Characteristic variation of Mach number in subsonic co-flowing jets by varying lip thickness

Abstract

Jet noise reduction is achieved by jet mixing enhancement which is attributed to potential core length reduction of the primary jet. Varying lip thickness can be considered as a passive control method to reduce the potential core, to enhance mixing. This article focuses on certain novel attributes of subsonic co-flowing jet Mach number decay for the wake dominated flow by varying the lip thickness, which is defined as the gap between the core nozzle and surrounding duct along with varying bypass ratio. Three different lip thicknesses namely of 2 mm, 10 mm, and 15 mm at jet exit Mach number of 0.6 was experimentally studied for the bypass ratios ranging from 0.7 to 6.4. To study the flow characteristics, Pitot static measurements was conducted experimentally in both axial and radial directions of the jet. To visualize the jet flow development for the tested cases, numerical simulations with experimental validation, were also carried out. For exit Mach number of 0.6, the single free jet has a potential core length up to X/D_p = 3.8, whereas for 10 mm lip co-flowing jet with bypass ratio 0.7, 1.4 and 6.4 the potential core length extends up to X/D_p = 2.8, 2.7 and 2.1 and their corresponding percentage reduction is 26, 29, 45% respectively. Similarly for 15 mm lip for co-flowing jet with bypass ratio 1, 1.7 and 6, the potential core length extends up to X/D_p = 2.7, 2.2 and 1.6 and their corresponding reduction percentage is 29, 42, 58% respectively. Concluding that for the thick lip co-flowing jet, the presence of recirculation zone at the near field of the nozzle wall, the centreline Mach number increases initially due to the wake dominant sub-atmospheric pressure, exists in the flow regime and also when the bypass ratio increases, the potential core length decreases.

Introduction

Noise is a major cause of disturbance to passenger comfort in a turbo fan engine driven aircraft. By enhancing the mixing between the exhaust gas stream and the ambient, the noise levels can be controlled. There are various active and passive control methods employed, out of which passive control methods outperform active control methods. Coaxial jets, chevrons, tabs, grooves, and cut-outs, notches are some of the passive control methods that have been employed in subsonic passenger aircraft for jet noise reduction. A single free jet comprises three regions namely the potential core region, characteristic decay region, and fully developed region¹. Figure 1 depicts the flow regions occurring for Co-flowing Jets (CFJ) with a negligible value of lip thickness. The Initial Merging Zone is defined as the region in space till the end of the annular jet potential core. The Intermediate Zone is the region in space where the annular jets and core jet interacts. A Fully Merged Zone as the name indicates is the region in space where the annular jet and core jet get merged fully². Additionally, a region named Influential Wake Zone has been observed for CFJ with finite lip thickness^3,4.

Fig. 1.

Schematic representation of flow physics caused by the thin lip coaxial jets.Region 1: Initial Merging Zone, Region 2: Intermediate Zone, Region 3: Fully Merged Zone, Region 4: Primary Shear Layer, Region 5: Secondary Shear Layer.

Thin lip co-flowing jet and bypass ratio effects

Forstall and Shapiro examined the variation in velocity ratio of a very low subsonic co-flowing jet enclosed by the airstream of a wind tunnel⁵. They found that the turbulent transport and spreading rate were controlled by employing the velocity ratio. In recent years, several aeronautical research works have mainly focused on high thrust and reduced jet noise. Georgiadis and Papamoschou numerically investigated coaxial jets with a lip thickness of 0.4 mm and with different diameter ratios and with constant primary (Mach 1.5) and varying secondary Mach numbers^6,7. They observed that the potential core length (PCL) of the main jet elongated when the outer jet Mach number increased. Additionally, when the outer jet diameter increased, the PCL of the core jet increased. Both of these signify mixing inhibition characteristics caused by the secondary jet. Thin lip thickness in co-flowing jets usually inhibits mixing. But Papamoschou found that they enhanced mixing. With a supersonic primary jet that is surrounded by a secondary jet stream of properties, namely velocity and density (co-flow or secondary flow), he observed that the decaying rate of the core jet declined due to the interference of high speed (from low subsonic M < 1 to sonic M = 1 to supersonic M > 1) co-flow jet. In his observation, shear action creates strong instability, aiding mixing enhancement. Shear action destabilizes the adjacent flow by employing parallel injection. Zaman et al. varied primary and secondary jet Mach numbers and found that the shear action between the jets decreases the static pressure at the beginning due to shear force dominance and then increases⁸. They measured the Mach number using a Pitot Static probe with a lip thickness of 0.7 mm (shear-dominated flows), with a varying bypass ratio of 0 to 10. But they had not varied the lip thickness.

Pinnam Lovaraju and Rathakrishnan performed an experimental analysis with coaxial jets with a constant separation distance of 2.65 mm and constant low bypass ratio of 0.56 with various Nozzle Pressure Ratios (NPR is the ratio of the inlet stagnation chamber pressure (p₀) to the ambient pressure (P_a)) namely 1.2755 (Mach 0.6), 1.52 (Mach 0.8), 1.89 (Sonic correctly expanded), 3.0, 5.0 and 7.0 (Sonic underexpanded cases)⁹. In all these cases, mixing was inhibited by the shielding of the primary jet by the secondary jet. A similar investigation was carried out by Srinivasarao et al., with the same coaxial nozzle but with NPRs 3.0, 4.0, and 5.0¹⁰. They concluded that supersonic core length increases with the presence of co-flow.

Wake-dominated flow regimes

Ryuichi Matsumoto and Kyoji Kimoto observed non-uniform velocity at the nozzle exit with a finite lip thickness of 4.5 mm¹¹. The flow characteristics of finite lip thickness are shown in Fig. 2. They performed an analysis, with a central jet velocity of 35 m/s, and a surrounding jet velocity of 29 m/s. This behavior is a unique characteristic found only in CFJ with finite lip thickness. The reason for non-uniformity in near-field axial velocity is because of the sub-atmospheric region in the near-field wake region between primary and secondary jets. For finite lip thickness, the static pressure varies both along and across the flow directions. A recirculation zone occurs in the wake region and it becomes dominant proportionally with the bypass ratio. Hence, the variation in the bypass ratio becomes significant when the CFJ bypass ratio increases. Huda et al. designed an optimal burner nozzle to achieve combustion stability¹². They varied lip thickness from zero mm to 16 mm and found that the 12 mm lip thickness nozzle showed perfect combustion both experimentally and numerically. Studies on low subsonic wake dominant co-flowing jets were found in plenty in the open literature^13–20.

Fig. 2.

Schematic representation of flow physics caused by the thick lip coaxial jet. Region 1: Initial Merging Zone, Region 2: Intermediate Zone, Region 3: Fully Merged Zone, Region 4: Inner Vortex, Region 5: Outer Vortex.

Srinivasarao et al. conducted experiments with co-axial orifices with separation distances of 1.5 mm and 4.5 mm and with a very low bypass ratio of around 0.19²¹. When compared to a single free jet, the potential core length of coaxial jets was shortened by 45% and 58% for lip 1.5 mm and 4.5 mm respectively. Srinivasarao, et al. studied co-flowing jets from coaxial nozzles by varying inner separation distances between 3 mm, and 15 mm²². They found that increasing lip thickness reduced potential core length from 60 mm (6D_p) to 40 mm (4D_p), which is a 33.33% reduction.

Shankar et al. numerically and experimentally studied wake-dominant co-flowing jets. They found that increasing lip thickness between primary and secondary jets enhances mixing to an extent and inhibits it^23,24. They proposed a critical lip thickness range over a varied range of lip thicknesses. Similarly, they varied the bypass ratio from 0.7 to 6.4 at a constant finite separation distance of 10 mm and found that increasing the bypass ratio shortens the core length of the main jet²⁵. Additionally, the near-field centreline static pressure can range up to 11% above and below barometric pressure. Hence the possibility of Mach number variance along the main jet axis is evident. An effort to find critical lip thickness within which the jet mixing improves and above which the mixing inhibition occurs was performed by Shankar et al. for the exit main jet Mach number of 0.6²⁶. This was done for the bypass ratio of 6.3 by varying separation distance from 10 mm to 150 mm. The critical range was found to be 10 mm to 25 mm. A similar work was conducted numerically by Shankar et al. with varying lip thicknesses from 2 mm to 150 mm with a constant velocity ratio of unity for nozzle exit Mach 0.6^3,4. Here the critical range was found to be 20 mm to 80 mm.

Previous literature refers to the dual stream concentric jets issued into a stationary environment that is said to be a co-flowing jet. If it is issuing into a flow, constituting a field with the jet surrounded by a flow field of differing velocity, it is also referred to as a co-flowing jet. Datta et al. (2015.a) studied the coflowing jet in numerical simulation with the spatial discretization of the sixth-order compact scheme and temporal integration of third-order low storage Runge- Kutta method at different velocity ratios Vr = 0.6, 0.54, and 0.212 respectively²⁷. The results show the expected lengthening of the potential core and reduction of jet spreading with an increased velocity ratio. The shape of the mean velocity profiles is insensitive to the velocity ratio. Datta et al. (2015.b) studied the co-flowing jet with spatial and temporal integration schemes that are identical to the former case at various convective Mach numbers from 0.3 to 0.7²⁸. The mean velocity profile is appropriate with the convective Mach number. The potential core length increases with the Mach number. The increasing convective Mach number reduced the jet spreading rate but increased the length of the developing region of the jet.

Perumal et al. reported that enhancing the jet mixing using passive control devices leads to the advantage of reducing the jet noise²⁹. Sathishkumar et al.³⁰ numerically investigated thin and thick lip nozzles in supersonic flow regimes and reported that flow from thin lip is shear dominated and the flow from thick lip is wake dominated. Radha Krishnan et al.³¹, also reported that, the jet mixing is better for the high bypass coaxial jet compared to the low bypass coaxial jet at all expansion levels. From the literatures, Zaman et al.⁸, has analyzed the Mach number variation for shear dominant flows. The Mach number variation on wake dominated jet characteristics by varying lip thickness has not been reported yet. Naren et al.^23–25 analyzed the coaxial jets with lip thickness variation by studying the axial total pressure and pressure profile along radial direction of the jet for high subsonic regimes. Previous researchers converted the measured total pressure values into Mach number using isentropic relation assuming static pressure as constant.

The lip thicknesses chosen for the study (0.2 D_p, 1.0 D_p, and 1.5 D_p) is the combination of prior experimental and numerical studies [e.g., Shankar et al.,³; Srinivasarao et al.,²², which identified critical ranges where wake-dominated flow behavior and mixing enhancement are prominent. These values also align with practical manufacturing constraints and nozzle geometries typically encountered in aero engine applications. The intent of the present study is to span the range from minimal separation (thin lip) to strong wake interaction (thick lip), thereby systematically capturing the effect of Mach number and bypass ratio on wake dominance jet mixing and potential core behavior.

From the literatures, plenty of researchers have explored velocity or pressure variation in coaxial jets, assuming no variations in static pressure. The present study provides, a detailed investigation into the effect of Mach number behavior caused by lip thickness variation under wake-dominated conditions, where the exit flow Mach number is oscillating in the near field because of the variation in near field static pressure. The total and static pressures are measured using a Pitot static tube, not by assuming the static pressure as constant to analyse the Mach number characteristics. This is achieved through direct experimental measurements of both total and static pressures, at Mach 0.6, which has not been systematically reported in earlier studies.

Experimental investigations

The experiments were carried out in the open jet facility at the high-speed jet laboratory, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai, India. The schematic representation of the open jet lab facility is given in Fig. 3a and b. The working fluid is the atmospheric air with mean sea level conditions. The air is first compressed using a reciprocating compressor, then fed to an air drier to remove moisture and then stored in the storage tank. The dry and compressed air from the tank is regulated by the pressure regulating valve and then sent to the settling chamber, where it reaches a settled equilibrium. The flow is streamlined by two wire-mesh screens, which are kept downstream. Static pressure in the test section is atmospheric. It is kept constant in the settling chamber by providing mesh screens and making the settling chamber velocity to zero. The model is fixed at the exit of the settling chamber with the help of a model holder. The compressed air from the settling chamber passes through the primary nozzle and the co-flow nozzle. The flow rate is controlled by means of a gate valve and pressure regulating valve, to set the desired pressure.

Fig. 3.

(a) Open jet facility depicted schematically. (b) Experimental setup - open jet facility.

A typical Pitot static probe (Fig. 4) is utilized to measure the stagnation and static pressure in the present study. The Pitot tube measures only total pressure whereas Pitot static tube as the name implies measures total pressure as well as static pressure. The stagnation probe has an external diameter of 0.6 mm and an internal diameter of 0.4 mm, to measure the total pressure. Static probes (4 numbers) of 1 mm diameter were placed 8 mm left from the stagnation point to measure the static pressure. The Pitot static probe is mounted on the 3D axis traverse mechanism and is moved along and in radial directions of the jet, manually. The ratio of the jet cross-sectional area to the predicted size of the Pitot probe has to be more than 64 to consider the probe obstruction impact as negligible. Here, the primary nozzle used to deliver the jet has 10 mm exit diameter, thus the probe blocking ratio, in this case, would be (10/0.6)² = 277.78, which was well above the blocking limit of 64 for considering the probe blockage to be negligible. Hence blockage will not be a factor and is completely negligible¹. From all the above-mentioned literatures, only the Pitot probe was utilized to gauge the velocity using the isentropic relation given below.

1

Fig. 4.

Schematic representation of the Pitot static probe in the jet field.

where P₀ is the total/stagnation pressure calculated by the Pitot tube, P_s refers to the static pressure, which is calculated by the static probes. In the present study, the Mach number has been computed by measuring total and static pressure and using the isentropic relation as shown in Eq. 1.

In this research, all the primary nozzles are made up of stainless steel, with a primary nozzle inlet diameter of 20 mm, a primary nozzle exit diameter of 10 mm, a secondary duct constant width of 5 mm, and length of core nozzle and surrounding duct as 60 mm. The geometrical details of lip thickness 2 mm, 10 mm, and 15 mm respectively are shown in Figs. 5 and 6, and 7³². The Experimental models are axisymmetric models. No passive controls are used in this study and it is a simple coaxial jet from axisymmetric coaxial nozzle with varying lip thickness^3,26,32.

Fig. 5.

Illustration of CFJ model with LT = s2mm.

Fig. 6.

Illustration of CFJ model with LT = 10 mm.

Fig. 7.

Illustration of CFJ model with LT = 15 mm.

Lip thickness 0.2 D_p CFJ has an area ratio of 3.8, and a velocity ratio of 0.95 leading to a bypass ratio of 3.61, which is constant throughout the study. For lip thickness of 1.0D_p and 1.5 D_p, the bypass ratio is massively varied. By changing the secondary jet flow area, the bypass ratio and mass flow rate of the surrounding jet can be controlled. By changing the jet flow area in the annular passage, the bypass ratio can be adjusted. This is achieved by fixing a disc (Fig. 8) with 60 mm diameter, at the inlet of the model. The disc has a 20 mm diameter hole in the center to permit the air to flow in the primary nozzle which has an inlet diameter of 20 mm. The disc also consists of 16 holes of 0.4 D_p (4 mm) and 12 holes of 0.5 D_p (5 mm), located in annular manner, to allow the air in to the secondary duct^9,22. The discs are placed in the inlet of the coaxial duct to reduce the mass flow rate of the secondary duct by passive means which results in bypass ratio variation. The annular jet emerges from 16 holes of 0.4 D_p diameter with a area ratio of 1.9 and Mach number ratio of 0.4 when the core jet’s exit Mach number is 0.6 and the co-flowing jets BR0.7. The annular jet from 12 holes of 0.5 D_p diameter with a area ratio of 3 and Mach number ratio of 0.4 when the core jet’s exit Mach number is 0.6 and the co-flowing jets BR1.4.

Fig. 8.

Schematic diagram of the bypass plate attached at the inlet of the co-flowing nozzle with lip thickness 1.5D_p: (a) BR 0.7, (b) BR 1.4.

It would be easy to compare the various co-flowing jet results by designating them with the values of bypass ratio and lip thickness. For example, the Lip thickness 1.0D_p, bypass ratio 6.4, and Mach number 0.6 configuration is designated as LT 1.0 BR 6.4 M 0.6. Similarly for Lip thickness 1.5D_p, bypass ratio 6.0, and Mach number 0.6 configuration is designated as LT 1.5 BR 6.0 M 0.6, and so on. Tables 1 and 2 represents the initial conditions for 1.0D_p and 1.5D_p lip thickness models. Based on the initial conditions, the following exit conditions were attained from the experiments conducted.

Table 1.

Designation of co-flowing jets according to initial conditions for separation distance 1.0 D_p.

Lip thickness of 1.0 Dp	Primary Mach number	Secondary Mach number	Main jet area (mm2)	Co– flow area (mm2)	Area ratio	Mach number ratio	Bypass ratio	Designation
Basic model	0.60	0.55	78.5	549.8	7.0	0.9	6.4	LT1.0 BR- 6.4 M 0.6
5 mm holes	0.60	0.28	78.5	235.6	3.0	0.5	1.4	LT1.0 BR- 1.4 M 0.6
4 mm holes	0.60	0.23	78.5	150.8	1.9	0.4	0.7	LT1.0 BR- 0.7 M 0.6

Table 2.

Designation of co-flowing jets according to initial conditions for separation distance 1.5 D_p.

Lip thickness of 1.5 Dp	Primary Mach number	Secondary Mach number	Main jet area (mm2)	Co–flow area (mm2)	Area ratio	Mach number ratio	Bypass ratio	Designation
Basic Model	0.60	0.40	78.5	706.9	9.0	0.7	6.0	LT1.5 BR- 6.0 M 0.6
5 mm Holes	0.60	0.33	78.5	235.6	3.0	0.5	1.6	LT1.5 BR- 1.7 M 0.6
4 mm Holes	0.60	0.24	78.5	201.1	2.6	0.4	1.0	LT1.5 BR- 1.0 M 0.6

The study is performed for the primary jet exit Mach number of 0.6. Based on the isentropic relation, the corresponding total pressure for Mach 0.6 jet is 1.27 bar. Hence the experiment is carried out with the nozzle inlet total pressure of 1.27 bar. Due to the single feed system from the settling chamber, for the primary and secondary nozzle, the secondary jet exit Mach number decreases because it exits from the holes from the disc and flows through annular duct. To find the secondary jet exit Mach number (which will be lesser than the primary jet exit Mach number), the Pitot probe is used to ensure the Mach number and is listed in Table 3. The total pressure along and in radial direction of the jet were measured using the Pitot static tube. The measured total pressures were converted to Mach number using the isentropic relation (Eq. 1).

Table 3.

Operating conditions.

S. no.	Lip thickness (mm)	Lip thickness (Dp)	Primary jet exit Mach number	Primary jet exit total pressure (bar)	Secondary jet exit Mach number	Secondary jet exit total pressure (bar)
1	2	0.2	0.6	1.27	0.57	1.24
2	10	1	0.6	1.27	0.55	1.23
3	15	1.5	0.6	1.27	0.4	1.12

Experimental results and discussions

Centreline Mach number decay by varying nozzle lip

The existence of a recirculation zone in the near-field of CFJ with a large separation distance causes the Mach number and static pressure to vary. When the LT is 0.2 D_p, a mild recirculation zone occurs between the main jet and the surrounding jet. When the separation distance increases to 1.0 and 1.5 D_p, a dominant recirculation zone occurs between the main jet and the surrounding jet. The Mach number variance in the near-field is mainly because of the static pressure variance in the near-field. However, the static pressure variance takes place because of the recirculation zone’s presence. As a result, when lip thickness increases, the recirculation zone becomes dominant, resulting in Mach number variance. Figure 9 shows centreline Mach number variation for CFJ with lip thickness of 0.2 D_p, 1.0 D_p, and 1.5 D_p at main jet exit Mach 0.6. The Mach number increases in the near field for a lip thickness of 0.2 D_p and becomes stable after an axial extent. This is due to the near-field wake, which lowers near-field static pressure and hence increases the Mach number in this region. This variation is not much pronounced because of the low value of lip thickness. As the lip thickness increases, the Mach number increases in the near field and then decreases as there will be a fall and rise in static pressure and these effects are due to the wake region and recirculation region in the near field respectively. An identical pattern is detected for lip thickness of 1.5 D_p and also for greater values of Mach numbers and hence not shown.

Fig. 9.

Centreline Mach number variation for CFJ: lip thickness 0.2 D_p, 1.0 D_p and 1.5 D_p at main jet exit Mach M = 0.6.

From the above results, the thickness of the nozzle lip plays a clear role in how the jet develops along the centerline. When the lip is thin (0.2 D_p), the jet issues cleanly with little disturbance at the exit. The shear layer protects the jet, which allows the potential core to extend further downstream. With the mid lip (1.0 D_p), the jet shows an intermediate behavior, with a balance between shear and weak wake effects. In contrast, the thick lip (1.5 D_p) introduces a stronger wake and higher turbulence in the near field. This increases entrainment of the coflow, accelerates mixing, and results in a faster decay of the centerline Mach number and a shorter core length.

Centreline Mach number decay by varying bypass ratio

The near field of the co-flow jet is highly wake-dominated, because of the higher values of lip thickness, and bypass ratio, which vary in the near field. Figure 10 shows the centerline Mach number variation of different bypass ratios for Mach 0.6 CFJ. When the flow becomes highly turbulent, there exists a non-uniform velocity at the outlet of the nozzle, and the potential core is not recognized¹¹. The potential core for the co-flowing jet is characterized as the axial extent up to which the main jet’s centreline Mach number is equal to nozzle exit jet Mach number. But in our work the near field Mach variation is not constant due to the variation in the static pressure⁸. Hence potential core is not recognized in the near field axial Mach number variation. As previously mentioned, CFJ with comparatively higher lip thickness values has more variance in Mach number than CFJ with lower lip thickness values. Similarly, CFJ with higher bypass ratios has more Mach number variance than CFJ with lower bypass ratios. Additionally, the separation distance of 1.5 D_p at the core nozzle exit Mach number 0.6 also follows the trend, and is evident from Fig. 11. Again, higher Mach numbers behave similarly.

Fig. 10.

Centreline Mach number variation for CFJ: LT 1.0 D_p and with bypass ratio 0.7, 1.4, and 6.4 at main jet exit Mach M = 0.6.

Fig. 11.

CFJ Axial Mach number variance: LT 1.5 D_p and bypass ratios 1.0, 1.7, and 6.0 at main nozzle exit Mach M = 0.6.

From the above results, the bypass ratio also has a significant influence on the centerline decay. At a lower bypass ratio, the coflow momentum is relatively small, and its impact on the jet is limited. As the bypass ratio increases, the stronger coflow interacts more actively with the primary jet. This energizes the shear layer, enhances entrainment, and promotes quicker mixing between the streams. In other words, a higher bypass ratio makes the jet break down faster and shortens the persistence of the centerline Mach number.

Radial Mach number variation

Radial profiles were used to analyze the jet spread characteristics such as primary jet core in radial direction, recirculation zone, wake region, secondary jet potential core. Figure 12 depicts the co-flowing jet’s radial Mach number variance of a Mach 0.6 jet at centreline distances of X/D_p = 0.1 to 4.0 for 0.2 D_p model. The main jet’s core can be seen from R/D_p = 0.0 to R/D_p = 0.4 in the case of X/D_p = 0.1. Then the Mach number decreases because of the presence of the wall. The wake region has 66% of the main jet exit Mach number. The curve then shoots up again due to the co-flowing jet Mach number, reaching 95.5% of the exit Mach number of the main nozzle at R/D_p= 0.8, creating a V-shaped bucket-like structure. The radial degree to which the wake region prevails like an inverted top hat profile. The width of the inverted top hat profile increases as the lip thickness increases. For the small lip thickness, this profile is just a single point. It has to be noted that the values of non-dimensionalized Mach numbers, starting at X/D_p = 0.1 and going up to 4.0 for all axial stations throughout the surrounding field, is a consequence of the static pressure variance in the near-field, as discussed earlier. This is a critical feature of CFJ with lip thickness, also known as wake-dominated flows in the literature. Furthermore, from R/D_p = 0.0 to R/D_p = 0.5, the increase in Mach number has a noteworthy impact on the near-field radial variance, especially in the potential core. The minimum Mach number obtained at axial position X/D_p= 0.5 is 74.7% of the exit Mach number, which is observed at R/D_p= 0.4. As the jet flows downstream, the wake effect or wall effect, which causes the Mach number to decay radially, diminishes. The secondary and primary jets join together as the axial distance grows longer, resulting in an equal Mach number.

Fig. 12.

Near-field radial CFJ Mach number variance: Mach number M = 0.6, LT0.2 D_p at the main nozzle exit.

Figure 13 shows the near-field radial profiles for 1.0 D_p lip thickness up to X/D_p= 4.0. The potential core is visible from R/D_p = 0.0 to R/D_p = 0.4 at X/D_p = 0.1. Then the Mach number is reduced due to the influence of the lip, which creates a wake region. The minimum Mach number prevails at the radial position of R/D_p = 6. The wake region has just 6.4% of the main jet outlet Mach number. It ranges from R/D_p = 0.6 to R/D_p = 1.3. The radial profile then increases after R/D_p = 1.3 due to CFJ interference and reaches 90% of Mach number, similar to that of the core jet at R/D_p = 1.7. The Mach number in the radial direction reduces in the remaining radial positions after R/D_p = 1.7. X/D_p= 0.1 revealing a Mach number bucket-like shape that is nearly symmetric. The base of the Mach number bucket shrinks as the axial location increases. This is because the secondary jet proceeds without entraining with the primary jet.

Fig. 13.

Near-field radial CFJ Mach number variance: Mach number M = 0.6, LT 1.0 D_p at the main nozzle outlet.

Figure 14 shows a near-field radial plots for lip thickness of 1.5 D_p up to X/D_p = 4.0. Potential core is observed at X/D_p = 0.1 from R/D_p = 0.0 to R/D_p = 0.4. The Mach number decreases due to the presence of a wall. The next radial position, R/D_p=6, has a very low Mach number due to the separation region, which creates a wake zone that can be seen evidently on the graph. The wake zone has only 6% of the core jet’s outlet Mach number. It spans the range of R/D_p = 0.6 to R/D_p = 1.9. The radial profile then increases after R/D_p = 1.9 due to CFJ interference, reaching 68% of the Mach number of the main jet at R/D_p = 2.2. The radial Mach number decreases in more radial positions after R/D_p = 2.2. This radial plot is almost similar to the radial variance of the CFJ with a lip thickness of 1.0 D_p, except that the wake region has been extended. Also, the maximum Mach number attained by the secondary jet decreases when lip thickness increases. For separation distances of 0.2 D_p, 1.0 D_p and 1.5 D_p the maximum secondary jet Mach number attained are 95%, 90%, and 68% respectively. This is because the co-flowing jet has a single feed system and as lip thickness increases; the incoming air at the secondary inlet becomes less distributed. Hence maximum Mach number attained by the secondary jet varies based on the variation in lip thickness.

Fig. 14.

Radial surrounding field Mach number variance for the co-flow jet with LT1.5 D_p at main nozzle outlet Mach M = 0.6.

Analysis of uncertainty

The barometric pressure was measured at 734 mm Hg, with a margin of error of 0.5 mm Hg (734 ± 0.5 mm of Hg). In this particular instance, the uncertainty measured was 0.068%. The outlet diameter of the main nozzle was 10 mm with a margin of error of 0.025 mm (10 ± 0.025 mm). By measuring the total pressure, a notable error of ± 1% was obtained (Pitot tube used for measuring the gauge pressure). The uncertainty in the gauge pressure is equal to 0.507% and the uncertainty associated with the Mach number of the jet is ± 1%.

Numerical simulations

To further understand the flow physics and the jet flow development of the varied lip thickness models, a detailed numerical simulation has been carried out using commercial simulation software.

Geometry creation and computational grid

A 2D constant area single jet model was created with a nozzle length of 60 mm, an inlet diameter of 20 mm, and an exit diameter of 10 mm (equal to 1.0 D_p) in the GAMBIT software. Due to symmetry, only the top half of the model was designed. A rectangular block was created from the exit of the nozzle to study the flow physics, and it is referred to as the computational domain. A domain region of 10 D_p x 40 D_p was chosen after the nozzle exit to study the mixing of the jet at the nozzle exit. The computations were carried out on a controlled grid generated by GAMBIT 2.3.1, as shown in Fig. 15. Along the computational domain, about 43,300 cells were spread out. Grid points at the nozzle and the nozzle exit were fine for determining near-field characteristics such as the recirculation region, the potential core, and so on.

Fig. 15.

Computational domain region and mesh setup for lip thickness 1.0 D_p.

Boundary conditions

The numerical boundary conditions for the simulations with all turbulence models were similar to the experimental conditions of the flow. The CFJ nozzle inlet is designated as a pressure inlet with a total pressure value of 1.27 bar, which corresponds to Mach 0.6, and its walls, the nozzle upper wall, and the domain left side wall are designated as wall boundary conditions. The bottom of the domain is designated as an axis throughout the length of the domain. The top and right-hand sides of the domain are designated as pressure outlet boundary conditions with an ambient pressure of 1 atm. The boundary conditions are given in Table 4. By changing the boundary condition of the co-flowing jet inlet, the bypass ratio could be changed. In this case, the co-flowing jet was studied using a separate inlet as shown in Fig. 16.

Table 4.

Boundary conditions.

Boundary Conditions	Regions
Wall	Nozzle wall and domain wall
Pressure inlet	Primary nozzle inlet and Secondary nozzle inlet
Pressure outlet	Domain (top and exit)
Axis	Primary nozzle axis and domain axis

Fig. 16.

Computational model showing computational domain with a separate inlet for the primary nozzle and co-flowing duct, jet domain for lip thickness 1.5 D_p CFJ.

Turbulence model comparison for computational analysis

To understand the prominent flow physics of the wake-dominated jet flow, a detailed numerical study is carried out in the flow field at both near and far-field. The solver used for the numerical simulation is Ansys Fluent. The solver type is a density-based solver. Absolute velocity formulation is used. Flow is steady and axisymmetric. The spatial discretization includes the least square cell-based gradient, the second-order upwind scheme flow, the first-order upwind scheme turbulent kinetic energy, and the first-order upwind scheme turbulent dissipation rate. The numerical simulation is carried out with various turbulence models and the results were validated with the results of the experimental centreline total pressure profile. Eddy-viscosity formulations can be solved using a variety of turbulence models. Simulation employed with one-equation Spalart–Allmaras (SA) model³³, linear two-equation k- ε model of Chien³⁴, shear-stress transport (SST) model of Menter³⁵, two-equation realizable k-ε model, Wilcox’s standard k–ω model³⁶, and Reynolds-stress model³⁷ were compared in the turbulence model study, along with the experimental results. The standard models’ dearth is the delayed initial jet mixing rate in comparison to experimental results³⁸. Figure 17 shows the centreline total pressure variation for all the schemes of turbulence models, as well as the experiment co-flowing jet lip thickness of 0.2 D_p for Mach 0.6. The SA model generates results that are in well agreement with experimental data. The Spalart-Allmaras model (Spalart & Allmaras³³ has been formulated to produce good results for boundary layers subjected to adverse pressure gradients and was designed specifically for aerospace applications involving wake-dominated and wall-bounded flows^33,39. Hence, the Spalart–Allmaras (SA) turbulence model was chosen for this study based on its demonstrated ability to capture the near-wall behavior and wake-dominated flow physics typical of co-flowing jets with finite lip thickness. The one-equation formulation of the SA model makes it computationally efficient while maintaining good accuracy for attached boundary layers and mildly separated flows, which are prevalent in the present configuration. However, it is important to note the known limitations of the model. The SA model tends to under predict turbulence generation in flows with strong adverse pressure gradients, large-scale separations, or highly three-dimensional unsteady vortical structures. Therefore, while it is well-suited to the wake-dominated but largely axisymmetric flow field studied here, caution is advised when applying the model to configurations where separation and secondary flows dominate the physics.

Fig. 17.

Turbulence model comparison for centreline total pressure distribution: CFJ by 0.2 D_p, at main jet exit Mach 0.6.

However, the k– ε standard model reveals more slow decay compared to the experimental values along the characteristic decay region. Other turbulence models decay at a slower rate when compared with the experimental decay.

Figure 18 shows the centreline absolute pressure variance with lip thickness of 1.0 D_p for a co-flowing jet at Mach 0.6. For all the schemes of turbulence models as well as the experiment, recirculation is observed adjacent to the lip, which regulates the flow field.

Fig. 18.

Turbulence model comparison for centreline absolute pressure variance with LT 1.0 D_p for a co-flowing jet, at main jet exit Mach 0.6.

In SA model, the percentage variation is very minimum of about 4%. Transition K- KL-Omega model under predicts the core, decay and fully developed regions, hence given in negative in Table 5. Other models overpredicts as listed in Table 5.

Table 5.

Percentage variation with respect to experimental results.

Turbulence model	Maximum error percentage
Spalart- Allmaras model	4%
K-epsilon standard	30%
K-epsilon RNG	50%
K-epsilon realizable	44%
K-omega standard	61%
K-omega BSL	24%
K-omega SST	25%
Transition K- KL-omega model	-27%
Transition SST	25%
Reynolds stress model	24%

Grid independence study

The mesh is generated with a finer grid in the near field and a coarser grid in the far field. For the finer grid used in the study, the ⁺ value at the wall-adjacent cells was maintained as 0.5 (y⁺_max = 0.5) throughout the nozzle and near-field regions, ensuring that the viscous sub-layer was fully resolved in line with the requirements of the Spalart–Allmaras turbulence model. The mesh refinement was carried out systematically, increasing the number of cells from 24,000 (coarse) to 43,300 (medium) to 171,800 (fine), with finer near-wall and near-lip resolution (Ng & Spalding⁴⁰. Convergence was monitored and ensured by achieving residuals 10⁻⁶ for continuity and momentum equations, and by verifying that key flow metrics (such as potential core length and centerline Mach number) varied by less than 2% between the medium and fine grids. Figure 19 shows the centreline decay of total pressure in the central jet plume, comparing numerical and experimental results, for a separation distance of 1.0 D_p. The results show that all three types of grids apprehend the flow field characteristics in the jet plume.

Fig. 19.

Grid independence study on co-flow jet with LT 1.0 D_p, at M = 0.6.

Centreline Mach number decay

Figure 20 represents the centerline Mach decay profiles comparing the present experimental and numerical study for the coflow jet nozzle with lip thickness of 0.2D_p, 1D_p and 1.5D_p at Mach 0.6. Comparing the results, it is observed that the results of the experimental and numerical values fit closer to each other with a percentage deviation of ± 2.

Fig. 20.

Centreline Mach decay profiles for various lip thickness comparing experimental and numerical results.

Velocity contours of co-flowing jets

The velocity contour plots are shown for all lip thicknesses and bypass ratios for Mach number 0.6. These contours are clear indicators of jet flow development across the plane. The contour for the lip thickness 0.2D_p CFJ is given in Fig. 21. It is perceived from this contour that the surrounding jet separated at a distance of 2 mm from the primary jet, providing a shielding effect to elongate the potential core of the primary jet, and inhibiting mixing⁹. Figures 22 and 23 show the jet development for different co-flowing jets at lip thickness 1.0 D_p with bypass ratios, 0.7 and 6.4 respectively. It is seen in centreline decay plots that the relatively low bypass ratio CFJ is having a longer potential core as compared to the relatively high bypass ratio CFJ. For CFJ with a separation distance of 1.0 D_p, there is a gradual decrease in potential core with the increase in bypass ratio. In the region between the core and the annular jets, a low-pressure region prevails and the region becomes sub-atmospheric. The strength of the secondary jet increases along with the bypass ratio. The merging point where the inner and the outer jet reattach moves far axial as the bypass ratio increases which can be seen from the contours below. It can be visualized that, as the bypass ratio increases, the main jet potential core shrinks, and for the bypass ratio of 6.4 and lip thickness 1.0 D_p, it gets almost chopped off in the near field¹⁷. A recirculation zone occurs in the middle of the core jet and the surrounding annular jet. It becomes influenced as the bypass ratio increases. For lip thicknesses 1.0 D_p with increasing bypass ratios, the recirculation zone occurs in the near-field region and becomes dominant thus vigorous mixing occurs between primary and secondary jets, thereby decreasing the main jet potential core. Furthermore, as the lip thickness is increased, the merging location of the two streams moves away from the nozzle, and the recirculation zone expands.

Fig. 21.

Velocity contour for CFJ: bypass ratio BR 3.6 and Mach M = 0.6 on LT 0.2D_p.

Fig. 22.

Velocity contour for CFJ: bypass ratio BR 0.7 and Mach M = 0.6 on LT 1.0 D_p,

Fig. 23.

Velocity contour for CFJ: bypass ratio BR 6.4 and Mach M = 0.6 on 1.0 D_p.

Total pressure variation along axial directions for various bypass ratios

From the total pressure contours, we can identify the distinct regions of the CFJ, such as the Initial Merging Zone, Intermediate Zone and Fully Merging Zone. Additionally, it is observed that for finite lip thickness, when the bypass ratio increases from 0.7 to 6.4, the wake dominance or the sub atmospheric pressure intensifies. Figures 24 and 25 show the pressure contours for CFJ of lip thickness 1.0 D_p with Mach number 0.6 of low and high bypass ratios of 0.7 and 6.4, respectively. By comparing the co-flowing jets with different lip thicknesses and bypass ratios, it was found that the potential core length for relatively higher bypass ratios was reduced to a greater extent. This is due to the fact that when the bypass ratio is increased, the jet becomes wake dominant. In the fully merged zone, the coaxial jet becomes a combined jet and due to the shielding effect, the potential core of the combine jet occurs from X/D_p = 6 to X/D_p = 11, as seen in Fig. 10. This phenomenon occurred due to the fact that the secondary jet possessed more strength to shield the primary jet in the characteristic decay region when compared with the other lower bypass ratios. The point where the co-flowing jet meets the main jet is termed in the literature as merging point²⁰. For comparatively higher bypass, after the merging point, the co-flowing jet shielded the main jet. After this point, the co-flowing jet attained a self-preserving state and started behaving as a single jet. For lower bypasses, merging point could not be clearly seen from centerline pressure plots. This could be due to the fact that low bypass co-flow possessed only lesser strength when compared to high bypass, and it did not have the ability to shield the main jet after the merging point to a significant axial distance.

Fig. 24.

Pressure contour for CFJ: bypass ratio BR 0.7 and Mach M = 0.6 on 1.0 D_p.

Fig. 25.

Pressure contour for CFJ: bypass ratio BR 6.4 and Mach M = 0.6 on 1.0 D_p.

Conclusions

Experimental and numerical simulations were carried out to investigate the Mach number variations and potential core dynamics of wake-dominated co-flowing jets with varying lip thickness and bypass ratios, for a jet exit Mach number of 0.6. The results provide novel insights into the influence of lip thickness and flow parameters on jet mixing behaviour. It is observed that for exit Mach number of 0.6, single free jet has a potential core length up to X/D_p = 3.8, whereas for 10 mm lip co-flowing jet with bypass ratio 0.7, 1.4 and 6.4 the potential core length extends up to X/D_p = 2.8, 2.7 and 2.1 and their corresponding percentage reduction is 26, 29, 45% respectively. Similarly for 15 mm lip for co-flowing jet with bypass ratio 1, 1.7 and 6, the potential core length extends up to X/D_p = 2.7, 2.2 and 1.6 and their corresponding reduction percentage is 29, 42, 58% respectively. The most impactful finding is that a 45% reduction in the possible core length is achieved with an increase in lip thickness from 0.2 D_p to 1.5 D_p by increasing the bypass ratio from 0.7 to 6.4, inducing significant axial and radial Mach number oscillations in the near field due to increased recirculation and wake effects. Further, the maximum secondary jet Mach number was found to decrease by nearly 30% as lip thickness increases, highlighting the sensitivity of flow entrainment to nozzle geometry. These results show the effectiveness of lip thickness and bypass ratio as passive control parameters for enhancing jet mixing in wake-dominated regimes. The study also highlights that increased bypass ratios and finite lip thickness intensify wake dominance and recirculation, altering the axial and radial flow fields and promoting vigorous interaction between primary and secondary jets. The fluctuating static pressure and Mach number in the near field obscured the potential core in axial plots, while the slope of the characteristic decay region diminished in the wake zone.

Author contributions

K.S.K.: Responsible for conceptual development, methodology design, and conducting the investigation. V.G.G and R.N.S.: Oversaw the research process, carried out formal analysis, contributed to conceptual ideas, and participated in reviewing and editing the manuscript. R.B.: Handled data analysis, drafted the original manuscript, contributed to validation, and was involved in reviewing, editing, and conceptual input. P.R.: Contributed to visual representation and took part in formal data analysis. I.E.L.: Engaged in formal analysis, investigative tasks, and managed the overall project administration. All authors have read and agreed to the published version of the manuscript.

Funding

The authors wish to thank the financial support provided by the Department of Science and Technology, Science and Engineering Research Board (DST-SERB-TARE scheme), Government of India for the research grant on coaxial jets, Grant no: TAR/2023/000022 and TAR/2021/000093. The authors gratefully acknowledge the financial support received from Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, under the Research Development Fund (RDF), Grant No. VTU / RDF / FY 2025-26 / 042. This support was instrumental in facilitating the successful execution of this research work.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.