Flow separation control in a conical diffuser with a Karman-vortex generator
Introduction
As a device for converting kinetic energy into pressure energy and retarding flow [1], conical diffusers are an essential component of wind tunnels, power generation turbomachinery and aircraft propulsion units. Azad [2] noted that the highest pressure recovery coefficient of a conical diffuser occurs when the total divergence angle and the flow is accompanied by a slight separation. In industrial applications, diffusers usually have a large divergence angle to ensure that the structure is compact. Nevertheless, the geometric mutation near the throat and strong adverse pressure gradient in the expansion section cause massive separation. The unsteady flow separation is accompanied by undeniable energy loss and pressure distortion, which impose a detrimental impact on the subsequent components [3], [4]. The flow control technique is crucial for suppressing flow separation and improving the performance of diffusers.
The flow control method can be classified into active or passive methods, depending on the energy expenditure and control loop involved [5]. In terms of active flow control, the conventional methods include blowing and suction boundary layers [6], [7], [8]. In addition, vortex generator jet [9], [10], synthetic jet [11], [12], and plasma actuators [13], [14] have also attracted much attention in the past two decades. A properly designed actuator can achieve a remarkable flow control effect, but the requirement of an extra auxiliary apparatus makes its application relatively expensive and complex. In regard to the passive flow control technique, the devices are economical and easy to deploy. The classic vane-shaped vortex generator (VG) [15], [16], [17] and rapidly developed micro vortex generator (MVG) [18], [19] are the most popular strategies.
Most of the aforementioned vortex generators are wall-mounted and generate quasi-steady streamwise vortices. The vortical flow draws high-momentum fluid from the potential flow region to the downstream boundary layer, and the flow separation is effectively alleviated [18]. As a novel off-surface vortex generator, a “rod” [20], [21], “flow control rail (FCR)” [22] or “Karman-vortex generator (KVG)” [23] were employed to improve diffuser performance. All of these cylindrical or ring-shaped vortex generators utilize highly unsteady spanwise Karman vortexes for flow control. Zhang et al. [23] collectively defined the device as a KVG, and this paper follows that definition. Taking external flow control into account, “rods” [24], “spanwise cylinders” [18], [25], “off-surface elements” [26] and “microcylinders” [27] have similar shapes and flow control mechanisms and can also be deemed KVGs.
Moore and Kline [20] mounted a rod (cylindrical KVG) at the lip of a two-dimensional diffuser entrance, and the total divergence angle 2β of the diffuser was 45°. A massive separation was effectively inhibited, and the pressure recovery coefficient of the controlled case was nearly twice that of the baseline diffuser. In subsequent studies, Waitman et al. [21] and Hoffmann [28] set a rod upstream of the throat of a two-dimensional diffuser to investigate the effects of inlet turbulence on the performance of the diffuser. The results demonstrated that a cylindrical-shaped KVG could significantly increase the turbulence intensity in the downstream near-wall region and alleviate the flow separation in the expansion section. In regard to the external flow control cases, Veldhuis and Steen [26] utilized several types of vortex generators to control flap separation with deflect angles and 32°. The results demonstrated that the off-surface KVGs, off-surface vane-shaped VGs and MVGs had an equal separation control capacity to the on-wall devices when . However, the off-surface KVGs obtained the greatest pressure recovery for the case. Wang et al. [24] utilized an upstream rod to suppress the flow separation and reduce the drag of a circular cylinder. The flow visualization experiments indicated that there are several flow regimes as the size and location of the rod varies. The maximum flow control effect occurs when the KVG is set immediately before the cylinder with an appropriate size and distance combination at the cavity mode. For the optimal scheme, the drag of the controlled cylinder was only 2.34% of the baseline cylinder.
Most of the aforementioned KVG applications were conducted by experiments, and numerical simulations have recently attracted much attention. Zhang et al. [23] introduced a ring-shaped KVG to alleviate the massive separation in a conical diffuser with an area ratio and a . Unsteady Reynolds-averaged Navier-Stokes (URANS) equations, detached eddy simulations (DESs) and delayed DESs were employed to simulate the unsteady flow details and obtain diffuser performance parameters. In the optimal case, the flow separation was almost eliminated, and the static pressure recovery nearly doubled. Wang and Zhao [29] utilized large-eddy simulation (LES) to investigate the heat and fluid transfer characteristics in a fully developed channel with a cylindrical KVG. The gap G from the KVG to the wall ranged from 0–6.0 times the cylinder diameter . The channel obtained the best performance at and 3.0, and the synthesis efficiency increased by 17.8% and 15.2%, respectively. In regard to external flow control applications, Luo et al. [27] utilized a microcylinder to alleviate the stall of an airfoil at a large angle of attack. The optimal KVG significantly suppressed the flow separation on the suction surface and improved the lift-to-drag ratio.
The aforementioned KVG applications reported that the unsteady wake of upstream KVGs has a significant influence on the downstream flow, and KVGs have great potential in suppressing the flow separation of diffusers. In most applications, off-surface KVGs should be installed at a certain distance away from the wall and separation point to form vortical flow for flow control. Nevertheless, the flow details of the baseline diffuser and the controlled cases are seldom analyzed in relevant studies. The flow control mechanism and the design principle of the size and location are also ambiguous. Considering that the flow pattern and pressure recovery performance of diffusers are very sensitive to the turbulent fluctuation of the incoming flow [21], [30], [31], a diffuser with a fully developed channel or pipe flow is suitable for fundamental research due to distinctly defined boundary conditions.
In this paper, a ring-shaped KVG is mounted upstream of the throat to suppress massive flow separation in a conical diffuser with an and a . The inflow of the diffuser is a fully developed pipe flow, and the Reynolds number based on the mean velocity and diameter of the inflow pipe is . KVGs with different size and location combinations are numerically studied by an implicit large-eddy simulation (ILES) method. Based on the analysis and comparison of the baseline diffuser and some controlled cases, the flow control mechanism and the corresponding design principle are discussed.
Section snippets
Numerical method and validation
The numerical simulation method adopted in this paper is an ILES based on the finite volume method framework. The ILES method utilizes numerical dissipation to model unresolved turbulence. The Riemann solver is based on the simple low-dissipation advection upstream (SLAU) splitting method [32]. As an improved scheme based on the AUSM-family [32], the SLAU method maintains the advantages of fast calculation speed and high discontinuous resolution. In addition, the SLAU method exhibits good
Grid convergence of the baseline diffuser
A Reynolds-averaged Navier-Stokes (RANS) simulation based on Menter's SST turbulence model [43] is conducted to establish an initial flow field and accelerate the convergence of the ILES. The computational time-step of the ILES is , which is the same as the saved pipe slices to avoid a numerical deviation of time interpolation. Based on the RANS result, the flow undergoes to achieve a statistically fully developed flow. After that, at least are collected for
Conclusions
In this article, an implicit large-eddy simulation is conducted to investigate the flow control mechanism and corresponding design principal in a conical diffuser with a fully developed pipe flow at a . Based on the comparisons and analysis of the averaged and instantaneous flow results for the baseline diffuser and the controlled cases, some conclusions can be drawn as follows:
For the baseline diffuser, severe flow separation begins near the throat and extends after the end of the
Declaration of Competing Interest
The authors declare that they have no known commercial interests or personal relationships that represents a conflict of interest in connection of the present work.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 91852108 and 11872230).
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