Viscous Numerical Simulations Research Articles

Dissipative potential flow models and energy evolution characteristics for curtain-wall caisson breakwaters under wave action

Curtain-wall caisson breakwaters are a kind of coastal protection structure, which is composed of semi-submersible vertical thin curtain walls, a rear vertical caisson, and wave chambers formed by the curtain walls and rear caisson. When water waves interact with the curtain-wall caisson breakwater, the wave energy may be partially dissipated owing to the flow separation and vortex formation near the edges of curtain walls. The conventional potential flow solution without considering wave energy dissipation gives unreasonable results of full wave reflection by the curtain-wall caisson breakwater. To address this issue, this study develops a dissipative potential flow model for predicting the hydrodynamic performance of the curtain-wall caisson breakwaters. The wave energy dissipation near the breakwater is considered by introducing a quadratic pressure loss condition at the entrances of wave chambers. By adopting appropriate dimensionless dissipation coefficients, the analytical predictions of the reflection coefficient and the wave amplitude inside chambers are in good agreement with published experimental results. The differences in the hydrodynamic quantities predicted by the dissipative and conventional potential flow solutions are examined, and further discussion based on the dissipative analytical solution is performed. Moreover, viscous numerical simulations based on a meshless particle method are carried out to clarify the characteristics of wave energy evolution, wave energy dissipation, and local fluid motion near the curtain-wall caisson breakwaters. The results show that the front curtain wall plays the leading role in the wave energy dissipation process of the whole double-chamber curtain-wall breakwater.

Trends in torques acting on the star during a star-disk magnetospheric interaction

Aims. We assess the modification of angular momentum transport in various configurations of star-disk accreting systems based on numerical simulations with different parameters. In particular, we quantify the torques exerted on a star by the various components of the flow and field in our simulations of a star-disk magnetospheric interaction. Methods. In a suite of resistive and viscous numerical simulations, we obtained results using different stellar rotation rates, dipole magnetic field strengths, and resistivities. We probed a part of the parameter space with slowly rotating central objects, up to 20% of the Keplerian rotation rate at the equator. Different components of the flow in star-disk magnetospheric interaction were considered in the study: a magnetospheric wind (i.e., the “stellar wind”) ejected outwards from the stellar vicinity, matter infalling onto the star through the accretion column, and a magnetospheric ejection launched from the magnetosphere. We also took account of trends in the total torque in the system and in each component individually. Results. We find that for all the stellar magnetic field strengths, B⋆, the anchoring radius of the stellar magnetic field in the disk is extended with increasing disk resistivity. The torque exerted on the star is independent of the stellar rotation rate, Ω⋆, in all the cases without magnetospheric ejections. In cases where such ejections are present, there is a weak dependence of the anchoring radius on the stellar rotation rate, with both the total torque in the system and torque on the star from the ejection and infall from the disk onto the star proportional to Ω⋆B3. The torque from a magnetospheric ejection is proportional to Ω⋆4. Without the magnetospheric ejection, the spin-up of the star switches to spin-down in cases involving a larger stellar field and faster stellar rotation. The critical value for this switch is about 10% of the Keplerian rotation rate.

AN EXAMINATION OF THE “LANIER WING” DESIGN

AbstractSix patents were secured by E. H. Lanier from 1930 to 1933 for aeroplane designs that were intended to be exceptionally stable. A feature of five of these was a flow-induced “vacuum chamber” which was thought to provide superior stability and increased lift compared to typical wing designs. Initially, this chamber was in the fuselage, but later designs placed it in the wing by replacing a section of the upper skin of the wing with a series of angled slats. We report upon an investigation of the Lanier wing design using inviscid aerodynamic theory and viscous numerical simulations. This took place at the 2005 Australia–New Zealand Mathematics-in-Industry Study Group. The evidence from this investigation does not support the claims but, rather, suggests that any improvement in lift and/or stability seen in the few prototypes that were built was, most probably, due to thicker airfoils than were typical at the time.

Viscous Damping Performance Analysis and Prediction of Axisymmetric Cylindrical Oscillating Buoys With Different Geometrical Configurations

Abstract With the intensification of the world's energy demand, clean and efficient marine energy has received more attention, and energy conversion devices are particularly important. As an important part of the oscillating wave energy conversion device, the hydrodynamic characteristics of cylindrical absorbers have a great impacton wave energy conversion efficiency. When cylindrical buoys with different bottom configurations heave under the action of waves, the oscillating motion and flow field become more complex. At present, potential flow theory is usually used to predict the motion response of cylindrical buoys in waves. Although the calculation speed is fast, there will be large errors due to the lack of consideration of the effect of fluid viscosity. To explore this error range, a three-dimensional numerical wave pool is established based on the viscous fluid theory and STARCCM+ software to study the response of buoy and wave coupling action considering the viscous effect. At the same time, based upon the potential flow theory, the analytical solution of the cylindrical buoy oscillating in waves is established. Combined with the computational fluid dynamics numerical simulation results, the oscillation laws of the buoys with different bottom configurations in waves with different periods are compared, and the effects of viscosity on the buoys' motion are also explored. According to the calculation results of floating buoy movement under viscous and nonviscous fluid, the statistical correction algorithmis adopted to obtain the viscous hydrodynamic correction algorithm of floating buoy movement based on the potential flow theory, and the feasibility is verified by viscous numerical simulation under other wave periods.

Efficient self-propelled locomotion by an elastically supported rigid foil actuated by a torque

A new theoretical model is presented for an aquatic vehicle self-propelled by a rigid foil undergoing pitching oscillations generated by a torque of small amplitude applied at an arbitrary pivot axis at which the foil is elastically supported to allow for passive heaving motion. The model is based on 2D linear potential-flow theory coupled with the self-propelled dynamics of the semi-passive flapping foil elastically mounted on the vehicle hull through translational and torsional springs and dampers. It is governed by just three ordinary differential equations, whose numerical solutions are assessed with full viscous numerical simulations of the self-propelled foil. Analytical approximate solutions for the combined effect of all the relevant non-dimensional parameters on the swimming velocity and efficiency are also obtained by taking advantage of the small-amplitude of the applied torque. Thus, simple power laws for the velocity and efficiency dependencies on Lighthill number and torque intensity are obtained. It is found that the swimming velocity and transport efficiency can be greatly enhanced by selecting appropriately the non-dimensional constants of the translational and torsional springs, which are mapped for typical values of the remaining parameters in aquatic locomotion. These resonant values serve to select optimal frequencies of the forcing torque for given structural and geometric parameters. Thus, the present model and analysis provide a useful guide for the design of an efficient flapping-foil underwater vehicle.

Three-dimensional Viscous Numerical Simulations of Focused Waves on Bottom-mounted Multiple Rigid Circular Cylinders

Three-dimensional Viscous Numerical Simulations of Focused Waves on Bottom-mounted Multiple Rigid Circular Cylinders

Two-dimensional numerical study of gap resonance coupling with motions of floating body moored close to a bottom-mounted wall

The piston mode fluid resonance in the narrow gap between a moored floating body and a bottom-mounted vertical wall is numerically investigated based on a two-dimensional potential flow model and viscous numerical simulations. This study focuses on understanding the effect of mooring stiffness on the coupling dynamics of the gap resonance and the sway or heave motion of the floating body in regular waves. Numerical studies show that the resonant wave amplitude in the gap is reduced by the sway and heave motions. The reduction is highly dependent on the mooring stiffness. Two resonant frequencies are confirmed, and both increase with the mooring stiffness. Different modes of motions are identified in terms of the phase difference between the oscillatory motions of the gap flow and the floating body. Higher harmonic components of responses are found for the specific mooring stiffness. The performance of potential flow models in predicting resonant responses is revisited based on the understanding that the overall damping effect consists of two parts: (1) radiation damping and (2) viscous dissipation. It is confirmed that a potential model is also able to produce reasonable predictions as radiation damping plays a dominant role, for example, at the second resonant frequencies of coupling the gap resonance with the sway motion. Otherwise, as viscous dissipation dominates radiation damping, noticeable over-predictions by a potential model occur as recognized before, for example, the present results at the second peak response of gap resonance with the heave motion. The relative viscous dissipation is quantified with the reflection coefficient of viscous numerical results, while the radiation damping is quantified based on a specially designed radiation potential model with inputs of viscous numerical solutions.

Design and manufacturing a small-scale radial-inflow turbine for clean organic Rankine power system

With growing on the energy demand and availability of the low-grade temperature heat source, the organic Rankine cycle as a power system can be efficiently utilized to generate electricity. The turbine design and its performance have the main impact on determining the system power and overall system efficiency. Therefore, design a small-scale organic Rankine system requires the development of an appropriate turbine. To achieve this aim, this work offers an innovative complete design method to develop a radial-inflow turbine for small-scale organic Rankine cycle power applications, which includes a preliminary design (i.e. one-dimensional design calculation phase) and a three-dimensional flow analysis using the computational fluid dynamic technique. A thermodynamic analysis of the organic Rankine cycle was integrated with the design methodology. Where the three-dimensional geometry model was built based on the thermodynamic and aerodynamic design, and then was imported into the ANSYS-CFX software to conduct viscous numerical simulations. The optimum design of the radial-inflow turbine was manufactured using a three-dimensional printing (pioneering) technique, and the experimental testing was conducted at off-design points to validate the turbine design.The evaluation of the turbine’s performance (efficiency and power) was presented under design and off-design points in terms of rotational speeds, expansion ratios, and inlet temperatures with five different organic fluids. The turbine numerical results showed that R600 as a working fluid has a higher predicted turbine efficiency of 78.32% and power of 4.8 kW with cycle thermal efficiency of 9.15% compared with 8.045% for R245fa. Depending on the experimental results at off-design points, the highest cycle thermal efficiency of 4.25% with a turbine efficiency of 45.22% was achieved. These results assured the precision of the proposed PD methodology at off-design points in making performance maps of the turbine.

Improved thermodynamic and aerodynamic design method and off‐design performance analysis of a radial inflow turbine for ORC system

Radial inflow turbine is one of the crucial components of organic Rankine cycle (ORC) system, which has great impact on the performance of system. R245fa was selected as the working fluid to recycle the waste heat source with a temperature of 350 to 400 K. The genetic algorithm (GA) was employed in thermodynamic design to optimize the 10 key design parameters, which are needed in aerodynamic design of the ORC turbine. Isotropic efficiency was the fitness function of 10 key variables in GA. The three-dimensional geometry model was built based on the thermodynamic and aerodynamic design and then was imported into the commercial software ANSYS-CFX to conduct viscous numerical simulation. Based on the three-dimensional simulation, the off-design performance in different mass flow rate, static inlet temperature coupled with different rotational speed was investigated respectively. The results show that at design condition, the maximum efficiency deviation is only 2.5% with the rotational speed variations among the range of 10%, so the radial inflow turbine designed in this research possesses great off-design performance.

Investigation of Unsteady Aerodynamic Excitation on Rotor Blade of Variable Geometry Turbine

To investigate the aerodynamic excitations in variable geometry turbines, the full three-dimensional viscous unsteady numerical simulations were performed by solving N-S equations based on SAS SST method. The aerodynamic excitations at varied expansion ratios with six different vane stagger angles that cause the unsteady pressure fluctuation on the rotor blade surface are phenomenologically identified and quantitatively analyzed. The blade pressure fluctuation levels for turbines with different vane stagger angles in the time and frequency domain are analyzed. As the results suggest, the blade excitation mechanisms are directly dependent on the operating conditions of the stage in terms of vane exit Mach numbers for all test cases. At subsonic vane exit Mach numbers the blade pressure fluctuations are simply related to the potential filed and wake propagation; at transonic conditions, the vane trailing edge shock causes additional disturbance and is the dominating excitation source on the rotor blade, and the pressure fluctuation level is three times of the subsonic conditions. The pressure fluctuation energy at subsonic condition concentrates on the first vane passing period; pressure fluctuation energy at higher harmonics is more prominent at transonic conditions. The variation of the aerodynamic excitations on the rotor blade at different vane stagger angles is caused by the varied expansion with stator and rotor passage. The aerodynamic excitation behaviors on the rotor blade surface for the VGT are significantly different at varied vane stagger angle. Spanwise variation of the pressure fluctuation patterns on is also observed, and the mechanism of the excitations at different spans is not uniform.

Experimental and numerical study on the local unstart mechanism of hypersonic inlet

Hypersonic inlet is a vital component of a scramjet, whose starting mode is the prerequisite of the normal operation. Relative researches and empirical formulae for hypersonic inlet, which have been conducted, are appropriate for low Mach number working condition. However, previous studies can not well reveal the performance degradation of inlet at high Mach number working condition. In this paper, local unstart flows of a hypersonic inlet are studied at freestream Mach number of 7.0 by experimental and numerical methods. Two operation modes of hypersonic inlet were observed at high Mach number, with the aid of bleed holes and downstream pressure variation simulator. Further, the detailed flow field of a quasi-two-dimensional hypersonic inlet was obtained by viscous numerical simulations. The present study shows that the local unstart of hypersonic inlet is the interaction between the separation region on the cowl and another separation bubble on the forebody, which may be of benefit to interpret the formation mechanism, prediction, and suppression of the inlet unstart mode.

Effect of Bowed/Leaned Vane on the Unsteady Aerodynamic Excitation in Transonic Turbine

To investigate the effect of bowed/leaned vane configurations on the aerodynamic performance and aerodynamic excitation in transonic high-pressure turbine, the full three-dimensional viscous unsteady numerical simulation was performed by solving N-S equations based on SAS SST method. The influence of bowed /leaned vanes on turbine efficiency and efficiency fluctuation was investigated. The action of vane modelling to the overall aerodynamic fluctuation level and the amplitude of each vane passing frequency were analyzed. By comparing instantaneous pressure fluctuation contours in the blade passage with space-time maps, the link of the pressure fluctuation on blade surface with flow distortions was achieved, which can reveal the mechanism of the impact of the vane modelling. As the results suggest, the turbine efficiency is promoted with positively leaned and bowed vane modelling, and the fluctuation of stage turbine efficiency is repressed, which contributes to the smooth running of the turbine stage. The blade aerodynamic excitation on the rotor blade is characterized by the motion of vane trailing edge shock system, and the vane configurations can reduce the fluctuation level on the rotor blade surface effectively. For the positively leaned vane configuration, the aerodynamic excitations at the root and tip region are affected by the impact of the amplitude of the first harmonic, whereas they are reduced with the decrease of the amplitude of the second and higher harmonics at midspan. For the positively bowed vane, aerodynamic excitation is repressed by reducing the amplitude of the third harmonic at the root region, and the first harmonic at the tip region, and the amplitude of each harmonic is reduced at the middle region.

Preliminary design and performance analysis of a radial inflow turbine for a large-scale helium cryogenic system

Large-scale helium cryogenic systems are widely used in superconducting systems, nuclear fusion engineering, space exploration and large scientific engineering, etc. However, its energy efficiency is quite low due to the extremely low operation temperature. The helium turbine constitutes the most vital component of a large-scale helium cryogenic system. Thus, it is essential to develop a high efficiency helium turbine in order to improve the energy efficiency of the cryogenic helium system. In this paper, a high speed radial micro turbine with the splitter blade was designed for a 40 L/h helium liquefier with Claude cycle. The turbine is designed for inlet and outlet temperatures of 14.4 K and 9.4 K respectively. The design speed of the turbine is 223570 rpm due to the small mass flow rate and impeller diameter. A one-dimensional mean line optimal design approach for radial inflow turbine is adopted in this study. Furthermore, detailed three-dimensional viscous numerical simulations are conducted in order to verify the one-dimensional optimal approach in design condition and predict the performance of the designed turbine in off-design conditions. The results indicate that the optimal helium radial inflow turbine for the design and off-design conditions can be designed through applying the proposed analysis method.

Unsteady RANSE simulation for ship resistance, heave and pitch in regular head waves

This study presents an attempt to perform a viscous numerical simulation for ship advancing in regular head waves. The simulation includes computations for total ship resistance, heave and pitch responses for the bare hull of the US Navy combatant DTMB 5512 ship model. The computations are carried out by making use of the commercial software Fine™/Marine provided by NUMECA, where the discretization in space is based on finite volume method using unstructured grid. The unsteady Reynolds-Averaged Navier-Stokes equation is solved while the turbulence is modelled by making use of k-ω shear stress transport model. The free-surface is solved based on volume of fluid method. Results are obtained for ship resistance coefficient, heave and pitch and compared with experimental results provided in the Gothenburg 2010 Workshop on the Naval Hydrodynamics. The comparison of the computed results showed an encouraging agreement with the measured results. Finally, a special investigation for the added resistance in waves is made by comparing the results obtained in this computation with other results obtained in calm water.

Periodic forcing of a shock train in a scramjet inlet-isolator at overspeed condition

Unsteady viscous numerical simulations are performed to explore the response of a shock train to downstream backpressure forcing in a scramjet inlet-isolator at the overspeed condition. A sinusoidal dynamic backpressure is applied at the exit of the isolator, thus leading a forced shock train oscillation. The results show that the shock train travels along a different path for the upstream and downstream movements. There is a clear hysteresis loop during the shock train oscillation. Under the low forcing frequency, the shock train travels in a clockwise loop. While it travels in a counter-clockwise loop under the high forcing frequency. Moreover, there is a lag between the shock train oscillation and the fluctuating backpressure. Especially for the high forcing frequency, the phase of the shock train oscillation is opposite to the fluctuating backpressure. The effects of the amplitude and frequency of the periodic fluctuating backpressure on the oscillation range of the shock train are also investigated. With the amplitude of the fluctuating backpressure increasing, the oscillation range of the shock train increases. With the frequency of the fluctuating backpressure increasing, the oscillation range of the shock train increases first and then decreases under high frequency.

Numerical study on hypersonic nozzle-inlet starting characteristics in a shock tunnel

An unsteady viscous numerical simulation is performed to study the starting process of a hypersonic nozzle coupled with a simplified inlet model in a shock tunnel under the condition of inflow Mach number higher than the design value. And the effect of the initial backpressure of test section in shock tunnel on the pulse-starting characteristics of the hypersonic nozzle-inlet is studied. It is found that the operation mode of inlet changes from local unstart to start with the initial backpressure decreasing. At high initial backpressure, two large separation bubbles are induced by the secondary shock at the nozzle walls, the separation induced shock waves repeat reflections between the nozzle walls and a shock train structure appears. The Mach number of the flow into the test section rises and falls repeatedly as a result of the presence of the successive shocks in the shock train structure. During the hypersonic nozzle-inlet starting process, a large separation bubble occurs at the forebody side and the inlet is choked. After the forebody shock moving close to the cowl lip, a bow shock is generated and moves before the cowl lip subsequently. Finally, the quasi-steady flowfield of the inlet is established with a bow shock before the cow lip and a subsonic region at the cowl side, namely the inlet is local unstarted. At low initial backpressure, the separation bubbles at the nozzle walls vanish and no shock train structure appears. Furthermore, an unsteady expansion wave may appear upstream of the secondary shock and the Mach number of the flow following the secondary shock is higher than that of the nozzle quasi-steady flow. The Mach number of the flow into the inlet increases to the maximum value quickly, the inlet starts successfully. The numerical results show that the inlet starts easier and faster with lower initial backpressure.

A conceptual design of shock-eliminating clover combustor for large scale scramjet engine

A new concept of shock-eliminating clover combustor is proposed for large scale scramjet engine to fulfill the requirements of fuel penetration, total pressure recovery and cooling. To generate the circular-to-clover transition shape of the combustor, the streamline tracing technique is used based on an axisymmetric expansion parent flowfield calculated using the method of characteristics. The combustor is examined using inviscid and viscous numerical simulations and a pure circular shape is calculated for comparison. The results showed that the combustor avoids the shock wave generation and produces low total pressure losses in a wide range of flight condition with various Mach number. The flameholding device for this combustor is briefly discussed.

Investigation of hypersonic inlet pulse-starting characteristics at high Mach number

An unsteady viscous numerical simulation is performed to study the hypersonic inlet pulse-starting in a shock tunnel under the condition of inflow Mach number higher than the design value with a simplified nozzle startup wave system. A local unstart of hypersonic inlet is obtained with the initial backpressure and temperature of test section equal to the hypersonic freestream static pressure and static temperature, respectively. During the hypersonic inlet pulse-starting process, the nozzle startup wave system (including the primary shock, contact discontinuity and secondary shock) propagates downstream and interacts with the hypersonic inlet, the secondary shock induces boundary layer separation on the compression ramp. A low velocity flow induced by the separation bubble enters into the internal duct with the passage of time. It thickens the boundary layer and then the cowl shock induces a large separation bubble on the compression side. The shock induced by the large separation bubble impinges on the cowl and induces a small separation bubble, which moves upstream and induces the reflection of the external compression shock at the cowl transiting from regular reflection to Mach reflection. Mach reflection results in the shock propagating forward to cause a shock detachment at the cowl lip. The hypersonic inlet is not fully started and this phenomenon is referred to as “local unstart of inlet”. Moreover, it is found that the hypersonic inlet starts with lower initial backpressure or higher initial temperature of test section, and the hypersonic inlet unstarts with higher initial backpressure. The effect mechanism is analyzed with the help of numerical simulations and unsteady one-dimensional shock theory. As there are three operation modes of hypersonic inlet at high Mach number: start, local unstart and unstart. The results of the hypersonic inlet pulse-starting in a shock tunnel should be carefully treated.

Hysteresis phenomenon of hypersonic inlet at high Mach number

When the hypersonic inlet works at a Mach number higher than the design value, the hypersonic inlet is started with a regular reflection of the external compression shock at the cowl, whereas a Mach reflection will result in the shock propagating forwards to cause a shock detachment at the cowl lip, which is called “local unstart of inlet”. As there are two operation modes of hypersonic inlet at high Mach number, the mode transition may occur with the operation condition of hypersonic inlet changing. A cowl-angle-variation-induced hysteresis and a downstream-pressure-variation-induced hysteresis in the hypersonic inlet start↔local unstart transition are obtained by viscous numerical simulations in this paper. The interaction of the external compression shock and boundary layer on the cowl plays a key role in the hysteresis phenomenon. Affected by the transition of external compression shock reflection at the cowl and the transition between separated and attached flow on the cowl, a hysteresis exists in the hypersonic inlet start↔local unstart transition. The hysteresis makes the operation of a hypersonic inlet very difficult to control. In order to avoid hysteresis phenomenon and keep the hypersonic inlet operating in a started mode, the control route should never pass through the local unstarted boundary.

Two-dimensional viscous numerical simulation of liquid sloshing in rectangular tank with/without baffles and comparison with potential flow solutions

A viscous fluid model based on non-inertial reference system is developed for the problem of liquid sloshing in rectangular tank with/without baffles. The accuracy of the numerical model is validated against available theoretical solutions, experimental data and numerical predictions by linear and nonlinear potential flow models and different Navier–Stokes solvers. The numerical examinations indicate that the dissipative effects have significant influence on the sloshing responses in both non-baffled and baffled tanks. The sloshing responses that are associated with the natural frequencies can be finally damped out due to the physical dissipations, while they are entirely retained in the potential solutions, which accounts for the general over-predictions of sloshing amplitudes by the potential flow theory. The sloshing in baffled tank involves more dissipation due to the stronger vortical flow. The resonant frequency and amplitude are highly dependent on the baffle width and position. The relative sloshing amplitudes around the resonant condition are found to decrease with the excitation amplitude in a power law. The necessity of using viscous fluid model for sloshing predictions is addressed. The extremely long numerical computations have to be carried out in order to obtain convincing stable solutions, especially for the weakly damped sloshing motion.