Session L5: Computational Fluid Dynamics VI

Periodic Cavitation in a High-Speed Water Inducer at an Off-Design Flow Coefficient

Time resolved numerical simulations were conducted on a high-speed water inducer designed to operate under cavitating conditions at both on and off-design flow rates. A segregated solver was employed and the turbulence model was the realizable k-epsilon approach. The solution discretization is second order accurate in space and first order accurate in time. Cavitation within the domain becomes periodic as the cavitation number decreases. At flow coefficients smaller than the design flow coefficient, a large time-varying volume of cavitation is observed upstream of the inducer causing the system to become unstable for practical use. Large regions of reversed flow at the blade tip cause the incoming fluid to increase in velocity and the effective mass flow area to decrease. It is this increase in velocity that leads to the formation of the periodic vapor cavity upstream of the inducer. The vapor cavity increases in size until it completely blocks the core of the passage, forcing the flow out toward the shroud. As the flow near the shroud accelerates, the reversed flow at the blade tip decreases and the vapor cavity decreases in size until it collapse completely, causing a large jump in pressure throughout the entire flow domain.   

Comparison: on-design and off-design flow through a high speed turbo pump inducer

A computational fluid dynamic comparison was performed between on-design and off-design flow rates through a four-bladed axial turbopump inducer. Using CD Adapco's Star-CCM as the CFD package an analysis of the two flow-rate cases was made. The simulations were run time-resolved and with two phases (water and water vapor). Turbulence employed the realizable k-epsilon model and cavitation was predicted using the Rayleigh-Plasset model. The solution discretization is second order accurate in space and first order accurate in time. The results show classical breakdown curves for both flow-rate cases. Breakdown is the condition where the entire flow path in the inducer becomes filled with vapor and the head rise over the inducer is decreased dramatically. Both cases experience breakdown at about the same cavitation number; however, because the off-design case generally has a larger head rise, its breakdown occurs at higher back pressures than the on-design case. Additionally, the off-design case experiences larger amounts of incidence that result in regions of reversed flow along the shroud and an increase of instabilities throughout the machine. Performance maps will be discussed comparing the two cases on head rise and efficiency.   

Optimal design of solenoid valve to minimize cavitation by numerical analysis

Keeping pace with the development of clean energy, hybrid cars and electric vehicles are getting extensive attention recently. In an electronic-control brake system which is essential to those vehicles, a solenoid valve is used to control external hydraulic pressure that boosts up the driver's braking force. However, strong cavitation occurs at the narrow passage between the ball and seat of a solenoid valve due to sudden decrease in pressure, leading to severe damage to the valve. In this study, we investigate the cavitation numerically to discover geometric parameters to affect the cavitation, and an optimal design to minimize the cavitation using optimization technique. As a result, we found four parameters: seat inner radius, seat angle, seat length, and ball radius. Among them, the seat inner radius affects the cavitation most. Also, we found that preventing a sudden reduction in a flow passage is important to reduce cavitation. Finally using an evolutionary algorithm for optimization we minimized cavitation. The optimal design resulted in the maximum vapor volume of fraction of 0.04 while it was 0.7 for reference geometry.   

Transient High-Pressure Fuel Injection Processes

The transient behavior of the jet emerging from the orifice during the start-up and shut-down portion of the injection is addressed. Use has been made of an unsteady axisymmetric code with a finite-volume solver of the Navier-Stokes equations for liquid streams and adjacent gas and a level-set method for liquid/gas interface tracking. The acceleration of the liquid during start-up is about 10$^6$ m/s$^2$ at the orifice exit. When the jet emerges from the orifice, drag forces due to the dense ambient air cause a deceleration. Also, the dynamic protrusions from the jet surface created by Kelvin-Helmholtz instability are subject to local accelerations that lead to Rayleigh-Taylor instability. The higher the Weber and the Reynolds numbers, the shorter the unstable surface wavelengths which appear; so, the more challenging is the resolution problem. Where resolving the entire jet becomes computationally expensive, we examine stream-wise segments of the jet, treating these segments as ballistic slugs coming from the orifice. This reduction of the computational domain is designed to give the required resolution to characterize the physics through our computations.   

Effect of a Magnetic Field on Turbulent Flow in Continuous Casting Mold

Electromagnetic Braking (EMBr) fields are applied to control the turbulent mold flow for defect reduction in continuous steel casting. The effect of EMBr depends on the path of induced electric current which is modified by presence of the highly conducting solidifying shell. The mold geometry is complex involving flow in a high-aspect ratio closed channel with bifurcated jet impinging obliquely on the side walls. The extremely transient nature and the anisotropic behavior of turbulence under the EMBr field make numerical studies challenging. We use large eddy simulations to study effects of EMBr with electrically insulating and conducting boundary conditions. Magnetohydrodynamic equations are solved using a fractional step method with second order spatial and temporal accuracy. The electric potential method is used as magnetic Reynolds number is low for liquid metal flows. The solver was first validated with measurements from scaled GaInSn model and simulations were then performed to study real casters at industrial conditions. Time averaged and transient behaviors of the flow were studied by collecting distributions of mean velocities, turbulent fluctuations and vorticity. The simulations reveal that the electrical boundary conditions have a major effect on the flow structure.   

Adjoint Airfoil Optimization of Darrieus-Type Vertical Axis Wind Turbine

We present the feasibility of using an adjoint solver to optimize the torque of a Darrieus-type vertical axis wind turbine (VAWT). We start with a 2D cross section of a symmetrical airfoil and restrict us to low solidity ratios to minimize blade vortex interactions. The adjoint solver of the ANSYS FLUENT software package computes the sensitivities of airfoil surface forces based on a steady flow field. Hence, we find the torque of a full revolution using a weighted average of the sensitivities at different wind speeds and angles of attack. The weights are computed analytically, and the range of angles of attack is given by the tip speed ratio. Then the airfoil geometry is evolved, and the proposed methodology is evaluated by transient simulations.   

Simulation of a valveless pump with an elastic tube

A valveless pump consisting of a pumping chamber with an elastic tube was simulated using an immersed boundary method. The interaction between the motion of the elastic tube and the pumping chamber generated a net flow toward the outlet throughout a full cycle of the pump. The net flow rate of the valveless pump was examined by varying the stretching coefficient, bending coefficient, the aspect ratio of the elastic tube, and the frequency of the pumping chamber. As the stretching and bending coefficients of the elastic tube increased, the net flow through the valveless pump decreased. Elastic tubes with aspect ratios in the range of 2$<$l/d$<$3 generated a higher flow rate than that generated for tubes with aspect rations of l/d=1 or 4. As the frequency of the pumping chamber increased, the net flow rate of the pump for l/d=2 increased. However, the net flow rate for l/d=3 was nonlinearly related to the pumping frequency due to the complexity of the wave motions. Snapshots of the fluid velocity vectors and the wave motions of the elastic tube were examined over one cycle of the pump. The relationship between the average gap in the elastic tube and the average flow rate of the pump was analyzed.   

Numerical Study of Thermoacoustic Spontaneous Oscillations in an Axisymmetric Closed Tube

We study the stability of thermoacoustic spontaneous oscillations (Taconis oscillations) by numerically solving the axisymmetric compressible Navier-Stokes equations. The flow fields in a cylindrical closed tube are simulated by the block pentadiagonal scheme with the second--order time marching and the fourth-order convective term. We consider the helium gas in the closed tube with both hot end parts and a cold central part. When the temperature ratio is larger than the critical value, the spontaneous oscillation is observed. In the case of $r$(the length ratio of the hot part to the cold part)=1, we observe the fundamental mode of a standing wave as the spontaneous oscillation. On the other hand, in the case of $r < $ 0.42 three different oscillation modes are observed: the fundamental mode and the second mode of a standing wave, and the oscillation with a shock wave.   

Numerical Analysis of Transport Phenomena for the Design of the Ejector in a PEM Fuel Cell

In the present study, Computational Fluid Dynamics (CFD) technique is used to design an ejector for anode recirculation in a specific automotive PEMFC system. A CFD model is firstly established and tested against well-documented and relevant solutions from literature, and then used to different ejector geometries under different working conditions. Results showed that one ejector with the optimized geometry cannot cover the required recirculation in the entire range of the current, and having two ejector for different range of currents is a new proposed alternative, in which the system can take a better advantage of ejector for recirculation purpose.   

Numerical Study of 3D Flow and Mixing Properties in the Rotated Arc Mixer

Laminar mixing of fluids is an important process in many industrial operations. However, insight into 3D flow and mixing in the devices remains limited. This is largely due to their complex construction, which makes experimental investigation difficult and representation by analytical solutions impossible. This motivates the current numerical study on essentially 3D flow and mixing properties in a device representative of a wide class of mixers: the Rotated Arc Mixer (RAM). Key aspects to be investigated are transient effects between consecutive mixing cells and role of fluid inertia. Two RAMs, comprising of 5 and 10 cells, have been investigated by resolving full 3D Navier-Stokes equations. Simulations exposed small backflow zones near to entrance (exit) of each cell. They also revealed that up to 40\% of cell length is involved in flow transition. However, the extent of this transition depends on flow parameters and cell geometry. The flow retains global spatial periodicity of the mixer. Moreover, essentially 3D internal symmetries within each cell exist in Stokes limit. Poincar\'{e} sections show that the transient and inertia effects cause a change in the location and size of non-mixing zones. This implies a significant impact of these effects on the mixing properties.