Numerical and experimental investigations have been made on the coefficient of discharge Cd, and the spray cone angle of a swirl spray solid cone pressure nozzle. The theoretical predictions are made from a numerical computation of flow in the nozzle using the standard k-ε model of turbulence. The values of Cd and have been evaluated from the radial distributions of velocity components of liquid flow at the nozzle exit. The experiments have been carried out to measure the values of Cd and of a solid cone spray nozzle at different operating conditions to validate the numerical predictions. It has been established, from a fair agreement between the theoretical and experimental results, that the adaptation of the standard k-ε model for turbulence in nozzle flow serves well the purpose of predictions of Cd and within the range of operating parameters studied in the present work. It has been observed that the coefficient of discharge and the spray cone angle remain almost constant with the Reynolds number (Re) of the flow at the inlet to the nozzle. The coefficient of discharge Cd is almost uninfluenced by the inlet swirl number (S), in its lower range, but decreases with S in its higher range. The spray cone angle , on the other hand, always increases with an increase in S. For a given Re, and increase in flow ratio (q) (the ratio of flow rate through the inlet central port to the total flow through the nozzle) increases the value of Cd and decreases the value of . However, the influence of qr on Cd is prominent at lower values of D2/D1 (the ratio of the diameters of inlet axial port to the swirl chamber of the nozzle). An increase in the value of Cd takes place with a decrease in D2/D1 ratio mainly in the range of a higher qr and for the values of D2/D1 less than 0.17. The spray cone angle on the other hand, is almost uninfluenced with D2/D1, expect in the situation when increases with an increase in D2/D1 , from 0.38 to 0.75 mainly in the lower range of flow ratio qr.
Aircrafts no longer require piston powered engines to operate with the introduction of gas turbine engines now in commission. The main aims and objectives for jet powered engines is to be able to produce thrust on request for pilots to operate the aircraft in a safe, reliable and cost effective method. A gas turbine engine consists of a number of components i.e. Combustions chambers, Compressors and turbines, with all parts contributing towards efficiencies.
Temperatures within a gas turbine engine exceed the used materials limitations, making cooling systems an increasingly important component for safe and reliable operation. The advancements in gas turbine powered technologies are one of the many reasons for requiring continues cooling support, also known as simplex nozzle.
Within a gas turbine engine the use of swirl spray is important as here is where cooling of the rotating blades takes place. The importance of swirl spray pressure nozzle lies in its widespread industrial applications in combustion, evaporation, drying, humidification, cooling, air-conditioning and sprinkling to name a few. A unified design approach of nozzle in these fields requires the interrelations between different performance characteristics of the nozzle with pertinent input parameters such as, liquid properties, injection conditions and nozzle geometry. This needs a physical understanding of the flow inside the nozzle and mechanism of spray formations outside the nozzle. The simplest form of a pressure swirl nozzle is the one known as "Simplex nozzle". There are two basic types of simplex nozzles. In one type, liquid at high pressure is supplied to the nozzle through purely tangential ports and the nozzle produces a hollow cone spray. In another type, a high pressure liquid is fed to the nozzle through both axial and tangential ports. The nozzle, under this situation, produces a solid cone spray. A simple form of a solid cone spray nozzle is shown in Fig. 1. Liquid enters the swirl chamber partly through a central cylindrical port which provides a pure axial-type entry and partly through an annular vane swirler which imparts swirl to the liquid at inlet. Whilst simplex nozzles of hollow cone spray types are mostly used in the power industries, including aviation and space technology, the solid cone spray nozzles are largely employed in gas scrubbing, coke quenching, spray dryings, sprinkling, chemical processing, rinsing and agricultural fields.
Fig. 1: The geоmetry оf а ѕоlid Ñоne Ñ•Ñ€rаy nоzzle
Most of the work available in the literature in this area is empirical or semi-empirical in nature and pertains how to hollow cone spray nozzle. Taylor [1] gave the pioneering theoretical treatment for potential flow in a swirl spray nozzle and predicted that the spray cone angle was an inverse function whilst the coefficient of discharge was a direct of a single dimensionless parameter define as a nozzle contact, K = Ap /D1D0, where Ap was the area of tangential entry ports and D1 and D0 were the diameters of the swirl chamber and discharge orifice respectively. However, this theory referred to a simplified cylindrical swirl chamber and could not explain the dependence of performance parameters on the nozzle flow as occurs in practise. In subsequent work, Tayler [2] provided a theoretical treatment for the growth of boundary layer for a laminar swirling flow in a convergent duct. The classical studies in the field of pressure swirl nozzle include those of Binnie and co-workers [3,4,5 and 6], Tate and Marshal [7] whose work mostly dealt with the experimental investigations of swirling liquid flow through straight and convergent ducts. The development in the field of simplex type swirl nozzle have had significant contributions from many researchers, Kutty et al. [8], Som and Mukherjee [9], Rizk and Lefebvre [10 and 11], Jeng et al [12], Liao et al [13], Sakman et al. [14] and Datta and Som [15]. All these works brought about an understanding of the swirling flow inside a hollow cone spray nozzle and attempted to evaluate the liquid film thickness at the discharge orifice, flow number and spray cone angle of the nozzle either from the empirical studies or from simplified theory. The similar types of work on solid cone spray nozzle are sparse in the literature. Therefore, the present paper makes an attempt towards both the numerical and experimental investigations on the coefficient of discharge and the spray cone angle of a solid cone spray.
Theoretical Formulation:
The theoretical analysis refers to a typical solid cone spray nozzle as shown in Fig. 1. The entry of liquid to the nozzle is split through a central cylindrical port and an annular helicoidal vane swirler at the base of the chamber.
The standard k-ε model has been adopted for the computation of turbulent flow in the nozzle. This is despite the fact, that many researchers observed some shot comings in the ability of predicting the reticulating and swirling flow results, at the very least quantitatively. The implementation of modified k-ε models or higher order turbulence models (ASM, RSM) have been suggested by different researchers [16,17,18,19,20,21,22 and 23] in the computations of recirculation flows with improved accuracy. However, there is no conclusive information available in the literature regarding the accurate adaptability for any of such models in a confined swirling flow. The higher order turbulence models are relatively complex and time consuming and sometimes are found to be inaccurate in predicting the strong swirling flows. Ramos [24] in his numerical study on a swirling stabilized combustor, employed the standard k-ε model and argued that the consideration of a scalar viscosity in confined incompressible swirling flows was indeed adequate. One of the basic objectives of using the standard k-ε model for the present work is to investigate whether the model can predict the nozzle performance parameters like the coefficient of discharge and the spray cone angle within a reasonable accuracy as compared with the experimentally measure values under identical situations.
Equations 1, 2, 3, 4, 5 and 6 were solved simultaneously satisfying the respective boundary conditions by an explicit finite difference computing technique developed by Hirt and Cook [25] following the original, Marker and Cell (MAC) method created by Harlow and Welch [26]. The steady state solution of flow was achieved by advancing the equations in time till the temporal derivatives of all the variables fall below a pre-assigned small quantity, δ.
The space derivatives of the diffusion terms were discretised by the central differencing scheme while the advection terms were discretised by the hybrid differencing scheme based on the local Peclet number (Pe), associated with the cell. A 66 x 44 variable sized adaptive grid system was considered with clustered cells near the inlet and wall. The variations in the size of the grids were made uniformly. It was checked by further refinement of the cells (with doubling and quadrupling the number of grids in both the directions) did not change the velocity (both axial and swirl) components and turbulent kinetic energy by more than 2%. The choice of time increment (∆t), was made to ensure stability in the computation in accordance with criteria of cell transit time of fluid due to convection and diffusion respectively.
The annular helicoidal slots were made at the base of the nozzle to give a swirl number S from equation 8f of 3.0. The coefficient of discharge and spray cone angle of the nozzle were measured for different flow rates through the nozzle in order to verify the numerical predictions.
An experimental test rig was made to measure the coefficient of discharge and the spray cone angle of the nozzles for different flow rates in order to verify the numerical predictions. A Line diagram of the test rig is shown in Fig. 2. A multistage centrifugal pump (P) was used to supply water through both the central port and the annular vane swirler of the nozzle (N). The flow rates through the central port and the vane swirler were controlled by using the valves (V1, V2 and V3) and measured by the rotameters (R1 and R2). The inlet pressure to the nozzle was recorded by a bourdon type pressure gauge (G), which was calibrated with a dead weight tester before the experiment took place. The rotameter was calibrated against the direct method of flow measurement by collecting water in a volumetric task during a known interval of time
Figure 2: Line diagram of the experimental setup
The uncertainties in the measured values of flow rate and pressure drop were found to be ±2.5% and ±3.3% respectively, with a 95% confidence limit. Finally, the uncertainty in the measured values of the coefficient of discharge was determined from the uncertainties of the the measured quantities, namely, flow rate and pressure drop, and was found to be within ±3.5% with a confidence limit of 95%. The calculation for this is shown in Appendix A.
The spray cone angle was measured by taking the photographs of spray with the help of a wide angled lens camera with flood light illumination. The photographs were scanned and magnified in a computer for the measurement of the spray cone angle. Fig. 3 shows such a photograph under the given operating conditions. The uncertainty in the measure values of the spray cone angle was found (From the bias error and precision error) to be ±2.5% with a 95% confidence limit.
Fig . 3: A typical spray from a solid cone spray nozzle
Calculating the pressure drop and the cooling effectiveness of the pre-swirl chamber is a very important aspect that should be taken into consideration. Not only that but also the heat transfer between the cooling air and the turbines disc, specifically the possible conception of non-uniform temperatures in the metal, in which could result to large thermal stresses should also be taken into consideration.
A number of experiments have taken place by Meierhofer and Franklin [27] in order to measure the effect of pre-swirl chamber on the temperature drop in a direct transfer system; these experiments have showed that swirling the air could dramatically cause reduction in the total temperature in the receiver holes of the turbine disc.
More experiments have been conducted by El-Oun and Own [28] in order to develop a theoretical model for the adiabatic effectiveness Ob,ad, which is based on Reynolds equivalence. The model had a good conformity with the temperatures measured on the rotating disc inside, which then showed that the total temperature (Tt,b), in the receiver holes will eventually decrease at a steady rate as Bp. However the re swirl ratio still increased even when Bp, was highly greater than unity.
These measurements of the adiabatic effectiveness made by Geis[29] showed that the vales of (Tt,b), were significantly higher than the values that have been originally predicted from the model. Theoretical models for the adiabatic effectiveness of the direct transfer system have been derived by Farzaneh[30]; this is taking into consideration the moment of the stator. The values that have been originally predicted from the model shows lower values of Ob,ad byKaraby [31] than that of other results that based their model on a cover plate system where it was conducted that the pre-swirl air flows outwards towards the rotating discs.
Popp [32] carried out computational fluid dynamics investigations of the cover plate system have taken place figuring the drop in the temperature and the coefficient of discharges. These results showed that CD, the coefficient of discharge for the receiver holes turned into the maximum when the relative velocity was approximately zero. This method was proved experimentally and the discharge of the coefficient was successfully measured in a direct transfer system by Dittman et al.[33] Further measurements by Yen et al [34] have taken place to determine the coefficient of discharge in the receiver holes but this time for a range of different rotational speeds as well as flow rates. Where
CD, have shown a monotonic increase as B1 increased from 0.3 to 0.9. It was also concluded that CD depends on the ratio of the area of the receiver compared to that of the nozzles. At a specific value for the pre-swirl ratio, CD increases as the area ratio increases.
As mentioned before heat transfer is also an important aspect to be taken into consideration during pre-swirl analysis. Investigations have been carried out by Wilson et al[35]. on the heat transfer computationally as well as experimentally. These experiments used flux meters in order to determine the Nusselt numbers. The computational fluid dynamics results provided reliable predictions of the temperature and velocity, however the results were not predicted when it came to measuring the Nusselt numbers. In order to determine the coefficient of the heat transfer, thermo chromic liquid crystal has been used. There is also another method of calculating the coefficient of heat transfer which is using Fourier's transient conduction equation
q'' = -k T
for a semi infinite solid which is exposed to slight change in the air temperature. It is highly unpredictable to achieve such a change in the air temperature of the pre-swirl chamber however another method known as the slow transient technique developed by Newton et al [36] have been used to measure the Nusselt number on the rotating disc for a direct transfer chamber for different speeds, pre-swirl ratios as well as flow rates. This method showed that the Nusselt number was nearly axis symmetric; however near the holes it wasn't axis symmetric as large differences showed. Further results showed that there was more than one flow system. When flow rates where high, inertial effects conquered and the flow imposed on the rotating discs which resulted in a peak in the Nusselt number. On the other hand when the flow rates were reduced a number of different effects also conquered, not only that but also the boundary layer flow controlled the heat transfer.
After all these experiments and results further computational flow dynamics should be carried out but in 3D in order to calculate the flow and heat transfer in the pre-swirl chamber. These calculated results are going to be compared with the measured values of the coefficient of discharge as well as the theoretical values of the adiabatic effectiveness and with the Nusselt numbers. These results will easily help in order to provide a physical insight of the highly complex flow and heat transfer that takes place inside the pre-swirl systems in a combustion chamber.
The pre-swirl ratio is not separately variable as it depends upon the number of pre-swirl nozzles, as well as â‹‹T and . In the experiments conducted two different values of the pre-swill nozzles have been used which ere 12 and 24(these values were used by Yan [34]). Using the value of 24 into the equations, it was shown that flow structures were very similar to those in an engine. However, a slight concern should be taken into consideration which is that in engines is of the order of 107, which is a larger magnitude than that; that could be experimented. The heat transfer highly depends on as well as Bp and â‹‹T .On the other hand Nusselt numbers will be highly smaller than those tested in engines.
Results and discussion:
Figure 4 depicts the flow field inside the nozzle of a given geometry and under given operating conditions. The flow fields at other operating conditions, as studied in the present work, are similar to that as shown in Fig. 4.
Figure 4: Velocity field in a solid cone swirl nozzle
Influence of Reynolds number (Re) and Swirl number (S) on the coefficient of discharge () and the spray cone angle
It has been observed from the numerical investigation from Fig. 5. and Fig. 6. that both the coefficient of discharge and the spray cone angle remain almost uninfluenced by the Reynolds number of the flow at the inlet to the nozzle for fixed values of S, qr and D2 /D1. However, a significant decrease (of about 5%) in the value of coefficient of discharge with the spray cone angle takes place in case of high value of inlet swirl number (S) equals to 3.0 (shown in Fig. 5). An increase in Reynolds number for a given value of flow ratio (qr) and swirl number (S) implies an increase in the flow through both the central port and the annular swirler. This causes an increase in both the average axial and tangential velocities at inlet to the nozzle, and gives rise to the counter weighting effects of increased strength of swirl and its subsequent decay due to friction in the nozzle. It finally results in almost constant values of Cd and with Re.
Fig. 5: Effect of inlet Reynolds number and swirl number on Сd
Fig. 6: EffeÑtÑ• оf inlet ReynоldÑ• number аnd Ñ•wirl number оn
It is further observed that Cd decreases and increases with an increase in swirl number (S) for fixed values of Re, qr and D2/D1 shown in figure 5 and Figure 6. The decrease in Cd is substantial (of about 6%) for an increase in S from 0.6 to 1.2, while it is considerable when S is increased from 1.2 to 3.0 of about 20%. The change in is more pronounced than that in Cd with S. An increase in , for given values of Re and qr, is associated with an increase in the tangential velocity component at inlet to the nozzle. This causes an increase in pressure drop within the nozzle for a given flow and an increase in the tangential component of velocity over the axial one at the nozzle exit.
Influence of flow ratio( qr) and diameter ratio (D2/D1)on the coefficient of discharge (Cd) and the spray cone angle ():
It is observed from the numerical predictions from Figure 7. that the coefficient of discharge is almost independent of the flow ratio at higher values of diameter ratio (D2 /D1 = 0.38 and 0.75 ). However when the diameter ratio decreases blow 0.38, coefficient of discharge increases with an increase in the value of the flow ratio. The trend is quite sharp Fig. 7. at a lower value of diameter ratio( = 0.125) and in the higher range of , beyond 0.4. An increase in the value of flow ratio for a given value of Reynolds number implies an increase in flow through the central port and a reduction in flow through the annular swirler at inlet to the nozzle. This causes an increase in the average axial velocity through the central port and a decrease in both the axial and tangential velocities through the swirler at the inlet. Under this situation, the swirling strength of flow within the nozzle is reduced with a subsequent reduction in the pressure drop for a given flow. This results in an increase in the value of Cd. However, the effect is more prominent at higher values of qr and values of D2 /D1.
Figure 7: Effect of flow ratio and diameter ratio on Cd
It is extremely important to mention in this context, that the value of Cd in the higher range of qr and at lower values of D2 /D1, exceeds unity (Figure 7). This appears to be in contrast with the conventional understanding that the coefficient of discharge of a nozzle defined by Equation 12, does not exceed unity. The discrepancy observed in this regard can be explained as follows; In usual circumstances, cases with plain orifice nozzle or nozzle with pure tangential entry, the average axial velocity of discharge at nozzle outlet is always less than the term (2 ∆p/Ï)1/2 and hence Cd becomes less than unity. But in a situation like the present one, where there is a very high axial flow velocity at some portion of the nozzle inlet due to the flow through a small central inlet port, the average velocity at the nozzle outlet may be greater than the term (2 ∆p/Ï)1/2 . This happens in the case when flow has high values of qr and lower values of D2 /D1. Under this situation the expression of Cd as define by in Equation 12, loses its conventional significance of coefficient of discharge not exceeding unity.
It is found from Fig. 8. That the spray cone angle is a monotonically decreasing function of flow ratio qr. It is further observed that at all flow ratio, the value of remains almost the same for D2 /D1 values from 0.125 to 0.38. However, a considerable increase in the value of takes place when the value of D2 /D1 increases from 0.38 to 0.75. In the lower range of qr and with higher values of D2 /D1 the average axial velocity of flow through the central port at nozzle inlet is considerably reduced while both the axial and tangential velocities of flow through the annular swirler are increased. This causes an increased strength of swirl in the flow through the nozzle and finally results in a higher value of .
Figure 8: Effect of flow ratio and diameter ratio on
Comparison of numerical predictions with the experimentally measured values:
Fig. 9a and 9b below show that the qualitative trends of Cd and with Re as predicted numerically, matches exactly with those observed in the present experiment for a nozzle given geometry. The numerically predicted values show a fair agreement with the experimentally measured values and are always a little higher than those obtained from the experiments. The deviations between the numerically predicted values and the experimentally measured ones lie between 5 - 9% for Cd and 2 - 6% for .
Figure 9a and 9b: Comparison of numerical and experimental results for the variation of Сd and with Re: (a) Сd vs Re (b) vs. Re
The Fig. 10a and 10b show an exact matching of qualitative trends and a quite reasonable agreement of quantitative results between numerically obtained and experimentally measured values on both Cd and for different values of flow ratio (qr) . The quantitative deviations of the numerically predicted values from the experimentally measured ones remain within 2 - 6% for Cd and 1 - 5% for
Figure 10a and 10b: Comparison of numerical and experimental results for the variation of Cd and with qr: (a) Cd vs qr (b) vs qr
It is readily established between the theoretical and experimental results, that the adaptation of the standard k-ε model for turbulence in nozzle flow serves well the purpose of predictions of the coefficient of discharge (Cd) and the spray cone angle () within the range of operating parameters studies in the present work.
Conclusion
After thorough investigations conducted by numerous researchers regarding the cooling process of blades within a gas turbine engine it can be concluded that the theoretical predictions of the coefficient of discharge and the spray cone angle of a swirl nozzle have been made from numerical computations of flow within the nozzle. The results of the experiments have shown the validation of these numerical predictions with little or no variation between the two.
Similarly, the coefficient of discharge and the spray cone angle are almost unaffected by the Reynolds number of flow at the inlet of the nozzle. The increase in inlet swirl number using the equation 8f directly increases the spray cone angle. The influence of the swirl number on the spray cone angle is profound in the entire range of the inlet swirl number from 0.6 - 3.0 as currently studied in the present work. The coefficient of discharge undergoes a marginal decrease of about 6% with an increase of the swirl number from 0.6 to 1.2 although in engineering terms this change is significant, on the other hand the decrease in the coefficient of discharge is considerable with an approximate decrease of 20%, this is only when the swirl number increased from 1.2 to 3.0. Hence the swirl number is indirectly proportionate to the coefficient of discharge.
The value of the flow ratio (qr) is directly proportionate to the coefficient of discharge, as when the flow ratio increased the coefficient of discharge followed pursuit. Taking these two results into consideration, a result in decrease of the spray cone angle ratio has been shown. However the influence of the flow ratio on the coefficient of discharge is outstanding only at lower values of the diameter ratio (D2/D1) previously mentioned. Therefore the value of the coefficient of discharge increases only when there is a decrease in the diameter ratio mainly in the range of a high value of flow ratio and at a specific value of a diameter ratio less than 0.17.
The spray cone angle, on the other hand is almost to be uninfluenced for all value of the diameter ratio below 0.38, while the spray cone angle increase when the diameter ratio increased by 0.38. The increase in the spray cone angle is more important in the lower range of flow ratio.
Finally the use of standard k-Æ model of turbulence for a swirling flow in the nozzle is vastly adequate for the accurate predictions of nozzle performance parameters, including the coefficient of discharge as well as the spray cone angle.
