coefficient and streamlining of boundary layer separation area. Keywords: diffuser, flow separation, finning, CFD, flow structure. INTRODUCTION. The diffuser ...
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 22 (2016) pp. 11081-11088 © Research India Publications. http://www.ripublication.com
CFD investigation of flow in finned plane and conical diffusers A.E. Zaryankin, I.V. Garanin, V.P. Khudyakova, V.O. Kindra1 and E.M. Lisin National Research University “Moscow Power Engineering institute” Krasnokazarmennaya str. 14, 111250, Moscow, Russian Federation.
Abstract In this paper, based on numerical flow simulation the investigation of longitudinal finning of diffusers influence on flow structure and parameters, accompanied by boundary layer separation from channel walls. The plane asymmetric diffusers with opening angle 7.5°, 8.5°, 10°, 15° and conical diffusers with opening angle of 15° and 20° was considered. Various forms of longitudinal fins was examined. It is found that a positive impact on flow parameters depending on the fin type can be provided, namely the small increase in pressure recovery coefficient and streamlining of boundary layer separation area. Keywords: diffuser, flow separation, finning, CFD, flow structure. INTRODUCTION The diffuser channels are essential structural elements of flow path of many energy machines. For example, they are applied in exhaust hoods of steam and gas turbines. Boundary layer separation occurred at certain opening angle of the diffuser. The presence of this phenomenon radically changes flow structure and leads to an increase of loss coefficient due to the additional energy cost for the formation, maintenance and development of eddy currents. However, the unsteady nature of this flow leads to a sharp deterioration of the diffuser vibration state, which causes additional dynamic loads on wall. The reliability of the elements with diffuser channels operating in regimes involving boundary layer separation, as a rule, is much lower than with channels without flow separation. In this regard, the investigation of structure and parameters of flow in diffusers is accompanied by boundary layer separation. The study of flow structure in plane asymmetric diffusers was carried out in [1]. This article is based on the results of numerical and experimental investigations of flow in a diffuser with the opening angle equal to 8.5°. The article adequately descfines characteristics and structure of flow. The work [2] is dedicated to the study of plane asymmetric diffusers with the opening angle of 10°. Methods for the prevention of boundary layer separation due to the change of opening angle of a plane diffuser descfined in the article [3]. Original research of plane asymmetric diffuser with the cross finning are shown in the paper [4]. The work [5] celebrates the numerical study of turbulent flow in a conical diffuser. The flow investigation in a conical diffuser with swirling flow is dedicated to the work of [6]. The work [7] proposes a method of improving the diffuser performance due to the change in shape of the outer perimeter. In general, we can conclude that the flow in a plane and conical diffusers investigated in sufficient detail with the use of numerical methods and physical experiments. Now it is
suggested to implement the effect on structure and parameters of separating flow by geometric effect in two ways: by changing the opening angle and shape of the outer perimeter of channel. At present, the use of fins was investigated only in event of transverse arrangement to the flow direction. In this regard, it is necessary to find new ways to improve the diffuser aerodynamic characteristics. To resolve this issue, it is proposed the method allowing to improve aerodynamic characteristics and to decrease vibration impact by the prevention of flow separation or decreasing the intensity of eddy currents [8, 9]. The new method consists in installation of special fin system to the diffuser wall in the longitudinal direction to the flow. This method was investigated experimentally in [10, 11]. However, in these works only integral parameters and diffuser vibration state are estimated. Effect of longitudinal finning on flow structure has not been descrined yet in the existing literature. This article focuses on description of changes in flow structure and investigation of different finning methods influence on flow.
THEORETICAL BACKGROUND Analysis of power factors, determining flow within the boundary layer, is based on the averaged Prandtl equations written for a plane flow: u dp u u , x y dx y p 0, y
(1) (2)
where u, ʋ – vectors projection of the velocity ̅c on the coordinate axes; ρ – density; x, y – coordinates; τ = τm + τt – the total friction stress within the boundary layer; τm = μ u – molecular friction stress; y μ – viscosity coefficient; τt – turbulent shear stress. At the outer edge of boundary layer following equation is performed: 0 . Thus, equation (1) becomes the Euler y
equation for a plane flow of ideal fluid. Further, next equation is performed for streamlined surface, following from equation (1):
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 22 (2016) pp. 11081-11088 © Research India Publications. http://www.ripublication.com
dp dx y
.
(3)
y 0
It is possible to obtain balance equation of all forces acting on the elementary fluid particles moving within the boundary layer by multiplying equation (1) on elementary volume of fluid dV = dxdydz: dFp = dFτ - dFu
(4)
The external force caused by the longitudinal pressure gradient is balanced by the friction and inertial forces in the equation. If the power dFp, according to a second Prandtl equation, does not change in cross section of boundary layer, the values dFτ and dFu always change in such way that their algebraic sum remained constant in any cross section of the boundary layer and equal to the force of external influence dFp. Accordingly, the movement of fluid along streamlined surface is nonseparable, while specified condition, i.e., the strain plots from distfinution of forces dFτ and dFu under an influence of external effects (geometric effects in this instance) provides the compensation of the force dFp. Likewise, the friction force dFτ changes in the boundary layer cross-section. Expression analysis leads to the conclusion that in the flow area of diffuser at a distance y < yc the frictional force pointed in the direction of liquid motion, namely the overlying layers at this distance carry away with them the underlying (inhibited) layers of liquid, thus providing the possibility in principle unseparated flow with a positive pressure gradient. If we now summarize the distribution of all forces acting within the diffuser boundary layer, when non-separable flow
always have to be realized over the power factors balance determined by the equation (4). Distance from the wall yc, on which a positive value of the transverse friction stress gradient (friction force dFτ) is stored, providing fluid possibility to move in the wall region against the force dFp, acting in the opposite direction, directly depends on the magnitude of positive pressure gradient. The more the longitudinal pressure gradient, the greater is value of the coordinate yc. In other words, the value of yc determines the degree of response of moving fluid on the external effect (geometrical effect in this instance) defined by pressure gradient. However, the ability of flow response to the external effect has certain limits, exceeding of which leads to flow separation. At the surface, where the speed is always zero due to "sticking" hypothesis (ie, the inertial forces are absent), the value y y 0 is the only form of flow response to an external geometric effects. Accordingly, the wider the range of possible changes of the transverse friction stress gradient, the more the maximum permissible value of the positive longitudinal pressure gradient dp , at which continuous flow can be implemented in diffuser dx
channel. In particular, the transverse friction stress gradient can be substantially increased by the longitudinal finning of streamlined surfaces of diffuser channels.
CFD DESIGN APPROACH. INVESTIGATED MODELS There were constructed and investigated 14 models: 6 basic models (without fins) and 8 models with longitudinal finning. The total list of basic parameters is shown in table 1.
Table 1: Investigated instances N 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Type Plane baseline Plane baseline Plane baseline Plane baseline Conical baseline Conical baseline Plane finned Plane finned Plane finned Plane finned Plane finned Plane finned Conical finned Conical finned
Name Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case 7 Case 8 Case 9 Case 10 Case 11 Case 12 Case 13 Case 14
Angle 7.5° 8.5° 10° 15° 15° 20° 15° 15° 15° 7.5° 8.5° 10° 15° 20°
The first group of basic models (Cases 1-4) includes four instances of plane asymmetric diffuser with a different opening angle. An image of plane diffuser three-dimensional model with the opening angle of 15° depicted on a Fig. 1 a. The second group of basic models (Cases 5-6) contains two versions of conical diffuser with the opening angles of 15° and 20°. Fig. 1 b
Fining type – – – – – – At outlet At inlet At Whole diffuser At outlet At outlet At outlet At outlet At outlet
Fin length – – – – – – 170 mm 100 mm 270 mm 170 mm 170 mm 170 mm 140 mm 150 mm
Fin height – – – – – – 5 mm 5 mm 8 mm 5 mm 5 mm 5 mm 2 mm 2 mm
shows an image of conical diffuser three-dimensional model without finning. According to the calculations results of plane diffusers, the most pronounced boundary layer separation was obtained in the diffuser with the opening angle of 15° (Case 4). In this regard, this variant was the basis for the investigation of fin system location influence. Options from 7 to 9 differ by fins
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 22 (2016) pp. 11081-11088 © Research India Publications. http://www.ripublication.com location (Fig. 2). In Case 7 fins are applied only in the central part of diffuser output. Case 8 has an input finned section. In Case 9, fins are arranged over the entire length of diffuser channel. The main parameters of fins were chosen in accordance with the recommendations contained in [11]. The used fins are wedge-shaped, fin height increases linearly along the channel length. The most successful way of the diffuser
finning with an opening angle of 15° is applied in Cases 10-12. Variants from 10 to 12 differ from each other by opening angles and they are designed to identify whether the same effect on flow parameters is exerted by longitudinal finning, when opening angle changes. Cases 13 and 14 have the same character of finning as Case 7, but they are used for conical diffusers with different opening angle: 15° and 20°.
a) plane asymmetric diffuser with the opening angle of 15°
b) conical diffuser with the opening angle of 15°
Figure 1: Examples of basic models
Case 7
Case 8
Case 9
Figure 2: Variants of plane diffuser finning The construction of three-dimensional models was carried out using SolidWorks software. Computational meshes for all the studied instances were built using the program ANSYS ICEM. All meshes are unstructured. They consist of two elements types: tetrahedral elements for the main volume, prismatic elements for the boundary layer regions. The size of computational meshes approximately equal to 6-8 million cells. Number of prismatic layers: 13-15. While mesh creating, an area of flow separation as well as finned surfaces and the space between them were additionally reduced compared to the main volume of mesh for the reason to obtain more accurate and stable solutions. Examples of computational meshes for different models are presented in Fig. 3. Flow simulation in the plane diffuser was carried out using the software package ANSYS CFX. The boundary conditions for all tasks were the same (Fig. 4). Nonuniform velocity field of developed flow was applied on the input section of the model. This field was obtained by flow calculation in a rectilinear channel of large length (L/d > 50). The outlet boundary
condition was static pressure. Turbulence model – k-omega. The flow characteristics were estimated qualitatively by visualization: velocities and pressures fields construction in control planes of the models, streamlines construction. To quantify the efficiency of diffuser, the distribution of pressure recovery coefficient CP was determined along its length according to the formula (1).
CP
p 2 p1 , 1 c12 / 2
(5)
where p1, p2 – pressure at the inlet and outlet of diffuser, Pa; ρ1 – density of medium, kg ; m3
c1 – flow velocity at the diffuser inlet, m . s
The parameters were recorded on the control surfaces, the location of which is presented in Fig. 5.
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 22 (2016) pp. 11081-11088 © Research India Publications. http://www.ripublication.com
a) plane asymmetric diffuser with the opening angle of 15°
b) conical diffuser with the opening angle of 15°
Figure 3: Computational mesh for the plane and conical diffuser model with α = 15°
a) plane asymmetric diffuser with the opening angle of 15°
b) conical diffuser with the opening angle of 15°
Figure 4: Boundary conditions
Figure 5: Location of the control planes of measurement
RESULTS AND DISCISSION The results of investigation of pressure recovery coefficient CP changing along the length of plane finned diffuser shown in Fig. 6. It can be seen that for Cases 1, 2, 3 considered characteristic behaves in a similar way. When α = 7,5° (Case 1) there is a slight flow separation, which is localized near the outlet section of the model. When an opening angle is 8.5°, the secondary flows progress. Further, with increasing of opening angle α, region occupied by the separated flow is increasing and when α = 15° it already takes a large space inside the diffuser channel (Fig. 7), thereby deteriorating the characteristics of his work.
To study the effect of finning location, the variant with the opening angle of 15° was selected as an instance with the most complex and developed secondary flow. For this purpose fins has been applied for the basic model fins: at the end of diffuser (Case 7), at the input region (Case 8), at the entire section of diffuser (Case 9). The analysis of pressure recovery coefficient values along diffuser length (Fig. 8) allows to conclude, that the fin installation does not significantly improves efficiency of diffuser. For all finning variants, except Case 7, energy loss has been increased. For Case 7 we have parity values in comparison with the base model. The flow region occupied by secondary vortices slightly decreases. The flow separation equally presents for the basic and finned models (Fig. 7).
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 22 (2016) pp. 11081-11088 © Research India Publications. http://www.ripublication.com wall of diffuser caused by flow separation. 0.4 0.4 0.3
0.2
Сp
Cp
0.3
0.2 0.1 0.1 0.0 0.0
0.2
0.4
0.6
0.8
1.0
y/L
0.0 0.0 Case 1
0.2
0.4 Case 2
y/L
0.6 Case 3
0.8
1.0
Case 4
Case 4
Case 7
Case 8
Case 9
Figure 8: Pressure recovery coefficient along diffuser length with different variants of fin system for the plane asymmetric diffuser with the opening angle of 15°
Figure 6: Pressure recovery coefficient along diffuser length for different opening angles of the plane asymmetric diffuser
Figure 7: The streamlines in the plane asymmetric diffuser with the opening angle of 15° (Case 4) The effect of finning on flow structure was estimated by analyzing the position of streamlines in diffuser (Fig. 9). It is worth noting that in all finned models the formation of structured flow is observed. Despite the fact that the center of gap shifts slightly, the whole area of separated flow becomes more stable, leading to a decrease of pressure pulsations on the
The result of applying of the same fin system as for Case 7, in plane diffusers with smaller opening angles shown in Fig. 1012. For the plane diffuser with the opening angle of 7.5° (Case 10) fins application significantly aggravate characteristics (Fig. 10). In this instance, the use of fins doesn’t lead to characteristics reduce and separation area structuration, but leads to the secondary flow formation, which arise earlier and more intensive. Similar pattern is observed for the diffuser with opening angle of 8.5° (Case 11). With further increase of opening angle, the negative effect of fins becomes less significant. When the opening angle is 10°, the line showing the change in pressure recovery coefficient along the diffuser length for instances with and without fins are almost identical. In this regard, we can conclude that the effect of fins of one configuration leads to a significantly different influence on the diffuser parameters. For the opening angle of 7.5° the pressure recovery coefficient for finned diffuser significantly worse than for the base, which isn’t finned. With the opening angle increase, the negative effect is gradually reduced, and for the opening angle of 15° the parameters of finned diffuser become slightly better than for non-finned.
а) Case 4
b) Case 7
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 22 (2016) pp. 11081-11088 © Research India Publications. http://www.ripublication.com
c) Case 8
d) Case 9
Figure 9: The streamlines in a plane asymmetric diffuser with the opening angle of 15°
0.4
0.3
0.3 Cp
Cp
0.4
0.2
0.2 0.1
0.1
0.0
0.0 0.0
0.2
0.4
Case 1
y/L
0.6
0.8
0.0
1.0
Case 10
0.2
0.4 y/L
Case 3
Figure 10: Pressure recovery coefficient values along the length of plane diffuser with the opening angle of α = 7.5° for the base instance (Case 1) and the variant with fins (Case 10)
0.6
0.8
1.0
Case 12
Figure 12 Pressure recovery coefficient values along the length of plane diffuser with the opening angle of α = 10° for the base instance (Case 3) and the variant with fins (Case 12) 0.5
0.4 0.4 0.3 Cp
Cp
0.3 0.2
0.2
0.1
0.1
0.0 0.0
0.2 Case 2
0.4
0.6 y/L
0.8
0.0
1.0
0.0
0.2 Case 5
Case 11
Figure 11: Pressure recovery coefficient values along the length of plane diffuser with the opening angle of α = 8.5° for the base instance (Case 2) and the variant with fins (Case 11)
0.4
y/L
0.6
0.8
1.0
Case 13
Figure 13: Pressure recovery coefficient values along the length of conicial diffuser with the opening angle of α = 15° for the base instance (Case 5) and the variant with fins (Case 13)
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 22 (2016) pp. 11081-11088 © Research India Publications. http://www.ripublication.com To assess an impact of optimal fin system prepared for plane diffuser, calculations of two variants were carried out for conical diffuser (Case 13 and Case 14). The use of fins for conical diffuser with the opening angle of 15° in the second half of diffuser as well as for the Case 7 leads to a slight positive effect (Fig. 13). Structuration of secondary flow observed for this instance is similar with plane diffuser. This is clearly seen
by comparing the flow structure in a conical diffuser without fins (Fig. 14 a) and with fins (Fig. 14 b). Secondary flow occupy all space between the fins and become periodic in the circumferential direction Application of the same fin system on conical diffuser with the opening angle of 20° deteriorates its characteristics (Fig. 15).
a) Case 6
b) Case 13
Figure 14: The streamlines in a conicial asymmetric diffuser with the opening angle of 15° coefficient. The positive effect was identified for two instances: Case 7 and Case 13. In other instances, fins are clearly reduced aerodynamic characteristics of the channel. According to the results, it is possible to recommend the use of fins only at the central output section of diffuser. Installation of fins at the input section provokes an earlier flow separation and significantly reduces the pressure recovery factor. For plane diffusers with opening angle less than 10° installation of fin systems could be also considered not advisable: it leads to additional aerodynamic resistance without a significant ordering of secondary flows. The use of a fin system for conical diffuser with opening angle of 20° clearly degrades its performance. In this regard, optimum fins location is the central outlet region. The use of such fins configuration, according to the obtained results, is advisable only for the diffusers with opening angle of 15°.
0.4
Cp
0.3
0.2
0.1
0.0 0.0
0.2
0.4
0.6
0.8
1.0
y/L Case 6
Case 14
Figure 15: Pressure recovery coefficient values along the length of diffuser with the opening angle of α = 20° for the base instance (Case 6) and the variant with fins (Case 14)
CONCLUSION According to the results of conducted research, it can be concluded, that the use of a special fin system can have a positive effect on the diffuser characteristics, namely significant structuration of the secondary flows, occurring in near the wall region, improving the vibration condition. Herewith it is possible to increase the pressure recovery
ACKNOWLEDGEMENTS This study conducted by National Research University “Moscow Power Engineering Institute” has been sponsored financially by the Russian Science Foundation under Agreement for Research in Pure Sciences and Prediscovery Scientific Studies No. 14-19-00944 dated July 16, 2014. REFERENCES [1] Törnblom O. Experimental study of the turbulent flow in a plane asymmetric diffuser. Universitetsservice US AB: Stockholm, 2002, 94 p. [2] Buice C.U., Eaton J.K. Experimental investigation of flow
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Conference on Adaptive Modeling and Simulation, Lisbon, Portugal, 2013. [8] Zaryankin A., Rogalev A. Mechanical model of the turbulence generation in the boundary layer. Applied Mathematical Sciences 2015: 9(100): 4957-4970. [9] Zaryankin A., Rogalev A., Garanin I., Komarov I., Kurdiukova G. Flow separation from the smoothcountered streamlined surfaces. Applied Mathematical Sciences 2015: 9(120): 6007-6019. [10] Zaryankin A.E., Gribin V.G., Paramonov A.N., Noskov V.V., Mitrokhova O.M. The effect the aperture angle of flat diffusers has on their vibration state and ways for reducing this vibration. Thermal Engineering 2012: 59(9): 674-682. [11] Zaryankin A.E., Grigiriev E.Yu., Noskov V.V. New methods of flow stabilization in a flat, conical and annular diffuser turbomachines channels. Vestnik ISPU 2012: 5: 510.
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