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米爾恩范文第1篇

In a sense,the life of each of us is made up of family, friends and career. If any of them is lacking,our life is not intact and we may feel embarrassed, regretful, or even painful.

One's family is his harhour where he can rest and relax himself when he sails home through winds and waves of the outside world. One's friends are his most trustworthy and most valuable companions. He and his friends will help and encourage each other on the long journey of life. One's career is the reflection of his talent and value which he offers society.

Anyone who longs for a delightful life should cherish his family, take sincere care of fi'iendship and devote himself to his career。

米爾恩范文第2篇

Abstract

This paper deals with new design of low head turbines, as feasible solutions to solve the lack of energy in rural and remote areas, or to provide energy from urban water pipe systems. Propeller turbines are then the subject of this research because they are suitable for small heads, discharges with little variability, easy to manufacture and with low costs associated. Hence, the aims are the design of quite simple tubular propeller turbines and the analysis of hydrodynamic behaviour for different number and configuration of blades, based on CFD analyses and experimental tests development. An advanced hydrodynamic code based on the finite volume method, as well as blades configuration and mesh specific models are used for the impeller and the turbine design. The blade geometry is optimized using mathematical formulations and experimental results, concerning the possible range of operation under best efficiency conditions. Performance curves are obtained for typical characteristic parameters allowing comparisons between CFD and experimental results. Based on the similarity theory applied to turbomachines it is possible to evaluate the hydrodynamic behaviour through a tubular propeller for different sizes, in a scale model application.

Key words: Low head turbines; Fluid dynamics; Tubular propeller; CDF analysis; Performance curves

Ramos, H. M., Sim?o, M., & Borga, A. (2012). CFD and Experimental Study in the Optimization of an Energy Converter for Low Heads. Energy Science and Technology, 4(2), -0. Available from: URL: /index.php/est/article/view/10.3968/j.est.1923847920120402.142

DOI: /10.3968/j.est.1923847920120402.142

INTRODUCTION

Hydrodynamic models of fluid mechanics, also known by computational fluid dynamics (CFD), allow the evaluation of the flow behaviour, for a specific system configuration with associated boundary conditions. These models need the development of theoretical analysis on the physical behaviour of the flow based on mathematical formulations in three-dimensional analyses, with enough accuracy not only for laminar and turbulent flows, but also for the various forms of energy transfer, changing phases of the flow, vorticity occurrence, levels of turbulence and shear stress between interfaces. Hence, this study deals with a new propeller solution based on a facility implementation in order to predict the real evaluation of the pathlines, turbulence and losses effects, for different operating conditions.

Pico turbines are cost effective means of producing electricity of low power being under analysis for new improvements, despite the less attention that researchers and manufactures have been paid to those engines’ technology. Thus, the challenge of this work is therefore to provide new engineering designs and implementation methods that can be effectively customized and applied for possible energy recovery projects in water systems of low head and relative flow rates, such as from natural small rivers or streams, water supply, irrigation and drainage systems, treatment plants or aquaculture factories.

Definitions for pico-hydropower vary, but the term generally refers to power systems below 5 kW. At isolated regions, such systems are suitable for individual households and powering data loggers or management control systems in water companies.

A fixed geometry propeller turbine was built and tested for a runner speed of 1000 rpm, suited to 35 m head and about 5 l/s flow rate, reaching good efficiencies (Howey, 2009). It was also designed and installed in field a fixed geometry propeller turbine with a spiral casing showing an overall mechanical efficiency of 65% (Simpson & Williams, 2006). Recent optimizations of low-head axial-flow hydro turbines have enabled to reach interesting operating efficiencies. Several researchers (e.g. Demetriades, 1997; Upadhyay, 2004; Alexander et al., 2009) have developed models of medium sizes for propellers turbines, but until now there are no any relevant expression studies for propellers working as micro turbines, allowing new developments of improvements in its design, efficiency and versatility of operation based on both computational modelling and experimental analysis. A new fixed blade runner called “mixer” suitable for upgrading old units of Francis turbines installed in low head hydropower plants was recently developed by (Skotak, 2009). This new turbine suitable for a head of 5 m, with a runner diameter of 2250 mm and a discharge of 23 m3/s allows obtaining higher efficiency by optimizing the shape of the runner blades.

These new design solutions are usually appropriate to hydropower schemes with large discharge values, leaving an open field for developing new geometries optimization models with smaller sizes, in order to cover a large range of applications, where low power are available, especially in water pipe systems.

Through turbo machine similarity it is possible to estimate different operating conditions from an equivalent turbine, even though the scale effects associated. The behaviour of the system as a whole can differ, depending on the scale adopted, and the configuration of the runner, in particular the blades shape (Ramos et al., 2009). Consequently, the design and the development of micro turbines cannot be only based on the methodology of exactly scaling down from large turbines. Economic, hydrodynamic and manufacturing constraints give opportunities to create new designs adequate to each type of water system or infrastructure, depending on its main characteristics.

This study provides analysis based on a new blade model configuration and CFD analysis, as well as new hydraulic energy converters suitable for applications of micro-scale for low head and flow rate conditions, which can be easily implemented both in remote areas, as well as in water pipe systems in urban environment, with non-negligible flow energy available that would be wasted or dissipated. The proposed new tubular propeller turbines (with 4 and 5 blades) represent a cheap and easy installation solution to cover a range of low power, head and discharge values which are not available in the market.

1. FLUID DYNAMICS

1.1 Fundamentals

In computational fluid dynamics, the CFDs are important tools to estimate real results from the calibration based on experimental tests, which allow for better understanding the phenomenon associated with the flow behaviour in turbines for different flow conditions (Ramos et al., 2010). In fact, these CFD are advanced models of fluid mechanics widely used in the analysis of complex in setting hydraulic systems, leading to optimal design solutions. FLUENT is a hydrodynamic model that applies the technique of finite volumes to solve the equations that describe the flow, as the continuity equation and the Euler or Navier-Stokes’ equations also known as Reynolds equations. This model features two types of calculation algorithms that can be solved by a system of equations. Regarding the latter option the algorithm SIMPLE is a way to resolve the coupling between velocity and pressure. In the case of Reynolds stress it is used the k-ε model since it is a robust model with proven results on the turbulence analyses. The model includes two equations regarding the properties of turbulence flow, which allows accounting for all purposes of the convection and diffusion of the turbulence intensity. One of the variables is the turbulent kinetic energy, k, while the other represents the rate of dissipation, ε. In summary the dissipation variable determines the scale of turbulence, while the kinetic energy the turbulence intensity.

1.2 k-ε Model

The effect of turbulence normally occurs for high values of Reynolds, and is the cause of production some eddies within the fluid. Associated with turbulent flow it can be identified zones with rotation, diffusion intermittence, highly disordered and dissipative effects. Regions with greater turbulence, which are normally associated to fluctuations of low frequency, can be considered as a boundary condition of the flow and its size can reach the same order of magnitude of the flow itself. As a result, turbulent flow characteristics require specific models to determine the correlation between velocity and pressure. According to the simplifications in the fluid transport equation (Equation (1)), it is possible to make a parallel between these equations and those used by the turbulence k-ε model.

(1)

This k-ε model is a semi-empirical based on transport equations of kinetic energy turbulent (k) and its dissipation rate (ε). The flow transport equations for the k model, are derived from the exact equation, while the transport equation for the ε model is obtained through physical relations (Fluent, 2006). In the derivation of the k-ε model it is assumed the flow is turbulent, and the effects of molecular viscosity are negligible. Thus, the turbulent kinetic energy and its dissipation rate are obtained, respectively, by Equations (2) and (3):

(2)

(3)

where C1ε, C2ε are constants, and σk, σε correspond to the variables turbulent Prandtl k and ε, respectively, determined experimentally with air and water affected by friction in flows with homogeneous and isotropic turbulence (Scott-Pomerantz, 2004). The experience shows that these values provide good results for a wide range of defined border and free of friction. Once, the following constants were adopted: C1ε = 1.44, C2ε = 1.92, σk = 1.0, σε = 1.3. Pk is the product of turbulence due to viscous forces and fluctuations,

(4)

The turbulent dynamic viscosity, μt, is calculated by combining k and ε as follows:

(5)

where, μt is defined as the turbulent dynamic viscosity and is an empirical constant specified in the turbulence model (approximately 0.09).

For high Reynolds numbers, the rate of kinetic energy dissipation is obtained by multiplying the viscosity with the fluctuating vorticity. An exact equation for the transport of vorticity floating is the rate of dissipation, which can be derived from the Navier-Stokes equations transforming the turbulent kinetic energy and the dissipation rate in Equations (6) and (7).

(6)

(7)

where G and are given by

(8)

(9)

To establish a first image of the turbulent regime, it is consider that the flow rate increases and the impeller rotational speed also rises induced by the gradient along the solid walls and the amounts up the viscous stresses. However, the occurrence of different viscous tensions from point to point, determines the curved trajectories of the flow particles, a phenomenon which increases as they approach to the solid boundaries, given the increased role of concentrated stress gradients.

1.3 Mesh Specification

The success of 3D computational modelling in fluid mechanics requires a special attention during the mesh generation. When a flow passes through a turbine, the turbulence (from the effective viscosity variable in space) plays an important role in the dynamic convection, requiring that in complex flows, the amount of turbulence are duly solved with high precision. Due to the strong interaction between flow and turbulence, numerical results tend to be more susceptible to the grid dependency than for a laminar flow. Thus, it is recommended that the study considers sufficiently thin meshes in regions where occur rapid flow changes and concentrated large tangential tensions. In this way, the use of a mesh generation model (workbench-mesh creation) to describe the volumes, allows the calculation space and the appropriate definition of the boundary conditions (Ansys CFX, 2006).

For the mesh occupied by the flow, it is defined a physical preference in the CFD model and an initial control method, setting mesh defaults changing only one parameter “growth rate” to 1.5 since this value is crucial in the choice of the mesh size, concerning the number of elements and nodes. This model use an advanced size function where all the faces are identified, since the entire turbine, until the ones that correspond to more restrictions in places where the mesh is difficult to create, which usually coincides with rather small volumes. Thus, the mesh created on all sides surrounding the body of the impeller, comprised of the blades, interior bulb, and the shaft to connect the generator, corresponds to 333793 elements and 65103 nodes (Figure 1).

Figure 1

Schematic of the Mesh Created for a Tubular Propeller

The boundary conditions specify the values of characteristic variables in the physical limits of the device. As part of the simulations for each case study, there are four types of boundary conditions: inlet and outlet pressure, rotor or impeller and the tubular wall. Areas designated by impeller are defined as moveable walls, with rotational speed around the rotation shaft, which corresponds to the centre of the runner. In other areas of the field corresponding to solid surfaces is imposed the condition of impermeability and uses the standard wall law for turbulent flow simulations. The faces of the elements belonging to periodic surfaces (the area occupied by the fluid) are treated as inner faces of the domain. All simulations were carried out with the fluid corresponding to water density and constant viscosity, with values of ρ = 998.2 kg/m3 and n = 1.01×10-6 m2/s.

2. BLADE MODEL CONFIGURATION (BMC)

In the design of the impeller blades it is important to analyse different slopes (i.e. angle variation) in order to determine the best results that lead to a best efficiency point (BEP). In the blades design it was adopted a minimal thickness as possible in order to avoid disturbances in the flow, causing additional losses that might constrain its effectiveness. For the flow rates considered in micro turbines, the maximum thickness of 1mm was taken into account for the blades due to limitations of the mesh generation. Figure 2 shows the velocities triangles to take in the optimization of the blade configuration. It shows the parameters are associated to each other from the direction of the blades, as the angle variation by the vectors indicated. Hence, a blade model configuration (BMC) was developed to estimate the best blade orientation to get the best efficiency operating conditions. It is a lengthy process that requires special care and sensitivity analyses to various characteristic parameters associated to the inlet and outlet velocity triangles.

Figure 2

Velocity Vectors in a Blade of a Turbine Propeller

In Figure 2, velocity vectors are identified by the vectors of absolute (v), periphery (c) and relative runner blade velocity (u). From them and according to the shown detail in Figure 2, it is established some essential relationships to calculate the turbine discharge for a given configuration. Knowing the periphery velocity (c) at the inlet and outlet of a blade, which depends on the impeller rotational speed (ω) and the blade radius (r),

(10)

and the absolute velocity (ν) depends on the discharge (Q) that pass through the impeller (Ramos et al., 2009),

(11)

being S the tubular cross section area, re and ri the tip and hub blade radius between the runner periphery and internal bulb, respectively.

According to the angles of a blade on the periphery of the inlet and outlet (subscript 1 and 2, respectively) of the impeller yields the following Equations (12) and (13),

(12)

(13)

To reduce the losses in the turbine, it is assumed the flow at downstream of the impeller is irrotacional, influenced by a vortex formation, depending on the radius of the blade, the flow cross-section and the discharge value as presented in Equation (14),

(14)

In fact as the angle of the blade changes from the inlet to the outlet, between the upstream section, where the flow impulse the blade, to downstream section, the efficiency changes and may lead to better or worse values depending on the angle variation along the blade profile.

Based on the Equations (12) to (14), the blade model configuration determines the angles for a given rotational speed, leading to an optimum performance. The input values known as the head, discharge, rotational speed for the rated conditions, runner diameter, relation between the runner bulb and periphery diameter, the open blade angle (ap) which depends on the number of blades, the angles of the inlet and outlet from the axis to the periphery in each blade are calculated, as well as the power, the specific speed and the constant vortex velocity by Equation (14). Knowing all the data provided by the input conditions, the correct blade configuration from the bulb section (ri) to the periphery (re) (Figure 3) is then determined.

(a)

(b)

Figure 3

Scheme of a Propeller: (a) Plan View with Five Blades and Five Profiles in a Blade; (b) Parameters Associated to the Tracing Profiles in Each Blade

The five profiles (i.e. P1 to P5) in each blade are then drawn from two fundamental equations (Equations (15) and (16)), where, j, represents the number of chosen points required to perform the tracing blade profile; yc and xc are the centre of the blade; x1 and x2 the inlet and outlet coordinates of the blade represented in Figure 3 (b); and rh the radius of the blade curvature.

(15)

(16)

The representation of the profiles on each blade configuration (Figure 3 (a)) corresponds to each line between (ri) and (re), the bulb radius and the runner periphery, respectively.

As the upstream of momentum per unit time is given by Equation (17),

(17)

deriving it, the Equation (18) is then obtained,

(18)

which by algebraic manipulation yields Equation (19),

(19)

After its integration the binary is obtained by Equation (20),

(20)

As the motor or mechanical power is given by Equation (21),

(21)

and the hydraulic power by Equation (22),

(22)

the efficiency is given by Equation (23),

(23)

In order to design the tubular propeller to the available lab conditions, it is considered the outer impeller diameter of 100 mm, with a bulb diameter of 50 mm. According to Table 1 the blades design is built to operate with a discharge of 4 l/s at 300 rpm for the rotational speed.

Table 1

Values for the Blade Profiles Design

(a) Propeller with Five Blades

(b) Propeller with Four Blades

Figure 4

Design of Different Profiles for Each Blade (Impellers Configuration)

To design the blades profile presented in Figure 4 (for five (a) and four (b) blades) the variables presented in Table 1 are used in Equations (15) and (16).

3. CFD analyses

3.1 Performance Curves

For the two designed impellers (with five and four blades) which are characterised by its specific speed Nsqt as stated in Equation (24):

(24)

were developed comparisons between the blade model configuration (BMC) and CFD analyses. Table 2 confirms a good agreement between BMC (for a maximum theoretical efficiency of 100 %) and the CFD simulations, even the existing losses, turbulence effects, anisotropy in zones of high flow circulation, scale effects, which are not considered in the theoretical methodology of the BMC. CFD simulations use, in a first stage, the angles obtained by BMC, but sensitivity investigation regarding the best efficiency operating conditions induces small corrections to those angles as shown in Table 2.

Table 2

Comparison Between Tip and Hub Angles for the Tubular Propeller with Five Blades

Methodology

It is notorious the difference in power values of power between impellers diameter of 100 and 200 mm. This difference allows concluding that for the propeller with five-blades higher discharge values are need.

Two geometrically similar turbines operating at rotational speeds that satisfy the condition presented in Equation (25), have usually different values of efficiency in particular when the relationship between homologous lengths is high.

(25)

This is due to scale effects noticed between the two machines, driven by the effect of viscosity which causes loss of pressure, preventing thus a quadratic variation to the flow velocity. For different rotational speed values and flow conditions, the efficiency are obtained (Figure 5), for the tubular propellers with five and four blades.

Figure 5

Performance Curves of Efficiency and Head Versus Rotational Speed, for a Runner Diameter of 200 mm: (a) with Four Blades; (b) with Five Blades

Figure 6

Performance Curves of Head and Mechanical Power Versus Discharge for a Runner Diameter of 200 mm: (a) with Four Blades; (b) with Five Blades

Figure 7

Performance Curves of Efficiency and Head Versus Rotational Speed, for a Tubular Propeller, with a Diameter of 100 mm: (a) with Four Blades; (b) with Five Blades

Figure 6 shows the curves of head and mechanical power versus discharge for the two impellers analyzed. In Figure 7, the turbine with a smaller runner diameter (D =100 mm) is performed and it is most suitable for small discharge values as happen with small drinking systems as well as in water distribution lab conditions in which the maximum discharge value is around 5 l/s.

Table 3

Reference Values for Tubular Propeller (D = 200 mm)

Table 3 presents some reference values obtained by CFD modeling for an impeller diameter of 200 mm, with 4 and 5 blades. These values represent a wide range of operation for different rotational speed, discharge and head values.

Based on CFD 3D hydrodynamic simulations for small discharge range values, performance curves are obtained based on the following dimensionless parameters:

Discharge number: (26)

Head number: (27)

Power number: (28)

Figure 8 shows the performance curves for head and power number and efficiency versus discharge number variation for the tubular propeller of D =100 mm with four and five blades, respectively.

Figure 8

Comparison of Power and Head Numbers and Efficiency vs Discharge Number for 4 and 5 Blades Propellers of D = 100mm

For the impeller with 4 blades the BEP is obtained for a rotational speed of 300 rpm (Nsqt = 91 rpm (m, m3/s)), a discharge of 4 l/s. The BEP for the propeller with five blades is obtained for a discharge of 3.4 l/s, a rotational speed of 300 rpm (Nsqt = 80 rpm (m, m3/s)).

3.2 Hydrodynamic Behaviour

Established the BEP for the tubular propellers (with four and five blades) based on CFD simulations, detailed analyses are developed in order to better understand the 3D hydrodynamic behaviour of the flow throughout each impeller. For the tubular propeller (D = 100 mm) with five blades and according to a discharge, rotational speed and head, the flow velocities, total pressure, turbulence intensity, wall shear stress and pathlines are presented in Figure 9.

Figure 9

Fluid Performance Inside Tubular Propeller with Five Blades

Figure 10

Fluid Performance Inside Tubular Propeller with Four Blades

This 3D fluid computational analysis considers steady pressurized flow conditions, keeping a constant rotational speed where the singularities reflect an increasing of turbulence. Analysing Figure 9, there are some instabilities in the flow inside the turbine. This is not only due to the rotation of the impeller as it is associated to the circulation flow, making an anisotropic behaviour in different turbine zones, but also the way of the flow enters into the turbine section, through the propeller and leaves with a rotational movement (in vortex configuration) towards the draft tube or downstream pipe.

Given the characteristic curves of the tubular propeller with four blades, and after established the BEP, it is observed a similar behaviour for the velocity, pressure, turbulence, shear stress, and pathlines as showed in Figure 10.

At upstream of the turbine, the flow has a low velocity, with higher pressure values in this region, presenting irrotacional behaviour. However, when it enters in the field of the impeller rotation, the flow becomes a rotational behaviour. At turbine section, the flow goes through the impeller being influenced by the impeller contour inducing the effect of flow separation with significant effects on the turbulence intensity and wall shear stress. It is also noticed the shear stress is higher near the periphery of the blades conferring some significant flow resistance in this zone.

For these tubular turbines are specified four sectioning plans (Figure 11) to analyse the behaviour of the flow in zones where the flow range can vary and where it is needed a better comprehension about the variation of the flow velocity.

Figure 11

Schematic Representations of the Sectioning Plans for Instantaneous Velocity Analysis

In Figure 12 the fluid enters the turbine with an average speed of 0.32 m/s, decreasing as it approaches the tubular walls due to the well known effect of wall friction effect. As it approaches the curve and the impeller, the flow presents asymmetry behaviour in the velocity distribution.

In Figure 13 the velocity distribution shows a similar behaviour. Along the axis the flow tends to be influenced by the shaft rotation inducing the formation of separation zones.

Figure 12

CFD Simulations for the Variation of the Flow Velocity Across Turbine with Five Blades

Figure 13

CFD Simulations for the Variation of the Flow Velocity Across Turbine with Four Blades

Althougth the number of blades are different, in general way the hydrodynamic behaviour is similar. Comparing Figure 12 and Figure 13, there is an agreement associated with the effects of the flow rotation, the friction and the existence of seperation zones, which induce a variation behaviour along the turbine, which is the base of the efficiency variation for different operational conditions.

4. EXPERIMENTAL TESTS

Figure 14 shows the schematic facility for the analysis of the propeller turbines with five and four blades and an impeller diameter of D =100 mm placed in a loop pipe in order to maintain a steady state flow conditions. This setup comprises a pipe system with a pump, for the recirculation, an air vessel to control the pressure at upstream, an electromagnetic flow meter and a downstream reservoir provided with a triangular (90?) weir. There is a valve for the flow control at downstream the air vessel and when it is fully open the maximum possible turbine flow is 5.2 l/s.

Through the turbine upstream curve, the shaft transmits the momentum to a torque balance or a generator.

During the tests it was observed an isotropic behaviour of the flow at upstream of the turbine and an anisotropy through the impeller influenced by the flow rotation and separation of the boundary layer that exists at downstream of the internal impeller bulb. The BEP for the tubular propeller (D =100 mm) under lab conditions is for a rotation speed of 200 rpm (Nsqt = 84 rpm (m, m3/s)), as shown in Figure 15, with dimensionless curves based on head number and efficiency versus discharge number for the impeller with four and five blades, respectively.

Figure 14

Tubular Propeller Installation

Figure 15

Characteristics Curves of Tubular Propeller: (a) with Four Blades; (b) with Five Blades

The behaviour of tubular turbine with five blades (Figure 15 (b)) shows that this turbine is most adequate to operate with higher discharge values that there are not available in the facility.

According to the lab conditions, the experiments are obtained by regulating the discharge control valve, measuring the runner speed in a tachometer Hibok-24 for different flow values measured in an electromagnetic flow meter, and pressure head in transducers at upstream and downstream of the turbine, in undisturbed flow zones. These measurements are then compared with the CFD-3D model simulations. Using an Ultrasonic Doppler Velocimetry (UDV) in the zone of the turbine (Figure 16), the velocity profiles throughout the system are analyzed. With the UDV sample placed on vertical-sloped position of 25?, this device measures the flow velocities allowing the evaluation of the flow behaviour in real time.

Figure 16

Experimental Facility of the Tubular Propeller: UDV (Left); Balance Torque (Center); Rotational Speed Measurement (Right)

Figure 17

Separation of the Boundary Layer and Velocity Profiles

Figure 17 shows different velocity profiles along a runner boundary layer, where they represent the behaviour of the flow separation zone in which the velocity profile inversion tendency is visible.

The most important features to retain in the identification of a turbulent flow are essentially through (i) the flow irregularity by the occurrence of three-dimensional vorticity fluctuations, i.e. the turbulent movements are rotational, (ii) the continuity valid for the turbulent movements, since the smallest scales of these vortices are generally superior to the molecular fluid scale, (iii) the energy dissipation, i.e. the turbulent phenomenon is associated to a significant energy loss, where the turbulence is damped quickly by giving a greater homogeneity and isotropy to the flow motion, (iv) the diffusivity corresponding to a rapid mixing within the fluid domain, followed by transfer of momentum, heat and mass in rapid variations or fluctuations in the flow.

Based on these premises, Figure 18 shows the mean velocity profiles along the turbine for the plans referenced in Figure 11.

Figure 18

Flow Velocity Profiles Obtained by UDV in Sections Represented in Figure 12 (a) to (d)

From these profiles and comparing Figure 18 with Figure 13 a similar behaviour of the fluid is visible, as well as the identification of the section where the separation effect is notorious. When the fluid comes closer to the curve there is certain anisotropy with velocity retardation induced by the shaft rotation, and as soon it passes through the bulb the pressure and velocity decreases induced by the depression existed at downstream the impeller, leading to a separate zone (Ramos et al., 2012). When a fluid moves in the turbulent regime, its domain can be subdivided into two regions, where the movement has its own characteristics: a thin layer near the solid walls in which the tangential stress play an important role (the boundary layer); and the remaining part occupied by the fluid field, where the shear stress is presented with less significance.

5. COMPARISON OF PERFORMANCE CURVES

Dimensionless characteristic parameters of CFD simulations and lab tests were selected and compared as shown in Figure 19, in which H0 and Q0 are the rated values of head and discharge. The comparison of CFD simulations for the two impellers (i.e. with five and four blades) with the lab tests shows typical trends and a reasonable fit in the head performance behaviour.

Figure 19

Comparison Between CFD Simulations and Experimental Results of Tubular Propellers

Figure 20

Performance Curves Between CFD Simulations and Experimental Results: (a) Turbine Tubular Propeller with Five Blades; (b) Turbine Tubular Propeller with Four Blades

Regarding the efficiency values it is noticed a discrepancy justified by scale and losses effects that the CFD does not take into account in the simulations. Figure 20 presents comparisons between efficiency vs specific speed (m, m3/s) curves two rotational speed values (i.e. 70 and 200 rpm). The efficiency values by CFD analyses are higher than the experimental ones, essentially due to negligible factor owing to the friction losses in the mechanical system, such as bearings and seals that CFD codes cannot perform.

In Figure 20 (a), as increasing the rotational speed, there is a higher difference between simulations and tests, due to lab discharge limitations, forcing the propeller with five blades to run out of the optimal operation point. For the propeller with four blades, Figure 20 (b), the lab conditions are much closer to the rated operating point and consequently the results fit better.

CONCLUSIONS

Optimizing analyses for new tubular propellers (with five and four blades) adequate for low-head pipe systems and small discharge values are key solutions of the utmost interest to water companies to supply energy to data acquisition systems, control of the operational management in rural and isolated areas or even supply renewable energy to small regions, where it is very expensive to extend the energy line to these locations. These solutions are also adequate for small pumping systems and water treatment plants. The proposed new tubular propeller turbines (with 4 and 5 blades) represent a cheap, easy installation, good performances and competitive solutions to cover a power, head and discharge values lower than 8 kW, 20 m and 200 l/s respectively, corresponding a range of application not obtainable for existent commercial turbines available in the market.

These devices can be installed at the entrance and the exit of reservoirs or tanks or in some off-grid treatment plants, where are located the most electromechanical equipment which needs energy, or even in pipe systems for water drinking or drainage, where is necessary to provide power to supply control systems or for collect data.

Table 4

Main Characteristics of New Tubular Propeller for Low-Head Solutions

1) CFD analysis for lab conditions; 2) Experimental tests; 3) CFD turbomachine similarity from a propeller with 100 mm

Table 4 shows a summary of the main characteristics of the converters developed in this study which aim at providing small power outputs, usually available in most of the pressurized pipe systems.

A significant range of possible applications is presented in which traditional turbines cannot still cover in a cost-effective manner. These machines are economic solutions, because they are quite simple, normally composed by a runner installed in a pipe-curve, without volute, neither a guide vane. They are appropriate for operation under almost constant-flow conditions, as for water pipe systems equipped with a discharge control valve.

Fluid computational 3D analysis together with a blade model configuration (BMC) and experimental tests help to better understand the phenomenon associated with the hydrodynamic and turbine behaviour, leading a greater knowledge of interaction between the machine geometry, the hydraulic flow conditions and the turbine performance. These developments allow finding the best solution in terms of design, behaviour and configuration, whereby a good basis of calculations has become a point of promising research. This work provides also a good guideline for possible new design of low power turbines in order to highlight the continuity development of new energy converters to support cost-effective micro-hydro solutions.

ACKNOWLEDGMENTS

To projects HYLOW from 7th Framework Programme (grant No. 212423) and FCT (PTDC/ECM/65731/2006) which contributed to the development of this research work, allowing components of computational dynamic and laboratorial investigation associated to the performance of tubular turbines.

REFERENCES

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[6] Skotak, A., Mikulasek, J., & Obrovsky, J. (2009). Development of the New High Specific Speed Fixed Blade Turbine Runner. International Journal of Fluid Machinery and Systems, 2(4).

[7] Ramos, H. M., Borga, A., & Sim?o, M. (2009). New Design Solutions for Low-Power Energy Production in Water Pipe Systems. Water Science and Engineering, 2(4), 69-84. doi:10.3882/j.issn.1674-2370.2009.04.007

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米爾恩范文第3篇

China’s new generation of leaders extended invitations to the Palestinian and Israeli leaders shortly after assuming office， so signifying the importance they lay on the Middle East situation.

The Palestinian problem is a world hotspot that remains unresolved after more than half a century. Rather than avoiding it or taking a detour， about two months after assuming office the new generation of Chinese leaders confronted this complicated issue. This shows that China， in line with its responsibilities as a permanent member of the UN Security Council and a world power， is ready to participate in resolving international conflicts. This stance is evident in China’s support for negotiated settlements of the Palestinian matter and its concern over the extended deadlock in the peace process. China advocates resumption of Israeli-Palestinian peace talks， and encourages both sides to take practical action towards creating an atmosphere favorable to resumption of peace talks. As Chinese President Xi Jinping said in his meeting with Abbas， both parties should follow the trend of the times and adhere to the path of peace talks through compromise and mutual understanding.

These meetings also signify China’s self-confidence in diplomatic dealings. After years of development， China has vastly improved its national strength as well as international status and influence.

China， moreover， has a distinct advantage in having maintained good bilateral relationships with both Palestine and Israel. It thus constitutes a driving force towards finding a solution.

During his meeting with President Abbas， President Xi raised four proposals on settlement of the Palestinian issue. Their aim was to encourage both parties to advance the peace process through negotiation and compromise. The proposals explicate a direction that adheres to the principles of Palestine independence and peaceful coexistence between Palestine and Israel while respecting Israel’s right to existence and security. They also make clear that negotiation is the sole way of achieving peace. The proposals define the primary principles to be adhered to and which the international community accepts， such as “l(fā)and for peace.” They call for a strengthened sense of responsibility and urgency from the international community through provision of guarantees that advance the peace process. The proposals embody China’s long-term stance and incorporate new factors resulting from changes in the Middle East. They reflect China’s hope that the Middle East peace process will be resumed without delay and that peace will prevail. The war-torn Middle East， meanwhile， remains in turmoil， even though peace， stability and development are the common expectations of countries in the region. It is hence in all parties’ interests to resolve the dispute through political means.

Abbas was the first Middle East leader that the new Chinese government invited to visit after taking office. The invitation highlights the importance Chinese leaders lay on the Middle East issue， and their consistent position on supporting Palestine.

During his maiden trip abroad， President Xi visited three African countries as well as Russia. This implies the importance China places on the continent that is home to such a large number of developing countries. WANA （West Asia and North Africa） encompasses many such countries that have unequivocably supported China on core issues. They constitute a force that China can trust and rely on. In the new historical era， consolidating and developing our relationship with these countries requires careful planning and proactive promotion. As Xi pointed out， Palestine has long been at the core of Middle East issues and hence wields global impact. Inviting Abbas to visit represented a key link in China’s comprehensive diplomatic layout and the maturity of its relationship with the Arab world.

Pushing forward development of the bilateral relationship， especially cooperation in economy， trade， science and technology， constitutes the main result of the visits. Since the 18th CPC National Congress， promoting sustainable development and rejuvenation of the Chinese nation have been the long-term goals of the new generation of leaders and the entire Chinese people.

The “Chinese Dream” will come true not behind closed doors， but through a more open approach. We should therefore promote international exchanges and cooperation in efforts to achieve mutual benefits for China and the world. Discussions on how to improve cooperation in economy， science and technology were key features of the visits of both the Palestinian and Israeli leaders. At this special historical stage， Palestine hopes that more Chinese companies and factories will explore and invest in the West Bank. Discussions with the Israeli prime minister included development and cooperation in broader areas.

The new generation of Chinese leaders is bent on promoting practical bilateral cooperation and broadening communication and exchanges. Promoting such bilateral cooperation with Palestine and Israel were consequently predominant aspects of the respective visits. China and Palestine signed agreements on strengthening cooperation in economy， trade， culture and education. They also discussed ways of encouraging Chinese companies to invest in the West Bank and utilize its resources. Palestine expressed willingness to take measures towards achieving mutual benefit and enriching the friendship between China and Palestine.

Since the establishment of diplomatic relations between China and Israel more than 20 years ago， their rapport has grown considerably. On this occasion both parties， in the spirit of equality， mutual trust and learning， tolerance， cooperation and win-win， held in-depth discussions on how to complement one another and deepen practical cooperation in science and technology， water conservation and clean energy. Both also agreed to establish a special coordination organization.

Both Abbas and Netanyahu voiced satisfaction at the results of their visits as well as their high regard for China， and expectations that the country might influence the Middle East peace process. The leaders also expressed hopes of a speedy resumption of peace talks. Abbas later remarked to Arab envoys that， from the first to the current generation of Chinese leaders， the principle and stance of supporting the just cause of Palestine has remained consistent. China is thus a trustworthy friend and brother.

Main Obstacle

Promoting a solution to the IsraeliPalestinian conflict is still a long way off. Unless it is resolved， the Palestinian issue will have negative influence throughout the Middle East. President Xi made this point in his talks with the leaders of Palestine and Israel. The Palestine issue involves Arabs and Jews， both of whom have long histories. In earlier times， both lived in the area perceived by Judaism， Christianity and Islam as the Holy Land. Resolving the Israeli-Palestinian dispute hence involves the relationship between the Arabic and Jewish nations and other multiple complex relations among nations， religions and countries. But land is the most fundamental issue. That other major powers also exert their influence in the region complicates the situation.

Palestine lost all its territory after the third Arab-Israeli War in 1967. Palestine and Israel signed the historically significant Oslo Accords 20 years ago. Today， although the Palestine Authority has been established for many years， the reconciliation process between Palestine and Israel has nevertheless experienced twists and turns. Palestine has long sought to establish itself as a country based on the borders defined in 1967. At the same time， it accepts certain territorial exchanges on the basis of such borders， whereby Palestine and Israel exchange small tracts of land under a “two-state solution.”

During my visit to Palestine at the end of April the leaders I met with expressed expectations that I would convey to Israel their hopes of its compiling a map showing the relevant borders for discussion. The status of Jerusalem is another thorny problem. After the 1967 war， Israel occupied Jerusalem. Palestine， meanwhile， insisted on establishing a country whose capital would be in east Jerusalem. Land ownership is thus the root of the issue.

Resolution of the Israeli-Palestinian dispute demands adherence to the “l(fā)and for peace” principle， which discussion is the sole political means of achieving. Abbas stressed that a political solution is the best and only way forward. Palestine insisted on peace and sought negotiation on the basis of the “two-state solution”to eventually achieve peaceful coexistence. Netanyahu said during his China visit that Israel desired peace， and that it would be willing to achieve it through negotiation. Israel also expressed appreciation of China’s efforts to promote the Middle East peace process and its desire to maintain communication with China.

Although both Palestine and Israel want to negotiate， neither trusts the other. Radical domestic forces in both countries moreover exacerbate the difficulty of the process. The Chinese government must support and promote the Middle East peace process through negotiation， based on mutually accepted principles like “l(fā)and for peace” and relevant resolutions of the United Nations and the Arab Peace Initiative. China is also willing to cooperate with the international community in promoting confidence-building and a negotiated settlement.

Broader Concerns

The regional situation of WANA is also a key issue that needed consultation among Chinese， Palestinian and Israeli leaders. As to political changes in Arabic countries that are experiencing turmoil， China from the outset stressed that it respected the choices made by their people. This policy has been proven through diplomatic practice. After regime changes in certain WANA countries， China maintained and developed good relationships that led to bilateral cooperation. China is willing to strengthen cooperation in governance and economic development. China moreover hopes that different political forces will seek shared interests and resolve differences through dialogue and negotiation， thus minimizing the transition period.

米爾恩范文第4篇

搶劫的前一天晚上，他心滿意足地躺在床上，把自己的那把六發(fā)毒氣槍又仔細(xì)檢查了一遍。埃米爾自然不打算開槍。如果迫不得已，那么一把毒氣槍也足夠應(yīng)付了?！懊缐?mèng)很快就要成真了！”

翌日早晨，鬧鐘準(zhǔn)時(shí)在九點(diǎn)整響起。起床后，埃米爾刮了刮胡子，并給自己做了頓早餐：兩只雞蛋、面包和咖啡。吃完早餐，他又重新核對(duì)了一遍自己的計(jì)劃。

十二點(diǎn)左右，運(yùn)鈔車將抵達(dá)中央銀行。接著，他們會(huì)在十五分鐘之內(nèi)把兩家公司的全部薪水裝進(jìn)車?yán)铩?/p>

十一點(diǎn)，埃米爾?雅恩克出門。他一身筆挺西裝，正要去火車總站――他已在前天晚上托運(yùn)了一只箱子過來，這是為那筆巨額現(xiàn)鈔準(zhǔn)備的。埃米爾從保管站取出箱子后，便往停車場(chǎng)方向走去。他來來回回反復(fù)打量著停放在那兒的每一輛汽車，考慮再三后終于選定了其中一輛深藍(lán)色的“歐寶上將”。

又過了一刻鐘，他順利到達(dá)實(shí)施大計(jì)的目的地。他拿出一條工裝褲換在身上，一個(gè)時(shí)髦小伙子便完全變成一副機(jī)械工的模樣了。一切就緒，估計(jì)不會(huì)出什么差錯(cuò)了。

埃米爾看了看表，十二點(diǎn)二十分。運(yùn)鈔車此刻肯定已經(jīng)在路上了。他好比一支即將離弦的弓箭正蓄勢(shì)待發(fā)，可就在這當(dāng)口，距離他兩個(gè)車位的前方，一輛綠色的小型福特貨運(yùn)車突然開動(dòng)了。真見鬼！但愿它趕緊開走，他心里詛咒著。

埃米爾越來越焦躁不安。從市中心開來的運(yùn)鈔車已經(jīng)到了，但那輛綠色的貨運(yùn)車正慢騰騰地往停車場(chǎng)的出口方向移動(dòng)。突然，司機(jī)迅速發(fā)動(dòng)汽車，但隨即又立刻剎住。這時(shí)，運(yùn)鈔車司機(jī)只得停下車。埃米爾看到，那司機(jī)搖下車窗，沖著綠色貨運(yùn)車的司機(jī)破口大罵，隨后響起了槍聲。福特貨運(yùn)車?yán)锾聝擅凶?，他們把運(yùn)鈔車司機(jī)和副手拖出車外，關(guān)進(jìn)貨運(yùn)車廂，接著，只見兩輛車同時(shí)開走了。

埃米爾?雅恩克呆呆望著駛離的運(yùn)鈔車，他的百萬馬克就在剛才、在自己的眼皮底下被幾個(gè)陌生人輕而易舉地奪走了！等著瞧吧，我要給你們點(diǎn)兒顏色看看！埃米爾迅速把車開往大街，尾隨兩輛車行駛了兩百米左右的路程，接著便在最近的一間電話亭旁停了下來。他迅速撥通報(bào)警電話，一股腦兒地把親眼目睹的一切告訴了警方。

半小時(shí)后，警方逮捕了那三名男子，當(dāng)時(shí)他們正在停車場(chǎng)，準(zhǔn)備將那筆巨額現(xiàn)金搬進(jìn)一輛紅色大眾汽車。同時(shí)，埃米爾也選擇了一個(gè)安全的位置，遠(yuǎn)遠(yuǎn)地注視著這一幕。這是他們應(yīng)得的下場(chǎng)。誰都不能這么輕而易舉地從埃米爾?雅恩克手里奪走本該屬于他的東西。

那場(chǎng)襲擊行動(dòng)后的第六個(gè)周二，埃米爾?雅恩克去了趟警局，他受到了表彰，獲獎(jiǎng)九萬馬克。

米爾恩范文第5篇

小熊維尼的原型是英國(guó)動(dòng)物園里一只擅長(zhǎng)表演的黑熊，米爾恩的兒子克里斯多夫·羅賓每次去動(dòng)物園都要擁抱它，認(rèn)為它和自己的玩具熊一樣可愛。米爾恩用綿綿的父愛書寫了這些故事，這些有趣的故事廣受歡迎，很快成為世界經(jīng)典。這些書在英國(guó)重版了七十多次，并被譯成二十多種語言。迪士尼接拍這部著名的兒童文學(xué)作品后，小熊維尼一下子風(fēng)靡全球，成為全世界兒童的至愛。

小熊維尼的全部故事都發(fā)生在百畝森林里，這是一處“長(zhǎng)滿綠樹野草、開滿鮮花的土地”。故事里面的人物——小熊維尼、小豬皮杰、老驢伊爾、野兔瑞比、袋鼠小豆都是克里斯多夫·羅賓的玩具。說他們是“玩具”他們可能不太同意，因?yàn)樗麄儠?huì)思考“怎樣去迷惑蜜蜂”這樣難度很大的問題，會(huì)制定計(jì)劃去做“捉拿長(zhǎng)鼻怪”這樣驚心動(dòng)魄的事情，還會(huì)背詩、唱歌、種菜、探險(xiǎn)。他們雖然個(gè)頭、性格迥然不同，但是都以自己鮮明的個(gè)性，參與了羅賓多姿多彩的童年生活，怎么能說他們僅僅是“玩具”呢？

米爾恩毫無疑問是所有孩子的父親。他把每個(gè)孩子的特點(diǎn)都寫得很清楚，你只要看上三兩行就會(huì)了解每個(gè)孩子的“個(gè)性特征”：小熊維尼善良憨厚，特別貪吃；小豬皮杰膽小怕事；野兔瑞比勤勞謹(jǐn)慎，但是性格里明顯有些急躁和尖刻；老驢伊爾是一個(gè)很消極的朋友；跳跳虎總是不斷地跳動(dòng)以致于干擾別人的生活，而自己一點(diǎn)意識(shí)不到。米爾恩似乎特別擅長(zhǎng)寫這些孩子的“缺點(diǎn)”，事實(shí)上在百畝森林發(fā)生的很多故事，就是這些孩子們身上的“缺點(diǎn)”在不斷地“碰撞”，從而使他們的歷險(xiǎn)過程顯得跌宕起伏。

在“捉拿長(zhǎng)鼻怪”這個(gè)故事里，貪吃的維尼和膽小的小豬計(jì)劃捉拿長(zhǎng)鼻怪，商量好用維尼最喜愛的蜂蜜做誘餌，放在小豬皮杰挖好的陷阱里。結(jié)果貪吃的維尼晚上睡覺的時(shí)候惦記著“長(zhǎng)鼻怪會(huì)給我剩下一點(diǎn)嗎”，他“想象著每只長(zhǎng)鼻怪好像都是沖著他的蜂蜜來的，而且還把他的蜂蜜都吃光了”，“就這樣在床上痛苦地翻來覆去了好長(zhǎng)一段時(shí)間”，最后實(shí)在受不了了，跑到陷阱里，把只剩薄薄一小層的蜂蜜舔了一干二凈。

而他那個(gè)膽小的朋友小豬皮杰，一睜開眼睛，就“用勇敢而肯定的語氣”鼓勵(lì)自己，然后“用更響亮的聲音使勁地高喊”，終于大著膽子來到陷阱旁邊。這時(shí)候維尼因?yàn)椤耙坏螞]剩”吃完罐底的蜂蜜，腦袋不幸被困在蜂蜜罐里，“悲傷而絕望地在陷阱里哭喊”。小豬恰好往陷阱里看了一眼，讀者都以為這下維尼終于得救了?？墒沁@個(gè)膽小的家伙只瞄了一眼，“扯著嗓子”喊了兩聲“救命”，就“驚恐萬分，連忙掉頭用最快的速度飛跑了回去”，“一邊跑一邊大叫著救命”，以致于“臉色發(fā)白，舌頭發(fā)直，不停地喘著粗氣，有些口齒不清了”。讀者看到這里，忍不住笑出聲來。

米爾恩非常擅長(zhǎng)描寫人物的心理，把他們細(xì)微的心理活動(dòng)描繪得惟妙惟肖。當(dāng)小熊維尼看到老驢伊爾過生日沒有得到禮物而傷心時(shí)，準(zhǔn)備把自己最心愛的一小罐蜂蜜送給他。小豬皮杰馬上接口說：“我能不能也把這個(gè)送給他，作為我倆送給他的禮物？”寫出了孩子的天真可愛。當(dāng)伊爾聽到小豬皮杰“愧疚而難受”地告訴他準(zhǔn)備送給他的生日禮物氣球弄破了以后，“兩個(gè)人都沒有說話，很長(zhǎng)一段時(shí)間的沉默，老驢眼眶里裝滿了晶瑩的淚珠?！边^了好長(zhǎng)一段時(shí)間，老驢終于開口了，他努力擠出了一句話：“唉！我的氣球！我的生日氣球，沒了?！比缓笏謶涯畹貑枺骸斑@個(gè)氣球是什么顏色的——在它還是完整的氣球的時(shí)候？”“當(dāng)它還是完整的氣球的時(shí)候，它有多大？”非常傳神地寫出伊爾在聽說氣球破碎后那種失望的心情。在“初涉長(zhǎng)鼻怪”這個(gè)故事里，維尼和小豬一起談?wù)撓葳謇锓攀裁礀|西做誘餌，小豬提議放橡子，維尼想到放蜂蜜。這時(shí)候，小豬皮杰“腦子里突然閃出一個(gè)念頭：如果在陷阱里放橡子，那我就得到橡樹上去摘橡子；如果放蜂蜜，維尼就得拿出他的蜂蜜，哈哈，那我就省力多了?！庇谑切∝i皮杰說：“那好吧，就放蜂蜜吧。”“其實(shí)維尼這時(shí)也想到了這個(gè)問題，他正準(zhǔn)備說‘那好吧，就放橡子吧’，但是他晚了一步，只能無奈地同意了這個(gè)決定”。這么細(xì)致入微的心理描寫，這么傳神生動(dòng)的演繹，讓讀者都有心頭一動(dòng)的感覺。這些孩童狡黠的“小心眼”，我們恐怕都曾有過吧。從這一點(diǎn)上，這位兒童文學(xué)家真是一位心理描寫的大師！

我們看到了百畝森林里的孩子們這么明顯的缺點(diǎn)，也看到了他們彼此的小心眼，但是沒有感覺那是瑕疵或者缺陷，反而感覺他們那么可愛，那么純真，渾身散發(fā)著和我們童年幾乎一模一樣的氣質(zhì)和情趣。只有米爾恩這樣用慈父的柔情和細(xì)膩的童心，才能寫出這么精彩真實(shí)的兒童心靈世界。

在閱讀《小熊維尼歷險(xiǎn)記》系列叢書的時(shí)候，讀者總是懷疑米爾恩手里有一支點(diǎn)石成金的神筆。因?yàn)樗v述的故事情節(jié)是那樣的簡(jiǎn)單，那樣的生活化，可是他總能將平淡簡(jiǎn)單的情節(jié)變幻得搖曳多姿，妙趣橫生?！耙翣柕膬蓚€(gè)生日禮物”里，小熊維尼本來是準(zhǔn)備送一小罐蜂蜜的，可是他因?yàn)轲I了忘記了這是送伊爾的禮物，就吃完了所有的蜂蜜，只拿來一個(gè)洗干凈的蜂蜜罐子；小豬皮杰送給伊爾的禮物氣球在伊爾還沒有看到之前就爆炸成碎片了。這樣的情節(jié)讀者都覺得沒戲可看了，但是米爾恩天才的點(diǎn)化卻有了神來之筆：伊爾覺得這是一個(gè)太合適的罐子，“他用牙齒把氣球碎片銜了起來，然后小心地把它們放進(jìn)罐子里”，“然后又把氣球碎片從罐子里銜出來，小心地放在地上”?！耙翣枎е淇斓男那橐淮斡忠淮沃貜?fù)著這些動(dòng)作。”

伊爾的這個(gè)動(dòng)作，使他的兩個(gè)好朋友都很開心。維尼說：“我真是太高興了，我能夠送你一個(gè)這么有用的罐子，可以裝東西?！毙∝i皮杰說：“我也好高興，我能夠送你這么一個(gè)東西，你可以把它裝進(jìn)一個(gè)有用的罐子里?！薄暗且翣査坪醪]有聽見他們?cè)谡f些什么，只是專心地把那些五顏六色的氣球碎片銜出來，又放回去……再也沒有比這更開心的時(shí)候了……”

應(yīng)該說，再也沒有比這更好的結(jié)局了！對(duì)于孩子來說，快樂是最重要的，就算在你眼中破碎不堪毫無用途的東西，他們同樣能從中找到快樂，這就足夠了。

米爾恩塑造的“百畝森林世界”不僅環(huán)境優(yōu)美，長(zhǎng)滿綠樹鮮花，而且祥和快樂，自由寬松。米爾恩像一位慈父，精心守護(hù)著這片樂園。他對(duì)孩子們極為寬容，小熊維尼可以說“親愛的蜜蜂釀蜜的目的，就是讓我去吃它”；小豬皮杰可以說“袋鼠只有在冬天才會(huì)變得兇猛”，他們說什么話都是合情合理的，米爾恩默認(rèn)這些，而且含著微笑點(diǎn)頭贊同。他不允許孩子之外的“異聲”，不允許有成人的觀點(diǎn)去否定孩子們自由發(fā)散的思維。在那片冬天里會(huì)鋪滿白雪的百畝森林里，留下了孩子們各式各樣的腳?。荷畹臏\的，大的小的，充滿疑問的，歡聲笑語的，那是他們成長(zhǎng)的腳印。

成年人面對(duì)大自然的神奇莫測(cè)，經(jīng)歷人生的艱苦磨難，會(huì)不由自主發(fā)出“天問”，問天，問大自然，想窮極宇宙里無盡的奧秘。孩子們?cè)谠囂街~出人生第一步的時(shí)候，也會(huì)發(fā)出孩子們的“天問”，他們用的是白雪一樣純凈的心靈，發(fā)出的是天籟一般稚嫩的疑問。米爾恩給他們盡可能多的自由和關(guān)愛，讓他們嗅著好奇的空氣，踩著想象的空間，做著他們想做的事情。這樣，他們的思維才不會(huì)被固定，他們的個(gè)性才能夠充分釋放，他們成長(zhǎng)的路才會(huì)充滿主動(dòng)性和進(jìn)取心。