1/s rotational speed of inner cylinder for equivalent single gap

CM

coefficient of the moment of resistance to rotation for equivalent single gap ρ, kg/m3 working fluid density l, m dynamometer shoulder Lef, m height of equivalent single gap M0, N·m characteristic moment of resistance to cylinder rotation for equivalent single gap M, N·m moment of resistance to rotation of “rotors” at current working fluid temperature M20, N·m moment of resistance to rotation of “rotors” at working fluid temperature of 20 °C N, W power NV, W/m3 specific power Ref, m average radius of multicylinder system Ro, m radius of outer cylinder for single equivalent gap Ri, m radius of inner cylinder for single equivalent gap Reo Reynolds number of outer cylinder for the case of single equivalent gap

complicate the conditions of operation of such heat generators. The devices with rotating mixers of various designs have the same shortcomings. Therefore, the use of smooth surfaces for heat energy production in a multi-cylinder system is more preferable. The problem of the flow structure and heat transfer in an annular gap between rotating cylinders is a classic one and has a long history. A large number of experimental and theoretical studies of the flow between concentric rotating cylinders (circular Couette flow) have been published since the time of the first investigations of Mellock (1888, 1896) and Couette (1890). Some results of these studies can be found in reviews and monographs [23,24]. The flow between rotating cylinders is determined by the ratio between the Reynolds numbers of the outer and inner cylinders. This follows from the data of experimental work [25], where the maps of flow regimes are constructed for a relatively thin gap between the co- or counter-rotating cylinders. In particular, for the case of counter rotating cylinders, interesting to us, a hierarchy of regimes was established in [26] depending on the ratio of Reynolds numbers of the inner and outer cylinders. The number of characteristic regimes could be ten and, as the maps show, there is no symmetry relative to the line of the equal speeds of rotating cylinders. Depending on the speed of rotation, heat transfer between the cylinders and processes of viscous dissipation may have their intrinsic characteristics, and the area of phase diagram corresponding to this regime will determine their intensity. To date, the works in this field, studying the features of the flow field between the cylinders, have been intensively developed [27,28]. Heat transfer between the cylinders was studied to a much lesser extent, so there are still many unexplored issues in this problem. Thus, relations between the average Nusselt number and effective Reynolds number for the results of experimental and numerical studies were proposed and compared in [29] with those existing in literature. Optimization of the parameter of thermal efficiency in a rotating gap was studied in [30]. The influence of the end walls on heat transfer intensity was numerically studied in [31], where an accurate data benchmark was obtained for this case. The process of dissipative heating of fluid in the annular gap between the rotating cylinders is particularly poorly studied [32]. Therefore, calculation of the optimal heat generator with direct conversion of mechanical wind energy is of great interest. This work deals with experimental investigation of characteristics of the heat generator consisting of two multi-cylinder rotors, nested in each other and forming a system of annular channels. The rotors could rotate at different relative speeds both in one and opposite directions. However, the most attention will be paid to the counter-rotating

autonomous sources of hot water and heat for individual buildings and structures, but they can be integrated into a complex system that produces electricity from other sources and in technological processes using heat pumps. An efficient way of using heat energy in the district heating network is presented in [6]. Such systems can play the role of a thermal storage. The efficient energy-saving method proposed by the authors increases operational flexibility of the units of combined heat and power engineering for incorporating wind energy sources into an integrated heat and power system. A good addition to improving the efficiency of integrated systems is the method proposed by the authors of [7] for calculating the expected wind energy taking into account the spatial distribution in power systems. The issue of optimal integration of various energy sources into a single system is currently receiving much attention [8–10]. There are many approaches and solutions [11–14], which depend on the specific conditions of their use: for direct heating of buildings [9], using the paired schemes of wind generator and cooler [12], and also in systems with boilers, heat pumps [13] and other more complex scenarios for improving the efficiency of heat sources [14]. The use of mechanical power of wind rotors to drive liquid heat generators has a number of specific features. In contrast to existing electromechanical heat generators, whose rotational speed can be quite high, the wind rotors, even at high wind speeds, but in the absence of a reduction system, rotate ten times slower. In this regard, to convert the wind energy into heat efficiently without additional mechanical gearboxes, which increase the rotational speed, but complicate the design of generator, a non-cavitational rotor heat generator with effective dissipation of mechanical energy is required. In particular, it is interesting to consider a device, where heat is released in a volume of fluid located in a narrow annular gap between the coaxial cylinders rotating towards each other, as such a heat generator. Such a heating device, proposed in [15], can be implemented using two wind rotors rotating in opposite directions. The idea of using heat generators with multislot channels with a developed surface is not new. Such constructions, which are a set of flat rotating disks, are proposed in patents [16,17]. However, in this case, it is impossible to organize counter-rotation of disks, which would lead to doubling of the relative rotational speed without gears. The use of rough surfaces [18] or installation of various ribs [19], obstacles [20], axial flows [21] or depressions [22] causes the growth of the viscous dissipation effect in annular gaps. At the same time, these elements of roughness and use of dry friction between the cylinders lead to a strong increase in their starting torque, which can significantly 2

Applied Energy 251 (2019) 113362

A.F. Serov, et al.

Fig. 2a. Here, in Fig. 2b and c, the photographs of the internal structure of the multi-cylinder system and appearance of the heat generator in assembly are shown. The heat generator consists of two “rotors” of the same type, nested in the annular gaps of each other and forming a system of cylindrical annular channels. Each of the “rotors” has 7 cylinders with a height of 50 mm and thickness of 1.5 mm, which form a coaxial multi-cylinder system consisting of 13 circular cylindrical channels: 7 channels with the width of 2 mm and 6 channels with the width of 3.5 mm. The volume occupied by fluid in the annular channels of generator is 1.4 L. All elements of the heat generator are made of aluminum alloy and have a mass of about 12 kg. The speed and direction of rotation of the lower 3 and upper 2 electric drives could be changed independently of each other using control units 10, and the rotational speed was measured using two tachometers 7. The measurement scheme is based on is two magnetic relays and using a GDS-840S dual-channel digital oscilloscope - frequency meter. The uncertainty of measuring the rotational speed was determined by the frequency meter and ratio of the circumferential local size of magnetic relay to the circumference of its rotation, and it did not exceed 1%. The system is filled with a working viscous fluid with desired properties, which, during operation of the heat generator, is heated up due to dissipation of mechanical energy in the annular channels. In the experiments, four variations of the working fluid were used: distilled water and three types of water-glycerin solution. The viscosity of solution was determined by its temperature and concentration of water and glycerin. Thermophysical properties of the working fluids are presented in Table 1. The temperature dependence of viscosity and density of fluids was studied in a special series of experiments; the results of measurements were tabulated and used in experimental data processing. The kinematic viscosity was measured using a glass capillary viscometer VPZH-2 according to GOST 33-82 with a measurement uncertainty of ± 1.5%. The moment of resistance to the rotation of “rotors” was measured using a strain gauge sensor of an analog dynamometer 4. The moment was transmitted through a lever arm with length l = 129 mm. Analog data from the dynamometer were recorded by a PC-Lab2000SE digital oscilloscope in the regime of recording the moment of resistance force.

regime, as the most effective for the purposes of generating thermal energy. The work continues the research started by the authors of [33], where the primary results of a small series of experiments on dissipation of mechanical energy in a gap space are presented. The principal possibility of thermal energy production using the proposed heat generator design is demonstrated in this brief report. Detailed results of studying characteristics of such a heat generator will be discussed in this paper. 2. Experimental setup and measurement methods The layout of experimental setup and its photograph with the main unit of heat generator model are shown in Fig. 1. The experimental setup is a device, where two vertically arranged electric motors are connected to multi-cylinder heat generator 1, which allows the most efficient implementation of a heat generator with cocurrent or counter-rotation of a wind energy source [15]. Low-speed electric drives 2 and 3 with adjustable speed act as the wind energy sources. The setup is equipped with a system for measuring the input power, which allows the study of the influence of the working fluid parameters and angular velocity of “rotor” rotation on the resistance to their counter-rotation, depending on the structure of the working fluid flow in the gaps. All measurements are carried out in the range of rotational speed of full-scale wind-powered devices, whose rotational speed does not exceed 5 Hz. To reduce heat losses, heat generator 1 (see Fig. 1) was covered with a 50-mm thick layer of thermal insulation 6 made of foam plastic. During heat generator operation, the working fluid circulated in a closed loop through the heat exchanger of heat accumulator 13 (see Fig. 1) under the influence of the impeller pump, mounted on the rotor disk, and the flow rate of the working fluid was measured by flow meter 9 and its temperature at the inlet and outlet of the heat exchanger were measured by temperature sensors 5. The amount of generated heat energy was determined by the difference between the enthalpies of the working fluid at the inlet and outlet of the heat generator. A fragment of the heat generator draft and photographs of the “rotors” and heat generator block assembly are shown in Fig. 2. The scheme of a multiring heat generator and photographs of its main components are shown in Fig. 2. A fragment of the heat generator draft with indication of the main dimensions in mm is presented in

1 –heat generator; 2 –upper electric motor, 3 – lower electric motor, 4 – digital dynamometer; 5 – temperature sensors; 6 – heat insulation; 7 – tachometer sensor; 8 – microprocessor-based data processing unit; 9 – flow meter; 10 – control unit of electric drive revolution; 11 – electron unit of thermometer; 12 – suspension of upper motor; 13 – heat accumulator.

Fig. 1. Scheme and photographs of the heat generator model. 3

Applied Energy 251 (2019) 113362

A.F. Serov, et al.

Fig. 2. Construction scheme (a), photographs of working cylinders (b), and general view of the multislot heat generator (c).

heat energy released was calculated by a change in the temperature of heat-insulated multicylinder system, taking into account the mass and heat capacity of the working fluid and system components. According to the results of these measurements, the heat power, generated by the generator, was determined. The measured values of power, produced by the heat generator, are compared in Fig. 3 according to the results of measuring the moment of resistance to rotation and change in heat content. The experiments were carried out using working fluid No. 4 (see Table 1). The measurement results obtained by two independent methods coincide with a good degree of accuracy (∼3%), which indicates the smallness of both mechanical and thermal losses and possibility of using the method of measuring the power, produced by the heat generator, by measurements of the moment of resistance to rotation of “rotors”.

The dynamometer gauge was calibrated in a special series of experiments using the loads of various weights and with a known lever size. According to calculations, the total uncertainty of measuring the moment of force did not exceed 2%. Fluid temperature was measured by platinum temperature sensors 5 and recorded by a digital thermometer unit in the range of (20–60) °C with an error of 0.10 °C. The signals from the sensors were sent through a microprocessor unit for data collecting and preprocessing 8 to a computer for final processing and storage. The contribution of parasitic mechanical losses from the support bearings to the moment of resistance was measured during a special series of test experiments. These experiments were carried out in the regime of measuring the losses in bearings and force of air resistance in the annular gaps of the heat generator. Experiments have shown that in this case the value of the moment of resistance force in the range of operating frequencies of rotor rotation did not exceed ΔM < 0.1 [N·m], while the values of the moment recorded during the experiment are within (0.5–10) [N·m]. When processing the experimental results, the value of losses was subtracted from the measured value of the resistance moment. The heat power released by the generator was determined on the basis of the measured moment of resistance to “rotor” rotation and rotational speed, using formula:

3. Measurement results and discussion 3.1. Effect of cylinder rotational speed on the power of heat generator In this series of experiments, the characteristics of heat generator with different speeds independently rotating upper and lower rotors were studied using the most viscous fluid No. 4 as a working fluid (see Table 1). Thus, the potential capabilities of heat generators of this type were determined. The effect of rotational speed of the “rotors” on the moment of resistance to rotation is demonstrated in Fig. 4. Here, ΩUp and ΩD are the angular speeds of rotation of the upper and lower “rotors”, respectively. We should note that here are the data, obtained with a stationary lower rotor and with opposite rotation of rotors. It can be seen that with an increase in the relative rotational speed of the rotors, the moment of resistance and, accordingly, produced thermal power increase. In the range of relative speeds of rotor rotation, investigated in experiments, a change in the moment of resistance to rotation was changed by the factor of 18. It is difficult to use the experimental data shown in Fig. 4, obtained for specific geometry and dimensions of the system of annular channels,

(1)

N = M·ΩΣ ,

where, N [W] is power, M [N·m] is measured moment of resistance to rotation excluding the losses, ΩΣ [1/s] is relative angular rotational speed of “rotors”. Formula (1) is obtained for the condition of complete conversion of mechanical energy of rotation into heat. To test the validity of this ratio under the conditions of experiments, special measurements were carried out, when heat energy, released in the generator, was directly determined for a known period of time simultaneously with the measurement of the moment of resistance to rotation of “rotors”. During the experiment, there was no working fluid circulation in the heat exchanger circuit of the heat accumulator 13 (see Fig. 1). The amount of Table 1 Characteristics of working fluids. No.

Concentration, %

Temperature, t, °C

Kinematic viscosity, ν, m2/s

Density ρ, kg/m3

1 2 3 4

Water Water Water Water

20 30 20 20

1.01·10−6 2.7·10−6 5.2·10−6 1.33·10−4

997 1121 1129 1179

100 55, glycerin 45 55, glycerin 45 12, glycerin 88

4

Applied Energy 251 (2019) 113362

A.F. Serov, et al.

respectively, should be determined by the relative speed of cylinder rotation ΩΣ = Ωo + Ωi. In this case, the Reynolds number, derived from the relative rotational speed, is written in the form ReΣ = ΩΣ Ref·δef/ν, where Ref = (Ro + Ri)/2 is the average radius of the annular channel, ν is the kinematic viscosity of the working fluid. Since the temperature of fluid in the heat generator depended on the intensity of rotation, which led to a change in its viscosity, all experimental data were reduced to conditions at constant temperature t = 20 °C. The reduced values of the moment of resistance and effective Reynolds number were calculated from the following relations:

M20 = M·(ν20/ ν ), (Re Σ )20 = Re Σ·(ν / ν20 ). Here, M(20), (ReΣ)20 are torsion and Reynolds number, reduced to viscosity of the working fluid ν20 at the temperature of 20 °C. The results of measurements in the form of dependence of the moment of resistance to rotation M20 on Reynolds number (ReΣ)20 are presented in Fig. 6. As it can be seen from the figure, taking into account the relative speed of the cylinders at their opposite rotation with different ratios of speeds, there is a tendency to experimental data generalization. This is especially noticeable in the range of small Reynolds numbers ReΣ < 100. Nevertheless, in the whole investigated region of Reynolds numbers, there is a small, but systematic increase in the value of the moment of resistance to rotation with an increase in the relative (opposite) rotational speed of cylinders. Data on the value of thermal power generated in the heat generator at various Reynolds numbers are presented in Fig. 7. The results of thermal power measurements as well as the data of Fig. 6 are reduced to the value of kinematic viscosity of the working fluid ν (20 °C). It follows form Fig. 7 that in the range of maximal ReΣ number, the value of thermal power for a given heat generator reaches the values of about 2 kW. The character of a change in the power corresponds generally to the behavior of the moment of resistance to rotation in Fig. 6.

Fig. 3. Comparison of measured thermal and mechanical powers, produced by the heat generator.

Fig. 4. Effect of “rotor” rotational speed on the moment of resistance to rotation (fluid No. 4).

3.2. Effect of fluid viscosity on heat release This series of experiments was carried out for four working fluids, whose viscosity differed almost 30 times. Data on the properties of these fluids are presented in Table 1. As in the previous section, two series of experiments were carried out to measure the moment of resistance force to rotation of “rotors”. In the first series, only the upper “rotor” rotated while the lower “rotor” was stationary, in the second series both “rotors” rotated in the opposite directions with equal angular velocities. Measurement results are shown in Fig. 8. For the case of counter rotation, the value of relative rotational speed ΩΣ = Ωup + Ωd was used in data processing. As expected, highly viscous fluids cause to an increase in the

for other geometry and dimensions of heat generators. One of the approaches to generalize data obtained with a possibility of transferring them to other geometry is to represent them as a single equivalent gap between rotating round cylinders. As the basic values of such an equivalent channel, we will assume that the radius of the inner cylinder is equal to the average radius of the multi-cylinder system (see Fig. 2) Ref = 0.129 m, the height of the channel is equal to the sum of the heights of all channels Lef = 13·0.05 = 0.65 m and its volume is equal to the volume of the multi-cylinder heat generator V = 1.4 l. Then, the width of the equivalent gap between two cylinders will be δef = V/ (2πRef·Lef) = 0.0027 m. Such an approach makes it possible to reduce the multi-cylinder systems to an equivalent single channel and transfer the obtained data to other dimensions and geometry of the channels. In subsequent processing of experimental data, the Reynolds numbers of the outer and inner cylinders of the equivalent annular gap were used, respectively, Reo = ΩoRoδef/ν and Rei = ΩiRiδef/ν. The experimental data in Fig. 4, processed in the form of dependence of the moment of resistance to rotation M on the Reynolds number of the outer cylinder Reo, are shown in Fig. 5. As it can be seen, the Reynolds number in experiments did not exceed Reo = 400. Experimental points in the range of small Reynolds numbers are stratified strongly depending on rotational speed of the inner oppositely rotating cylinder. As the Reo number increases, the data approaches and, in the range of Reo ≈ 100 ÷ 200, all data almost coincide, and with further increase in Reo, a greater effect of braking occurs at low speeds of opposite rotation. This somewhat unexpected effect is caused by a decrease in the viscosity of fluid due to its heating by more and more intensively rotating cylinders. On the principle of superposition of the motion of oppositely rotating cylinders, the moment of resistance and heating of fluid,

Fig. 5. Dependence of the moment of resistance to rotation on Reo number of the outer cylinder and speed of opposite rotation of the inner cylinder. 5

Applied Energy 251 (2019) 113362

A.F. Serov, et al.

unit volume of working fluid Nv = N/V, whose measurement results are shown in Fig. 9, have the same tendencies as the moment of the force of resistance to rotation. Moreover, a greater effect of a change in the fluid viscosity is observed at low speeds of rotation, and as the relative speed increases, this effect weakens. An important parameter in development of mechanical heat generators is the value of specific power Nv. Dependence of this value on the speed of rotation for fluids with different viscosities is shown in Fig. 9b. The specific power of the studied apparatus varies widely and its maximal value for highly viscous fluids approaches 1 MW/m3, which is a high indicator of this device effectiveness for direct conversion of mechanical wind energy into thermal energy. It should be taken into account that the maximal speed of “rotor” rotation at the same time did not exceed 5 Hz, which is quite achievable speed of rotation at moderate wind load. 3.3. Generalization of experimental data and comparison with theoretical dependences

Fig. 6. Generalization of experimental data for oppositely rotating cylinders. Indications of points correspond to Fig. 5.

To create an engineering basis for the method of optimization analysis of the characteristics of a multi-cylinder apparatus for direct conversion of wind energy into heat, we will generalize the experimental data. To do this, we use the approach described above, which is based on replacing a multi-cylinder system with an equivalent annular gap with effective dimensions. Then the coefficient of moment of resistance for the equivalent gap is written as: (2)

CM = M/M0 (π/2)ρΩΣ2

4

where, M0 = (Ref) Lef is a characteristic moment of resistance to rotation for the equivalent annular gap [34]. All experimental data obtained for different fluid viscosities and processed in the form of dependence CM = f(ReΣ) are shown in Fig. 10. The results of Fig. 8b were the initial data for this figure, and the difference in indication of points corresponds to different viscosities of the working fluid. The results of calculation of the flow in the annular gap are plotted by the lines in Fig. 10 for the laminar Fig. 7. The value of thermal power produced in the heat generator. Indications of points correspond to Fig. 5.

CM = 4/ReΣ , (ReΣ < 380)

(3)

and turbulent moment of resistance, regardless of the speed and mode of rotation. However, this growth is not proportional to the increase in viscosity and it is much smaller. It should be also taken into consideration that a change in viscosity as a function of the working fluid temperature in the channel, which largely depends on the relative speed of cylinder rotation and is largely determined by the composition of fluid, can make a strong contribution to the dissipation process. Power N released by the heat generator and its specific value per a

CM = 0.03·Re−Σ 0.2 ,

(ReΣ > 380)

(4)

flows [24,34]. Despite the significant difference between the multi-cylinder system studied by us and the classical channel between two rotating cylinders, for which relations (3) and (4) are valid, there is good agreement between the theory and experiment in Fig. 10. This is a very important conclusion, which gives the grounds for the practical use of the model

Fig. 8. Effect of fluid viscosity on the resistance moment of rotating “rotors”. (a) – lower braked “rotor”, (b) – opposite rotation. The numbers of lines correspond to the numbers of fluids in Table 1. 6

Applied Energy 251 (2019) 113362

A.F. Serov, et al.

Fig. 9. Effect of viscosity on the power of heat generation. (a) – thermal power; (b) – specific thermal power.

resistance reaches 2 times. If the relative speed of cylinder rotation is used as a characteristic value, the experimental data for the cases of opposite rotation tend to be generalized, taking into account the dependence of the fluid viscosity on the speed of rotation. When studying the effect of working fluid viscosity (its value in the experiments was changed by two orders of magnitude) on the process of mechanical energy dissipation into heat, it was found that the moment of resistance and heat release, respectively, increase with increasing viscosity. As expected, highly viscous fluids lead to an increase in the moment of resistance, regardless of the speed and mode of rotation. However, this growth is not proportional to the increase in viscosity and it is much smaller. The studies have shown that specific heat power, produced by the heat generator, can be about 1 MW/m3, which indicates the prospects of using such devices for direct conversion of wind energy into heat. From a technological point of view, it is important that transfer of rotational motion from two wind rotors to a heat generator can be carried out directly without additional transmissions and mechanical reducing gears. A simple model for replacing a multi-cylinder system with a single equivalent gap between two rotating cylinders is proposed. Despite significant differences in the designs and additional effect of the end and side walls on the flow in the heat generator, this approach proved to be effective and leading to good generalization of the experimental data. At that, the results of experiments are well described by the classical theory for a single equivalent gap in both laminar and turbulent flows. This important conclusion provides the basis for the development of engineering methods for calculating the thermal characteristics of various designs of multi-cylinder fluid heating systems, as well as an optimization analysis of parameters of heat generators for direct conversion of wind energy into heat.

Fig. 10. Dependence of coefficient of resistance moment on Reynolds number at opposite rotation of cylinders. Indications of points corresponds to Fig. 8.

of an equivalent single channel between rotating cylinders for describing resistance in complex multi-cylinder devices for conversion of mechanical energy of rotation into thermal energy. This approach can be used, inter alia, when carrying out optimization engineering calculations. Indeed, by choosing a working fluid with the known properties and relative speed of cylinder rotation, it is possible to easily calculate the required parameters of the heat generator, including the heat output, from relations (2)–(4) for the accepted thickness of the gap. There are no fundamental difficulties in solving the inverse problem, when the channel geometry and relative speed of cylinders are determined by the value of a given thermal power. Despite the seeming simplicity, the calculation of real heat generators is complicated by dependence of working fluid properties on temperature, which are determined by the intensity of rotation, as well as the speed of its flow through the apparatus. However, the entire calculation procedure can be easily implemented using the simplest schemes of numerical analysis based on the above algorithm.

Acknowledgment The work was financially supported by the Russian Science Foundation (project No. 18-19-00161). Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apenergy.2019.113362.

4. Conclusions Intensity of heat production in heat generators was studied experimentally using the multi-cylinder Couette-Taylor system with independently rotating cylinders. Rotation of one “rotor” with a stable second one and counter rotating cylinders were studied. The speeds of cylinder rotation varied in the range Ω = 0 ÷ 30 s−1. The strongest influence of counter rotation is observed at low speeds of the lower “rotor” and it decreases at high revolutions of counter rotating cylinders. So at equal speeds, the effect of intensification of the moment of

References [1] Cheng M, Zhu Y. The state of the art of wind energy conversion systems and technologies: A review. Energy Convers Manage 2014;88:332–47. [2] Herbert GMJ, Iniyanb S, Sreevalsanc E, Rajapandiand S. A review of wind energy technologies. Renew Sustain Energy Rev 2007;11:1117–45. [3] Díaz-Gonzáleza F, Sumpera A, Gomis-Bellmunta O, Villafáfila-Robles R. A review of energy storage technologies for wind power applications. Renew Sustain Energy Rev 2012;16:2154–71.

7

Applied Energy 251 (2019) 113362

A.F. Serov, et al.

[4] Alnasir Z, Kazerani M. An analytical literature review of stand-alone wind energy conversion systems from generator view point. Renew Sustain Energy Rev 2013;28:597–615. [5] Burton T, Sharpe D, Jenkins N, Bossanyi E. Wind energy handbook. New York: Wiley; 2001. p. 531–3. [6] Okazaki T, Shirai Y, Nakamura T. Concept study of wind power utilizing direct thermal energy conversion and thermal energy storage. Renew Energy 2015;83:332–8. [7] Zolfaghari S, Riahy GH, Abedi M, Golshannavaz S. Optimal wind energy penetration in power systems: an approach based on spatial distribution of wind speed. Energy Convers Manag 2016;118:387–98. [8] Zheng J, Zhou Z, Zhao J, Wang J. Integrated heat and power dispatch truly utilizing thermal inertia of district heating network for wind power integration. Appl Energy 2018;211:865–74. [9] Gu W, Wang J, Lu S, Luo Z, Wu C. Optimal operation for integrated energy system considering thermal inertia of district heating network and buildings. Appl Energy 2017;199:234–46. [10] Li G, Zhang R, Jiang T, Chen H, Bai L, Cui H, et al. Optimal dispatch strategy for integrated energy systems with CCHP and wind power. Appl Energy 2017;192:408–19. [11] Ting C-C, Lee J-N, Shen C-H. Development of a wind forced chiller and its efficiency analysis. Appl Energy 2008;85:1190–7. [12] Ting C-C, Lai C-W, Huang C-B. Developing the dual system of wind chiller integrated with wind generator. Appl Energy 2011;88:741–7. [13] Blarke MB. Towards an intermittency-friendly energy system: comparing electric boilers and heat pumps in distributed cogeneration. Appl Energy 2012;91:349–65. [14] Kensby J, Trüschel A, Dalenbäck JO. Potential of residential buildings as thermal energy storage in district heating systems – Results from a pilot test. Appl Energy 2015;137:773–81. [15] Serov AF, Mamonov VN, Terekhov VI, Nazarov AD. Opposite wind heat generator. Patent RU2612237; 2017. [16] Vetrova AA, Biryulin IB, Shkolnik BI, Belaya VA, Nugmanov MR. Wind thermoelectric generator. Patent RU2371604; 2008. [17] Biryulin IB, Solod NP. Wind thermoelectric generator. Patent RU2226620; 2002. [18] Nouri-Borujerdi A, Nakhchi ME. Heat transfer enhancement in annular flow with outer grooved cylinder and rotating inner cylinder: Review and experiments. Appl Therm Eng 2017;120:257–68. [19] Jeng T-M, Tzeng S-C, Lin C-H. Heat transfer enhancement of Taylor– Couette –

[20] [21]

[22]

[23] [24] [25] [26] [27] [28] [29] [30]

[31]

[32] [33]

[34]

8

Poiseuille flow in an annulus by mounting longitudinal ribs on the rotating inner cylinder. Int J Heat Mass Transfer 2007;50:381–90. Childs P, Long C. A review of forced convective heat transfer in stationary and rotating annuli. Proc Inst Mech Engin, Part C: J Mech Eng Sci 1996;201(2):123–34. Fénot M, Bertin Y, Dorignac E, Lalizel G. A review of heat transfer between concentric rotating cylinders with or without axial flow. Int J Therm Sci 2011;50:1138–55. Sodjavi K, Ravelet F, Bakir F. Effects of axial rectangular groove on turbulent Taylor -Couette flow from analysis of experimental data. Exp Therm Fluid Sci 2018;97:270–8. Kreith F. Convection heat transfer in rotating systems. In: Irvine TF, Hartnett JP, editors. Advances in heat transfer. New-York: Academic Press; 1968. p. 129–250. Dorfman LA. Hydrodynamic resistance and heat transfer of rotating bodies. Physmath Ed., Moscow, Russian 1960;260:P. Sparrow EM, Munro WD, Jonsson VK. Instability of the flow between rotating cylinders: the wide-gap problem. J Fluid Mech 1964;20(part 1):35–46. Andereck CD, Liu SS, Swinney HL. Flow regimes in a circular Couette system with independently rotating cylinders. J Fluid Mech 1986;164:155–83. Froitzheim A, Merbold S, Egbers C. Velocity profiles, flow structures and scalings in a wide-gap turbulent Taylor-Couette flow. J Fluid Mech 2017;831:330–57. Ostilla-Mónico R, van der Poel EP, Verzicco R, Grossmann S, Lohse D. Exploring the phase diagram of fully turbulent Taylor-Couette flow. J Fluid Mech 2014;761:1–26. Tzeng S-C. Heat transfer in a small gap between co-axial rotating cylinders. Int Comm Heat Mass Transfer 2006;33:737–43. Nouri-Borujerdi A, Nakhchi ME. Optimization of the heat transfer coefficient and pressure drop of Taylor - Couette - Poiseuille flows between an inner rotating cylinder and an outer grooved stationary cylinder. Int J Heat Mass Transfer 2017;108:1449–59. Poncet S, da Soghe R, Bianchini C, Viazzo S, Aubert A. Turbulent Coutte-Taylor flows with endwall effects: A numerical benchmark. Int J Heat Fluid Flow 2013;44:229–38. Coelho PM, Pinho FT. Fully-developed heat transfer in annuli with viscous dissipation. Int J Heat Mass Transfer 2006;49:3349–59. Mamonov VN, Nazarov AD, Serov AF, Terekhov VI. Experimental investigation of thermal processes in the multi-ring Couette system with counter rotation of cylinders. Thermophys Aeromech 2016;23:139–42. Schlichting H, Gersten K. Boundary, layer theory. New York: McGraw-Hill; 2000.