Engineering Applications of Computational Fluid Mechanics

Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 4, pp. 562–573 (2014)

NUMERICAL STUDY OF THE EFFECT OF WALL INJECTION ON THE CAVITATION PHENOMENON IN DIESEL INJECTOR Arash Hassanzadeh#*, Mohammad Saadat Bakhsh#, Abdolrahman Dadvand^ #

School of Mechanical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran, Iran. ^ Department of Mechanical Engineering, Urmia University of Technology (UUT), Urmia, Iran. * E-Mail: [email protected] (Corresponding Author)

ABSTRACT: Cavitation has an important effect on the performance of diesel injectors. It influences the nature of the fuel spray and formation of emissions. In contrast, cavitation increases the hydraulic resistance of the nozzle, creates flow instability, produces noise, and erodes the nozzle wall. In the present study, the effect of wall injection on the boundary layer separation in the cavitating and turbulent flow developing inside a diesel injector has been investigated numerically using two-phase mixture model. Simulations have been performed for different cavitation numbers, injection ratios and injection angles. Furthermore, the effects of various wall injection locations have been investigated and the results have been compared. The results indicated that for a particular injection angle, the highest discharge coefficient and the lowest number of cavitation bubbles were observed at a specific range of cavitation numbers. Also, with the injection from the orifice wall, the critical cavitation number diminishes, and only for a small interval of cavitation numbers, the discharge coefficient becomes a function of pressure difference between the two ends of injector. The idea of the current work could be a starting point for application of wall injection in injectors in order to increase the discharge coefficient, and, at the same time, to decrease the undesired effects of the cavitation phenomenon. Keywords:

cavitation, wall injection, diesel injector, numerical simulation, mixture model, boundary layer separation

characteristics of the spray issuing from the nozzle and also the spray jet atomization (Martynov, 2005; Sou et al., 2007; ShervaniTabar et al., 2012; Mohan et al., 2014). Cavitation is a phenomenon that may occur when the local static pressure in a fluid reaches below the vapor pressure of the liquid at the operating temperature. When cavitation occurs, cavitation bubbles are produced and they can collapse at the injector outlet as well as high pressure region so that they can produce pressure fluctuations and improve the atomization process of the spray. On the other hand, cavitation can decrease the flow efficiency (discharge coefficient) due to its effect on the exiting jet. Also, collapsing cavitation bubbles inside the orifice can cause material erosion thus decreasing the life and performance of the injector. Numerous experimental studies have been carried out on flows inside injector nozzles, and the cavitation phenomenon has been investigated. Bergwerk (1959) investigated the influence of the cavitation number, Reynolds number, the upstream edge sharpness, and the length/diameter ratio on the cavitation formation. It was shown

1. INTRODUCTION In diesel engines, the engine performance and the emission of NOx and Soot pollutants not only depend on the rate of fuel spray, but also they are influenced by the quality of liquid jet atomization and the mixing of fuel with air (Mobasheri et al., 2012). If the spray of fuel is in such a way that finer particles of fuel are formed, the combustion reaction will be speeded up, motor torque and efficiency will improve, and pollutants in exhaust emission will be reduced. Hence, it is very important to carry out research in order to better understand the flow dynamics inside the injector and the behavior of spray jet (Balasubramanyam et al., 2010). One of the most important parts of diesel engines is the injector nozzle. The geometry of nozzle affects the spray jet characteristics and determines the behavior of atomization and the formation of pollutants. To predict the formation and behavior of spray jet, it would be necessary to have a comprehensive understanding of the physics of flow inside the nozzle. Various evidences indicated that the cavitation occurring inside the nozzle changes the Received: 24 Mar. 2014; Revised: 6 Jun. 2014; Accepted: 29 Jul. 2014 562

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that the appearance of the jet was affected by cavitation pattern. Cavitation characteristics were determined for sharp-edged orifices in the work of Nurick (1976). Both circular and rectangular orifices were studied. It was concluded that cavitation would result in a substantial reduction of mixing uniformity for circular orifice. But under the same experimental conditions, the rectangular orifice did not experience a decrease in mixing uniformity. More recent experimental studies of the flow inside real-size and large-scale model nozzles have revealed the complexity of the two-phase flow structures over different operating conditions (Soteriou et al., 1995; Chaves et al., 1995; Arcoumanis et al., 1999; Payri et al., 2007). The size of the injector nozzle and the high speed of fluid flow make it difficult to carry out experimental observations, so the use of numerical simulations (Bierbrauer and Zhu, 2008; Christafakis and Tsangaris, 2008) is very useful to understand the flow features inside and at the exit of the injector nozzle. Different numerical simulations have been reported focusing on cavitation inside the diesel engine injector. Schmidt and Corradini (2001) reviewed the cavitation mechanism and models used for prediction of cavitation in the injector nozzles. Margot et al. (2012) investigated the effects of various parameters on the flow characteristics inside an injector and at the exit. For this purpose, a cavitation model based on bubble growth theory was used. Salvador et al. (2013) studied the influence of the needle lift on the internal flow and cavitation phenomenon in diesel injector nozzles using homogeneous equilibrium model implemented in Open-FOAM together with the Reynolds Averaged Navier–Stokes (RANS) equations. Validation against experimental data at full needle lift conditions demonstrated fairly good accuracy of their approach. Using the Computational Fluid Dynamics (CFD) method, Payri et al. (2002) studied the effect of geometry in two types of cylindrical and conical nozzles. Since this model is only able to predict the onset of cavitation, it is solely used for qualitative analysis. The results indicated that cavitation was not produced in conical nozzles. In another work, Molina et al. (2014) investigated the influence of different elliptical and circular orifices on the inner nozzle flow and cavitation development in diesel injector nozzles. Their results showed that the horizontal axis orifices are more prone to cavitation and have a higher discharge coefficient than the vertical axis ones. Ren and Sayar (2001) investigated the flow inside

the nozzle and the characteristics of spray jets, and concluded that the flow inside the nozzle orifice had a very significant impact on the atomization and form of spray jet. Echouchene et al. (2011) conducted numerical simulation by employing the commercial software Fluent to study the effect of injector wall roughness on the cavitation phenomenon. In the present work, the influences of wall injection on the cavitation phenomenon inside a diesel injector are investigated using the CFD. The results are validated through the comparison with available experimental data. The idea behind the wall injection is to control the boundary layer separation inside the injector, hence to avoid the cavitation phenomenon. This may be attributed to the fact that once a bubble enters the separation region it will remain in the low pressure region for a short time. Thus bubble does not have enough time to expand and then rapidly collapse at the high pressure regions. Smaller separation regions directly provide a safer working condition for injector, especially at high upstream pressures. In addition, in the current work, a detailed parametric study is carried out to study the effects of different cavitation numbers, wall injection ratios, wall injection angles, and wall injection locations on the cavitation phenomenon and discharge coefficient Cd. In commercial implementation, the wall injection can be done by using the continuous stream inkjet printing principle. The idea of the current work could be a starting point for application of wall injection in injectors in order to increase the discharge coefficient, and, at the same time, to decrease the undesired effects of the cavitation phenomenon. 2. GEOMETRY CONFIGURATION AND BOUNDARY CONDITIONS The geometry of the nozzle which is used for fuel injection in diesel engines can be observed in Fig. 1. According to this figure L, H, h, d, and  are the orifice length, input height, orifice height, length of wall injection and the angle of injection from orifice wall, respectively. To reduce the computation time, in view of the symmetry of geometry and flow, the nozzle axis has been considered as symmetrical, and the no-slip condition has been applied on the nozzle wall. At the inlet and outlet sections, static pressures are adopted as boundary conditions. The upstream (inlet) pressure varies between 1.9 and 1000 bar and the exit pressure is fixed at 0.95 bar. In this research, the parameters  , M, z/d, and P take 563

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pressure differences P , the length of the region in which these vapor bubbles appear will increase, so that at severe pressure differences, the vapor bubbles will be maintained even up to the nozzle outlet, and will collapse when they enter the combustion chamber. In the flow separation zone, the area of the effective cross section becomes smaller, which is called the contracted cross section. Considering the reduction of the cross section for the passage of liquid phase in the contracted region, fluid velocity will increase according to the conservation of mass law. With the increase in the flow velocity, the dynamic pressure increases, and the static pressure drops. If the static pressure reduces even lower than the vapor pressure of fuel, vapor bubbles will appear and the flow will become a two-phase. The intensity of cavitation inside the nozzle is determined by a dimensionless parameter called the cavitation number. Cavitation number is defined by using the upstream and downstream pressure difference. Different definitions have been presented for this number. In the present work, the cavitation number definition of Nurick (1976) has been used, P P (1) K  in v Pin  Pout where Pin is the inlet pressure, Pout is the outlet pressure and Pv is the saturation vapor pressure. If the K value which is calculated for a specific pressure difference is less than K crit (for which the flow becomes two-phase), the cavitation phenomenon will occur, and with the further decrease of this number, the intensity of cavitation will increase. In the studies regarding the occurrence of cavitation in injector nozzles, a parameter called the discharge coefficient is used, which is defined as the ratio of the actual mass flow rate to the ideal mass flow rate of fluid passing through the nozzle.

different values in order to assess their effects, which can be seen in Table 1. Also, M has been defined as M  l uw mue , where u e and u w are respectively the mean flow velocity at the nozzle outlet and the velocity of injection from the nozzle wall, which is a function of the insidenozzle main flow rate. The orifice wall has been divided into 32 equal sections, and z/d denotes the distance of the injection hole from the sharp edge. Parameter  denotes the angle of injection. Table 1 Different wall injection configuration. Parameter Variable



(degree)

10-90

M 0.25-1.25

z/d 1-32

P (bar) 1-1000

Nurick (1976) achieved extensive experimental data for cavitation phenomenon in a sharp-edged circular orifice. Geometrical parameters of the orifice were H/h=2.86, L/h=7.94. Their experiments were carried out at a fixed exit pressure, Pout  0.95 bar, but different upstream (inlet) total pressure, Pin , to produce different flow rates. In the present work, the injection hole length is considered to be equal to 1mm (see Fig. 1).

Fig. 1 Geometry of nozzle.

3. FLOW INSIDE INJECTOR NOZZLE

Cd 

m

(2)

A 2 l  Pin  Pout  where m , A, Pin , Pout, and ρl indicate the inlet

The fuel that enters the nozzle orifice undergoes wall separation because of the sharp bend at the inlet. The sharp bending of flow lines in the considered region will produce a strong adverse pressure gradient, leading to the generation of low pressure regions at the inlet section. With a severe pressure drop in this region, if the static pressure reaches a value less than the vapor pressure, there will be a phase change in the flow and cavitation bubbles will produce. Now, as we proceed with the flow, the pressure will gradually increase, leading to the collapse of formed cavitation bubbles (Sarre et al., 1999). At very large

mass flow rate, orifice cross-sectional area, upstream (inlet) pressure, outlet pressure, and liquid density, respectively. 4. NUMERICAL METHOD The RANS equations have been solved by using the CFD software Fluent. Fluent uses the finite volume method, and it has been extensively validated for the RANS method (Echouchene et 564

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al., 2011; Dular et al., 2005). Pressure based solver SIMPLE (Patankar, 1967) is used as the velocity pressure–coupling algorithm. The momentum equations are discretized using second-order upwind scheme, and first-order upwind for other equations. The flow is assumed to be steady and incompressible. The incompressible flow assumption is acceptable because the compressibility of the mixture, which is the inverse of the speed of sound squared is very low. In addition, a no-slip condition between the liquid and vapor phases is assumed.

According to Andriotis et al. (2008), there was no significant difference with different turbulence models in predicting cavitation inception and they suggested the use of standard k-ɛ turbulence model. Therefore, the present study uses the standard k   turbulence model with standard wall function. The turbulence kinetic energy k , and its rate of dissipation  , are obtained from the following transport equations (Launder and Spalding, 1972):

    kui   xi x j

4.1 Governing equations

u i 0 x i

 u i  t



      ui      t xi x j  

numbers for k and  , respectively. The turbulent viscosity,  t , is obtained by combining k and  as follows:

t   C 

(4)

 u i  t



k2

(10)



where C  is a constant. The model constants C1 ,

C 2 , C  ,  k , and   have the following default

the x i direction, p is the static pressure,  is the mixture viscosity. The RANS equations are obtained by applying the time averaging operation (denoted by the overbar) on Eqs. (3) and (4):

u i 0 x i

(9)

constants.  k and   are the turbulent Prandtl

(3)

(u i u j )   2u i p      x j  x i x j x j

    2   C1  Gk   C2   k k  x j 

In these equations, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients. C1 , C 2 , and C3 are

where, u i is the velocity component of fluid in



 k    Gk   (8)   x j 

and

For the multi-phase flow solutions, the singlefluid mixture model is employed (Echouchene et al., 2011). The Navier-Stokes equations are the starting point for any turbulence simulation. Eqs. (3) and (4) are respectively the continuity and momentum equations for the incompressible flow associated with Newtonian fluids (Batchelor, 1967).



 t    k 

values: C1  1.44 , C2  1.92 , C  0.09 ,

 k  1.0 ,    1.3 (Echouchene et al., 2011; Launder and Spalding, 1972; Zhang et al., 2008).

(5) 4.3 Cavitation model

(u i u j )   ui p   x j  x i x j x j 2

The mixed density  m is related to vapor mass

(6)

fraction f v , as illustrated in Eq. (11):

where u i is the time averaged velocity component

1

of the fluid in the x i direction, and p and  are the time averaged pressure and density, respectively. Using eddy viscosity approximation, Eq. (6) is simplified for the steady (in the mean) flow into Eq. (7) (Schetz, 1993):  u (u i u j )   2u i p (7)  i   (   t )  x j  x i x j x j  t where  t is the turbulent viscosity and it should be determined by turbulence model.

m



fv

v



where

1  fv

l v  0.026 kg / m 3

(11) and

l  1000 kg / m are the density of vapor and liquid, respectively. The value of v is obtained 3

at the saturation temperature T=296 K. The vapor volume fraction  v is derived from  v as:

 v  fv

m v

(12)

The vapor transport equation is written as (Singhal et al., 2002):

4.2 Turbulence model

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   m fv   . m vm fv  Re  Rc t





Rc  Cc

(13)

e

S

l

v

3

l



v

g



if p  pv

(15)

where pv is saturated vapor pressure. Ce and Cc were obtained by comparing the experimental and numerical results associated with various initial condition and geometries, reported by Singhal et al. (2002). Their values are 0.02 and 0.01, respectively. In Eqs. (14) and (15), S and f g are

Where Re and Rc are the rates of vapor generation and condensation, respectively. To solve the Equation, Re and Rc need to be given. Singhal et al. (2002) derived the expressions of Re and Rc : k 2 pv  p (14) R C  1 f  f , if p  p e

k 2 p  pv l v fv , S 3 l

surface tension and non-condensable gas mass fraction, respectively.

v

Table 2 Comparison of Numerical and Experimental data for Cd . K=1.003 Cell number 2800 5450 12500

K=1.226

Cd

Cd

Cd Num 0.6258 0.6235 0.6234

K=1.446

Exp 0.622

Error 0.61% 0.24% 0.23%

Num 0.6880 0.6910 0.6909

Exp 0.689

Error 0.15% 0.29% 0.28%

Num 0.7391 0.7460 0.7460

Exp 0.747

Error 1.06% 0.13% 0.13%

Fig. 2 Computational grid used for the sharp-edged orifice. Schematic of nozzle indicating sections 1–3 used for grid independence studies.

5. RESULTS AND DISCUSSION 5.1 Mesh independency The computational grid shown in Fig. 2 has two blocks with 40 30 and 170 25 cells (total of 5450 cells). Two other grids with 2800 and 12500 cells were also used for grid independence study. As shown in Table 2, the numerical results obtained using grids with 5450 and 12500 cells have minimum deviation from experimental results and thus a grid with 5450 cells is mainly employed in the numerical simulations. In order to perform the grid independence study, three different sections have been selected on the nozzle. Sections 1, 2 and 3 have been delineated at the 8, 16 and 24 mm positions on the nozzle, respectively and y is measured from the centerline (Fig. 2). Fig. 3 shows the changes of vapor volume fraction along the 3 mentioned sections

Fig. 3 Grid refinement studies: plot of cavitation scalar fraction variable along (a) section 1, (b) section 2, (c) section 3 using three different mesh sizes for Pin  340 bar.

for an input pressure of 340 bar. In each diagram (Figs. 3a-3c), the effect of grid resolution on the vapor volume fraction for 3 different mesh types have been compared with one another. Also in Fig. 4, the vapor volume fraction has been plotted on the centerline for an input pressure of 15 bar and for three types of meshes. In both of the above cases, the results indicate acceptable agreement between the two mesh configurations 566

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(5450 cells and 12500 cells). Considering the results obtained in the present work, the 5450 cell mesh has been used.

K crit diminishes (see Fig. 5). This means that the occurrence of cavitation will be limited to a smaller range of cavitation numbers. Moreover, for low cavitation numbers (K< 1.101), in spite of applying wall injection, the results will obey the relation Cd  Cc K , where Cc is the contraction coefficient, whose value is 0.61(Nurick, 1976). Considering the mentioned relation, it can be said that with the increase of cavitation intensity, the discharge coefficient will diminish (Echouchene et al., 2011). Also, Fig. 5 shows that K crit decreases with the increase of injection ratio (the curve becomes straight at smaller cavitation numbers). Furthermore, the changes of Cd with respect to wall injection at small cavitation numbers are more than its changes at large cavitation numbers. For example, for M = 0.75, the increase in the value of discharge coefficient relative to the case of without wall injection is 0.115 at K = 1.003, while it is 0.019 at K = 1.704 (Fig. 5).

Fig. 4 Distribution of the vapor volume fraction on the centerline for refinement in the z-direction for Pin  15 bar .

5.2 Effect of wall injection on the discharge coefficient  Cd  The increase in cavitation intensity is due to the increase of pressure difference between the inlet and outlet sections of injector. While a regular increase in fluid flow rate is expected with the increase of pressure difference, with the emergence of cavitation, the discharge coefficient diminishes. By increasing the cavitation number greater than a certain value K crit , the cavitation no longer exists. In Fig. 5, the numerical results for the case without wall injection have been compared to the experimental results (Nurick, 1976), showing a good agreement. But this figure also indicates a small discrepancy between the experimental and numerical results under noncavitating conditions (k>kcrit). These can be related to the cavitation model that used in the simulation. In the range of cavitation number which is under non-cavitating condition, cavitation model is still used. So if the single phase model would be used in this range, this discrepancy could possibly be disappeared. Also, similar discrepancy is observed in the numerical results of Echouchene et al. (2011). Also, three injection ratio cases with M = 0.5, 0.75, 1.0 and injection location of z/d = 4 and injection angle of   30 have been considered. The obtained results indicate that with the injection from the orifice wall, discharge coefficient increases and

Fig. 5 Compare discharge coefficient C d versus cavitation number K for different wall injection ratios with experimental results (Nurick, 1976).

5.3 Effect of injection angle on discharge coefficient and emergence of cavitation inside injector In this section, different injection angles, including 10º, 20º, 30º, 45º, 60º and 90º, have been selected and their effects have been evaluated. For each injection angle, the value of Cd has been calculated and the vapor volume fraction diagram has been plotted. In Fig. 6, the discharge coefficient has been plotted versus the 567

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injection angle, for different cavitation numbers. The results indicate that for all the cavitation numbers, the maximum discharge coefficient is obtained at the injection angle of 30º. At high pressure differences between nozzle inlet and outlet, cavitation occurs near the nozzle wall and continues up to the nozzle outlet; as a result, it can lead to the erosion of nozzle wall.

angles, the highest reduction in vapor volume fraction can be observed. As we know, the region of flow separation and flow reversal plays an important role in the formation of cavitation. To prove this claim, it can be seen that at the injection angle of   10 , the injection into the main flow is too weak to overcome the low-speed flow momentum of the main fluid in the separation region. By increasing the injection angle to 20º, the value of C d increases and the vapor volume fraction diminishes, and finally at   30 , the highest value of C d and the lowest amount of near-wall vapor volume fraction are obtained; because in this case, a large momentum enters the nozzle, which excites the returning or low-energy particles and causes the produced vapor bubbles to maintain less time in the separation region. With the increase of the injection angle to 45º, 60º and 90º, the value of C d is further reduced, and in the section downstream of the injection point, the flow becomes separated and this causes the reformation of vapor bubbles near the nozzle wall. It should be noted that by implementing wall injection at the injection angle of   30 , discharge coefficient increases and the near-wall bubbles become less, thereby reducing the damaging effects of cavitation on the nozzle wall. Also as illustrated in Fig. 8 at certain cavitation numbers, wall injection can lead to the formation of most of the bubbles in the central region of the nozzle exit and consequently to better spray of fuel (e.g.,   90 ). The contours of vapor volume fraction for the pressure inlet of Pin  340 bar , without wall injection and also with wall injection (M = 0.5 and z/d = 2), have been plotted in Fig. 9 for different injection angles. As it can be seen, for case (a) (without wall injection) vapor bubbles can be observed inside the nozzle as a result of flow separation near the sharp edge. Then in cases (b1) and (b2), with wall injection at 10º and 20º, the volume of vapor bubbles in the near-wall region diminishes. For case (b3), where the injection angle increases to 30º, a reduction of vapor bubbles is observed at the exit region near the wall; and this reduction of cavitation bubbles can alleviate the adverse effects of cavitation on the nozzle wall. By increasing the injection angle to 45º, a wake region is formed downstream

Fig. 6 Discharge coefficient Cd versus wall injection angle β for different cavitation numbers K (M=1, z/d=4).

Fig. 7 Distribution of the vapor volume fraction near the wall for different angle of wall injection.

The effects of wall injection angle on near-wall cavitation at Pin  340 bar, M = 1, and z/d = 4 have been illustrated in Fig. 7 for different wall injection angles. The results indicate that by applying wall injection, the amount of vapor volume fraction near the nozzle wall decreases, and the effect of this reduction is more prominent in the nozzle outlet region than the region close to the sharp edge. Also at the injection angle of   30 , in comparison with the other injection

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Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 4, pp. 562–573 (2014) Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 4 (2014)

Fig. 8 Distribution of the vapor volume fraction at the outlet for different angle of wall injection ( Pin  5bar , z/d=4). a (without wall injection)

b1 (   10 )

b2 (   20 )

b3 (   30 )

b4 (   45 )

b5 (   60 )

b6 (   90 )

Vapor volume fraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fig. 9 Contour plot of vapor volume fraction for Pin  340bar . (a) without wall injection, (b1 )   10 , (b2 )   20 , (b3 )   30 , (b4 )   45 , (b5 )   60 and (b6 )   90 .

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of the injection location, which causes the reestablishment of cavitation bubbles near the wall. These bubbles increase in quantity with further increase of injection angle, and move towards the injector’s outlet section.

increase of discharge coefficient and the reduction of cavitation’s undesirable effects) are not fulfilled.

a (without wall injection)

b1 (   30 )

b2 (   90 )

Fig. 11 Distribution of the vapor volume fraction near the wall for different injection ratio ( Pin  340bar   30 , z/d=2).

5.4 Evaluation of injection ratio The results pertaining to the change of near-wall vapor volume fraction with injection ratio for M = 0.25, 0.5, 0.75, 1.0 and 1.25 have been presented in Fig. 11. In this figure, the amount of vapor volume fraction for the case of without wall injection has been compared with its counterpart associated to the cases with wall injection showing the effect of wall injection on the cavitation phenomenon. The findings indicate that for M=0.25, because of a small inflow rate, the injected fluid doesn’t have enough momentum to penetrate the layers of fluid inside the injector, and it can only influence a specific region of the flow. With the increase of injection ratio to 0.5 and 0.75, the number of vapor bubbles near the nozzle wall is considerably reduced. But by increasing the value of M to 1.0 and 1.25, because of flow separation, the near-wall vapor bubbles downstream of the point of orifice wall injection increase in number. Also for M = 0.5 and 0.75, the lowest value of vapor volume fraction is observed at the nozzle outlet. Finally, the obtained results indicate that with wall injection, the near-wall cavitation diminishes for all values of M, and that the effect of injection is higher at the region close to the nozzle outlet than the region near the sharp edge.

Vapor volume fraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Fig. 10 Contour plot of vapor volume fraction for Pin  5 bar. (a) without wall injection, (b1)

  30 , (b2 )   90 .

Fig. 10 shows the contours of vapor volume fraction at Pin  5 bar, for the cases without wall injection and also with wall injection (M = 1 and z/d = 4) at injection angles of 30º and 90º. As these figures show, for case (a) vapor bubbles are observed inside the nozzle. Then in case b1, at the 30º angle, almost all the vapor bubbles inside the nozzle have disappeared, and also according to Fig. 6, the discharge coefficient either has a maximum value or is increasing. On the other hand for case (b2), at the injection angle of 90º, more vapor bubbles appear in the central region of nozzle exit, which could help in the atomization of fuel. However, as mentioned before, at this angle, the coefficient of discharge becomes smaller and the main objectives (the 570

Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 4 (2014)

parameters (injection angles, injection ratios and specific injection positions), and different results were obtained. The results from the evaluation of different injection ratios indicate that at a specific injection ratio, less bubbles form near the orifice wall. The evaluation of various injection angles showed that for all the considered cavitation numbers, the maximum value of discharge coefficient is obtained at the injection angle of 30º. Wall injection leads to a decrease in K crit ; and for

5.5 Effect of position of wall injection on discharge coefficient In Fig. 12, the effects of injection location on discharge coefficient have been investigated for different cavitation numbers. The results indicate that except for points near the sharp edge and nozzle outlet, the value of discharge coefficient remains constant for different wall injection locations and it doesn’t depend very much on the position of injection. It is also clear from the diagram that for high cavitation numbers, the changes of discharge coefficient near the sharp edge are negligibly small.

cavitation numbers larger than K crit , the value of discharge coefficient becomes independent of the pressure difference between the two ends of nozzle. It was observed that the C d changes more drastically at small cavitation numbers compared to large cavitation numbers. Also, for large pressure differences between the nozzle inlet and outlet or for small cavitation numbers, the effect of wall injection on the near-wall bubbles becomes more appreciable, and it can play a more effective role in the reduction of cavitation damaging impacts on the nozzle wall. Moreover, at certain cavitation numbers, wall injection can result in the formation of most of the bubbles in the central region of nozzle exit and consequently to a better spray of fuel. It may be noted that, the experimental tests and simulation of the three-dimensional model of the proposed wall injection concept for cavitating nozzles will be carried out in our future works.

Fig. 12 Discharge coefficient C d versus z/d for different cavitation numbers K (M=0.5,   30  ).

NOMENCLATURE A

6. CONCLUSIONS

Cc Cd Ce

The cavitating flow inside a fuel injector was studied and reasonable agreement was observed between the current numerical results and the available experimental data. However, there are little discrepancies between the experimental and numerical results under non-cavitating conditions (K>Kcrit). This may be attributed to the fact that the cavitation model (two-phase model) was employed for the entire range of cavitation numbers including both the cavitating and noncavitating conditions. This discrepancy can possibly be disappeared, if the single phase model is used in the non-cavitating range. By injection fluid from the orifice wall into the main flow (in order to control the boundary layer separation inside the injector), the impact of wall injection on cavitation was investigated. Fluid injection from wall was performed by changing various

d

fv g H h K k M

m Pin

Pout Pv Rc 571

Orifice cross-sectional area Empirical constant Discharge coefficient Empirical constant Wall injection length Vapor mass fraction Gravitational acceleration Inlet height Orifice height Cavitation number Turbulence kinetic energy Wall injection ratio Mass flow rate Upstream pressure Downstream pressure Saturation vapor pressure Rate of vapor condensation

Engineering Applications of Computational Fluid Mechanics Vol. 8, No. 4 (2014)

Re

Rate of vapor generation

S

Vm

Surface tension Mixture velocity

z/d

Position of wall injection

7.

Greek Symbols

P

v    t l m v

8.

Pressure difference, P  Pin  Pout Vapor volume fraction Injection angle Turbulence dissipation rate Mixture viscosity Turbulence viscosity

9.

Liquid density

10.

Mixture density Vapor density

Subscripts crit l m t v

11.

Critical condition Liquid Mixture Turbulence Vapor phase

12.

13.

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