Study on the Numerical Simulation of the Flow of Splitter Blade Impeller

Transcription

1 Study on the Numerical Simulation of the Flow of Splitter Blade Impeller Long Shao, Xinli Wei 2,*, Xinling Ma 2, Xiangrui Meng 2 School of Chemical Engineering and Energy Zhengzhou University, Zhengzhou, China 2 Department of Process Equipment & Control Engineering Zhengzhou University Zhengzhou, China Abstract Objective: To study the numerical simulation of the flow of splitter blade impeller in a power generation system. Method: CFD software simulation, theoretical analysis. Process: The multi grid method, the local time step, the implicit residual average, the boundary conditions and the results of the model are introduced. The flow characteristics of the impeller are analyzed and the two flow and the vortex system are analyzed. Result& Analysis: Through the numerical simulation analysis of the two flow and the vortex system analysis found that the a low speed Maher number area and a more serious two flow are in flow channel inside, complex flow state to a certain extent increased the flow loss, and to reduce the impeller aerodynamic performance. Result: The numerical analysis results are beneficial to the improvement of the split vane impeller of radial turbine. Keywords-numerical simulation; splitter blade impeller I. INTRODUCTION With the rising of the global energy price and the increasingly serious environmental pollution, energy saving and emission reduction has received more and more attention. []Centripetal turbine using the Coriolis force acting loss, with larger single stage power ability and high efficiency, coupled with has the advantages of compact structure, simple manufacturing process, and under the design condition of small flow rate still high efficiency and other advantages. It not only in aerospace, steam turbine, gas turbine, turbochargers need compact power source in the field is very significant and substantial was used to as refrigeration and apparatus for the liquefaction of natural gas turbine expander, as the recovery of mass energy and waste heat of gas expansion machine is widely application in all fields of energy saving. [2] In the ultra low temperature engineering the radial turbine has become the only form of the turbine expander used. [3] A. Development of Radial Turbine in Power Generation System In 939, German scholar Ohain Hansvon used to design the first jet engine. In recent years, with the expansion of new materials, micro machining and other fields, the production of various kinds of air vehicles is increasing, which is to meet the requirements of high energy storage, high power weight ratio. [4]With the actual needs of the drive, the radial impeller in the aviation field is used for micro turbine engine, rocket engine with the turbine pump, engine auxiliary power device and other equipment. For example, the diameter of the micro engine developed by Nanjing University of Aeronautics & Astronautics is 60mm, which uses the size of blade type radial impeller diameter is only 38mm (Fig. ). [5] Figure. MTE-A micro engine profile The centripetal turbine consists of turbine stator and rotor blades of impeller. [6] Turbine stator is divided into leaves and leaf free form and its components including the volute and nozzle ring, spiral case is generally cast, volute are usually equipped with nozzle ring, to ensure that the steam into the size and direction of the impeller speed. The radial turbine has a low requirement for the aerodynamic performance of the blade, even if the geometry of the blade is not very accurate, and the surface roughness of the blade is poor, and the efficiency of the turbine is not too large. [7] Therefore, the impeller is a precision casting or directly on the impeller milling molding. Although the years ago has emerged small radial steam turbine, but due to the energy price is cheap, as well as high speed transmission gear, impeller material strength, high speed bearings and other technical problems, making this type of high efficiency steam turbine has not been commercially used, until the early eighty's, with the smooth solution of the DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

2 above technical problems, coupled with the energy crisis caused by fuel price increases, so that the high efficiency of small power steam turbine to promote application. [8] In the future electric power industry, the micro gas turbine power generation system based on the radial turbine will play an important role, and the American ASME vice president Langston has pointed out in the 999 annual gas turbine industry review. [9] Radial turbine because of its low inlet temperature and high air / fuel ratio in the combustion chamber, NOx emissions are low (<9mg/kg), while the internal combustion engine emissions will exceed the NOx Z000mg/kg, in the case of the same power output, the radial turbine is better. [0] In 2002, the national science and Technology Department of the 863 planned energy technology field office will be micro gas turbine research and development as the "863" plan major projects. [] Currently at home and abroad for more and more studies on the centripetal turbine, hunt sman and Hodson et al of centripetal turbine rotor impeller at design and off design point boundary layer development do a lot of research; dambach study the centripetal turbine tip clearance leakage flow, radial turbine leakage loss is less than that of axial flow turbine; Khalil influence of centripetal turbine guide leaf internal friction loss and mixing loss mixed; [2] given Bhinder a simple turbine design method that. In China, such as hot spring meter of the centimeter scale micro aero engine radial turbine, and its experimental study and numerical simulation. The aerodynamic design method of the radial and oblique flow turbine was studied by Miao Fuxiang. Fengzhen Ping, Shen Zuda, et al. [3] Compared with the radial turbine and the axial flow turbine, the flow is more complex due to the bending of the flow channel and the two flow and the vortex system. Within the turbine, the two flow and vortex motion is one of the main reasons for the loss of flow. In this paper, a numerical simulation method is used to study the internal flow of the radial turbine, and the evolution and development of the two flow and the vortex system in the radial turbine passage are analyzed, which provided the basis for controlling the flow loss and designing the high performance of the radial turbine. [4] The radial turbine is composed of a spiral case, a nozzle ring vane, or a blade of a blade, and an impeller. In Fig. 2, the C0 of the radial impeller profile has a certain pressure P0, temperature T0 and the speed of the gas is preferred to enter the spiral case, the gas will be directed to the nozzle ring by the spiral case, and the gas expansion is accelerated. At the exit of the nozzle ring, the gas flows out from the angle of the circumferential direction of the l, the absolute velocity is C, the corresponding pressure and temperature are P and T. Along with the gas flows into the rotation of the impeller, impeller inlet air relative velocity W. in the impeller channel, gas expansion process of acting, the outflow from the impeller, relative velocity increased to W 2, corresponding to the absolute speed C 2, the circumferential velocity U 2. The pressure and temperature were reduced to P 2 and T 2. In Fig.3 showed that the impeller inlet and outlet flow velocity triangle. Figure 2. Schematic diagram of the radial impeller Figure 3. impeller inlet and outlet velocity triangle II. FLUID CONTROL EQUATIONS The flow field in the initial impeller passage can be a constant flow, and the gas flow is constant. In the Descartes coordinate system with the angular velocity of W, the calculation module of the NUMECA software is applied to the N-S equation with the Favre equation. A. Conservation N-S Equation Fluid flow follows the conservation law, which can be expressed in the form of control equation. Mass conservation equation: ( ui ) 0 () t xi Momentum conservation equation: DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

3 ( ui) ( uu i j) p ij Fi (2) t xj xi xj Forum (2) is called Navier-Stokes (N-S) equation, which is the main control equation to be solved in numerical simulation. P is the pressure exerted on the element, is the effect of the element on the surface of the viscous stress, viscous stress is generated due to the molecular viscosity; F is the volume force acting on the element. Newton fluid and non Newton fluid were established on the. When the gravity is not considered in the calculation, the F=0. For Newton fluid, the viscous stress is proportional to the deformation rate of the fluid, which is expressed as follows: ui uk ii 2 xi xk (3) u u i j ij x j x i Wherein, refers to the dynamic viscosity, refers to the viscosity of second, generally desirable 2/3. B. Favre Averaged N-S Equation For the density of the fluid, the NUMECA software is used to describe the turbulent flow in the N-S equation. The combined action of two kinds of flow, the time averaged and instantaneous, and the C of any physical quantity is: (4) Wherein, is the instantaneous value, is the last means, is the pulse value. C. Turbulence Model The core of S-A is to select relevant variables v, turbulent viscosity coefficient is obtained by calculating the transport equation containing v. Turbulent viscosity coefficient t can be expressed as: ˆ (5) Wherein, f vf v 3 3 Cv t 3. v ˆv (6) v Wherein, ˆv is the turbulent motion variables, which is obtained through S-A equation; V is laminar viscosity coefficient, C v as the model constants. Because in the wall to the logarithm of the memory in a relationship, so the definition of variables, the ky wall near the variable ˆv and away from the wall distance is linear change, such as turbulent dissipation rate epsilon turbulence quantitiesε, ˆv is more easy to solve. The formula for calculating the mesh precision is reduced, and it can meet the requirement of the algebraic model. Variable ˆv meeted the following transport equation: vˆ V v ˆ ( v ( c ˆ 2) ˆ ˆ b v c b2 vv Q t Wherein, V is velocity vector; Q as the source term, which is composed of the production term and the dissipation term. III. NUMERICAL SIMULATION METHOD A. Multigrid Method In this paper, the use of multiple grid technology to reduce the numerical error and shorten the convergence time. The basic idea of multi grid technique is that the iterative calculation is carried out on the fine grid first, and then the intermediate results are applied to the coarse mesh, so that the low frequency error can be attenuated more quickly. The grid can reduce the flow field scanning and shorten the time of calculation. After the calculation results of the coarse grid are returned to the fine grid, the error in the high, medium and low frequency errors can be reduced to a satisfactory result in the process of iteration, which can reduce the error of numerical calculation and shorten the convergence period. In the calculation of multiple samples, the multi grid technique can be easily used in the uniform grid, and the "first coarse and fine" is selected, and the optimized sample can be obtained in a relatively short time. At the same time, in order to avoid the calculation error caused by different mesh, the uniform topology and grid node distribution are used in the calculation of the subsequent optimization process. The number of meshes in the use of multiple grid techniques should meet certain requirements. 2 n n (8) 2 B. Local Time Step In this paper, the explicit time marching method is used in the calculation of this paper, and the equation is solved by multi-step Runge-Kutta. Because of the need to meet certain stability when solving the hyperbolic equation, this means that the time step size t is constrained by the CFL condition. Because the information dependence domain is required to be covered by a time interval, in which the propagation distance of the characteristic wave can not be greater than the length of the grid in the direction of a time step t. Time step t need to be a function of the grid. For viscous flows, the maximum and minimum mesh size is 08. In order to ensure the stability of the flow field calculation, the time step size t need to select the minimum grid size limited time step, the smaller the value makes the calculation convergence need a lot of time step, it is greatly increased the amount of calculation. However, in the calculation of the constant flow field, the time discretization and the space integral are not mutually (7) DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

4 affected. The constant solution is independent of the time step. Therefore, in the condition of the local CFL condition, the t can choose the maximum time step, to accelerate the flow field information transfer, to achieve the purpose of accelerating convergence. This method is called "local time step" method. The local time step is calculated when the viscous flow is calculated: t CFLVIS V 8 Si Sj Sk 2 SiSj SiSk SjSk (9) Wherenin, Subscript "V" is Viscosity;, the local laminar flow viscosity coefficient, and the sum of the local laminar flow and turbulent viscosity coefficient of turbulence; CFLVIS indicates that the viscous CFL number; is the control volume, is the control volume; Si, S j, Sk represent direction i, j, k of the grid center of the normal vector, the value of the grid area. C. Implicit Residuals Explicit Runge-Kutta formula can be expressed as a general form: m m m m m U U m tf( U ) U mr( U ) (0) Before using the formula, the R of the original display format can be found to be smooth, and the average residual R is obtained by using the central difference operator: ii j jkk R R () Wherein, i, j, k are represented as three directions i, j, k on the smooth coefficient; i, j, k are central difference operator. A can be determined: 2 l R Rl 2Rl Rl (2) Different definition of smooth coefficients corresponding to different residual smoothing method. In this paper, the constant pressure flow is calculated, and the Swanson-Turkel method is used for the NUMECA software: * l * * * * ( ( l / l l / l ) ) * Wherein, l i, j, k,, are CFL of the number of * the light respectively ; l is the spectral radius, which is defined as: * l ( unc) S l (5) D. Boundary Conditions The setting of boundary conditions determines the results of numerical simulation. In the NUMECA, the boundary conditions include: import, export, solid wall, periodic boundary and other forms of interface, etc.. In this paper, the boundary conditions are as follows. Inlet boundary: the total pressure, total pressure, total temperature and absolute flow angle Vr / V, Vt / V are applied in the Fine/Turbo module. Wherein, V r and V t are the absolute velocity components of the air flow in the radial and circumferential directions, and the V is the modulus of the absolute velocity. The exit boundary: the static pressure is applied in the Fine/Turbo module, and the static pressure value of a given static pressure along the radial direction is worked out. Solid wall: setting boundaries to meet the conditions: () solid wall flow infiltration and there is no relative slip; (2) stationary objects on the surface, the absolute velocity is zero; (3) to rotate the surface, the relative velocity W r, according to the right-hand rule judgment positive and negative direction of rotation. In the threedimensional flow field of the impeller, the casing is stationary, the blade surface and the hub rotate. E. Convergence of Calculation Results In this paper, the convergence of the results is determined by the following requirements: () the global residuals shall not be less than 3 orders of magnitude, as shown in Fig.4. (2) the quality of the inlet and outlet is stable, and the relative error is less than 0.5%, as shown in fig.5. (3) in the steady calculations, impeller overall performance (pressure ratio, efficiency, etc.) are nearly constant, with the increase of number of transport stack changes. (4) in the flow channel, the performance parameters of the impeller are periodic oscillations. Figure 4. Residual convergence curve DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

5 Figure 5. Convergence curve of mass flow IV. IMPELLER MODEL ESTABLISHMENT AND ANALYSIS DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

6 Figure 6. Frame diagram of numerical simulation of the impeller A. Impeller Mesh Model The impeller model is shown in Fig. 7. In view of the periodicity of the blades, a single channel mesh model of the impeller is constructed in AutoGrid. Turbine impeller grid by H-I type grid, along I to cross the direction of the blade), J (leaf height direction) and K to (the flow direction of the main grid density for 57 x 65 x 65; blade leading edge and trailing edge are treated for bluff body, being arranged in the direction of the pitch of the grid were 7 and 25 tip clearance and distance values were 0.6 mm, gap within grids along the axial and radial density for 7 * 7, total grid number at around 48 million. In the process of calculation, local encryption of the near wall, end wall and the front end of the region, and enhance the resolution of these complex areas of flow. Grid quality largely determines the reliability of numerical simulation. Grid quality is usually judged by the standard: Orthogonal, length and width ratio. In order to minimize the influence of the numerical error, the NUMECA requires that the mesh is not less than 5 degrees, and the length and width ratio is less than 5000, and the extension ratio is less than 0. In this paper, the minimum of the mesh quality is 0.0, the ratio of length to width is 68 and the maximum of the extension ratio is 2.7. The main body of the impeller is shown in Fig.8. Figure 7. Initial impeller model Figure 8. The main grid of the impeller For viscous flow, boundary layer loss in the flow loss accounted for a large proportion. When the boundary layer flow is treated, the first grid height of the boundary layer within the boundary layer is considered. The non dimensional grid scale y+ is introduced. The definition of y+ is: y yu t v (6) Wherein, y is the first layer grid thickness (m), ut is the friction velocity (M / s), V for the value of kinematic viscosity coefficient (m 2 / s);.y + vary according to the model of turbulence by spalart allmaras model, y + between -5 value. The first layer thickness y can be expressed as: 7 8 L 8 ref Vref y 6 y (7) v 2 Wherein:A - referenced speed, take the impeller inlet fluid radial velocity (m/s). B - referenced feature length, leaf blade inlet height (m). V -- kinematic viscosity coefficient (m2/s). If y + =, the y=0.0mm was calculated. B. Grid Independent Verification In numerical simulation, the grid independence is needed to determine the number of the grid and the results are not related. Carries on the grid division of the initial impeller model. Due to the flow field inside the impeller is mainly affected by the direction I (cross direction of the blade), J direction (leaf height direction) of grid, this change I, j in both directions on the sparse grid, keep K directions (streamwise direction) of grid nodes do not change, four sets DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

7 of different density of grid is calculated, as shown in Table.. TABLE.I DIFFERENT GRID SCHEME Plan Plan 2 Plan 3 Plan 4 Direction I Direction J DirectionK Total grid Efficiency(%) Flow whole flow is smooth, and the pressure side of the impeller leading edge is separated, which is caused by the horseshoe vortex formed at the leading edge of the impeller, which corresponds to the Maher number of the separation position is low. At the height of the 90% leaves, the air flow in the suction side of the impeller has been extended to the impeller outlet, and the Maher number of the whole channel region is higher than 0% and 50%, which is caused by the leakage flow of the tip gap. As can be seen from Table., the number of grid from to , the impeller efficiency, the increase in the number of flow with the grid is very small, the impact of the basic is not affected by the number of grid. It can be seen that the grid has reached to independent set nets lattice. C. Analysis on Flow Characteristics of İmpeller Fig. 9 shows the dimensionless static pressure distribution on the pressure surface and suction surface of the impeller. From the diagram (a) can be seen, in the pressure surface, isobar uniform distribution, basic vertical air flow. In (b) in a graph, air flows through the suction surface and by meridional curvature, leaf curvature effect larger isobars at the impeller inlet flange at the crossing of impeller passage extending from the hub and the emergence of significant bending, located close to the rim and impeller outlet part of the low pressure region, the CIS pressure gradient appears from the hub point to rim trend, it will exacerbate the trend of the secondary flow. (a)0% leaf height (a) pressure surface (b) suction surface Figure 9. static pressure distribution of the impeller D. Two Flow and Vortex System Analysis of the İmpeller Passage Fig. 0 shows the relative Maher number distribution in different leaves, and gives the corresponding limit flow chart. In 0% blade section, along the direction of 40% - 60% of the chord strengths close to the pressure side there is a low velocity zone, where flow is affected by the pressure gradient, to reflex of the pressure side flow and separation lines close to the pressure side of the intersection. It is shown that there are two phenomena of mixing in the passage vortex. In the 50% leaf high cross section, the (b) 50% leaf height Figure 0. Relative Maher number distribution, continued on next page DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

8 leakage vortex at the tip of the blade. In the same place at the root of the impeller, there is a passage vortex. When the air flow through the large turning to the Cut3, the flow of the air flow to the middle shift, the tip of the leaf tip leakage is less than cut2. At cut4, the flow of the channel is shifted to the hub, and the area of the vortex is reduced. To the near exit cut5, there is no vortex system in the impeller, the majority of the air flow from the pressure to the suction surface flow. Through the analysis of the vortex system in the flow channel, we can see that there is a strong vortex at the turning radius, and there is a leakage flow at the tip of the blade. On the whole, there is a serious phenomenon of the two flow in the process of gas flow, and the complex flow state can increase the flow loss and reduce the aerodynamic performance of the impeller. Therefore, the impeller type line still has the space to optimize and improve the aerodynamic performance of the impeller. (c)90% leaf height Figure 0. Relative Maher number distribution In this paper, we take the initial impeller five vertical section of meridional streamline, each section is given in the streamline patterns to analyze flow distribution inside the impeller. Fig. gives a schematic diagram of the flow channel cut,cut2, Cut3, cut4, cut5, five cross sections are located in0l, 0.3L, 0.5L, 0.7L, L. (a) cut Figure. Meridian streamline section Fig.2 shows the flow chart of each section. Each side of the cross section of the pressure surface, the right side of the suction side, the impeller rotates around the axis. In cut section, central air flow from the pressure surface transverse flow to the suction surface, suction side wall surface of the gas to the middle runner migration, two stocks in the opposite direction airflow merged each other mixing flow to the tip. In the cut2, there is a large size of channel vortex inside the channel, there is a strong channel vortex and (b) cut 2 Figure 2. section flow chart of impeller passage, Continued on next page DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

9 (c) cut 3 V. CONCLUSIONS In this paper, the theoretical basis of the numerical calculation of the radial impeller is introduced, and the convergence of the flow control equation, the numerical calculation method and the results are given. The initial model of the impeller is established, and the internal flow field of the impeller is analyzed. Through numerical simulation analysis of the two flow and the vortex system in the impeller, the flow loss is increased and the aerodynamic performance of the impeller is reduced in some extent. The main conclusions are as follows: the flow loss of the low velocity zone and the more severe two flow in the channel: () the limit line of the solid wall shows that the flow is more complicated and the flow is more complex in the inlet of the moving blade near the inlet of the moving blade, and the reflux phenomenon occurs in the centrifugal field. Near the exit, on the suction surface are secondary flow in the direction of the tip, which will weaken the fluid here to resist adverse pressure gradient, overcome separation ability. (2) due to the gap between the flow direction and the top of the passage vortex, the right amount of gap flow can play a role in a certain extent to weaken the vortex intensity and improve the flow of the top of the channel. ACKNOWLEDGMENT This work is supported by The Key Scientific and Technological Planning Projects of Henan Province ( ); The Education Department of Henan Province Science and Technology Research Projects (5A480002). (d) cut 4 (e) cut 5 Figure 2. section flow chart of impeller passage REFERENCES [] Guo X, Zhu Z, Cui B, et al., Effects of the short blade locations on the anti-cavitation performance of the splitter-bladed inducer and the pump, Chinese Journal of Chemical Engineering, vol. 3, NO., pp. 2-9, 205. [2] Yang W, Xiao R, Wang F, et al., Influence of splitter blades on the cavitation performance of a double suction centrifugal pump, Advances in Mechanical Engineering, vol. 6, NO., pp , 204. [3] Guo Z, Song L, Zhou Z, et al., Multi-Objective Aerodynamic Optimization Design and Data Mining of a High Pressure Ratio Centrifugal Impeller, Journal of Engineering for Gas Turbines and Power, vol. 37, NO. 9, pp , 205. [4] Guo X M, Zhu L, Zhu Z C, et al., Numerical and experimental investigations on the cavitation characteristics of a high-speed centrifugal pump with a splitter-blade inducer, Journal of Mechanical Science and Technology, vol. 29, NO., pp , 205. [5] Heo M W, Kim J H, Kim K Y., Design Optimization of a Centrifugal Fan with Splitter Blades, International Journal of Turbo & Jet-Engines, vol. 32, NO. 2, pp , 205. [6] Kaneko M, Tsujita H., Numerical investigation of influence of tip leakage flow on secondary flow in transonic centrifugal compressor at design condition, Journal of Thermal Science, vol. 24, NO. 2, pp. 7-22, 205. [7] Liu J, Zhao X, Xiao M., Study on the Design Method of Impeller on Low Specific Speed Centrifugal Pump, Open Mechanical Engineering Journal, vol. 9, NO. 9, pp , 205. DOI 0.503/IJSSST.a.6.2A ISSN: x online, print

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