Added mass coefficients for submerged bodies by a low-order panel method

SummaryThree low-order panel methods developed for the analysis of supersonic flows have been used to make calculations for a number of test configurations, with the aim of establishing the range of problems for which this class of computational method yields adequate solutions. The programs investigated were the Woodward USSAERO/C program, the related NLRAERO program, and the British Aerospace Warton supersonic panel program. Results obtained using these programs have been evaluated against theoretical and experimental data for a number of test cases covering wing-alone, body-alone and wing-body geometries. It is concluded that low-order panel methods can provide adequate solutions for supersonic flows about wings, bodies and wing-body combinations, provided the assumptions implicit in the linearised potential flow model are not violated. Examples show that the prediction of lift and pitching moment curve slopes for quite complex configurations may be acceptable, but that the detailed pressure distributions are not always predicted satisfactorily. In particular, serious problems are encountered in calculating the flow about wings with rounded supersonic leading edges due to the linearised flow model which is used.

Hydrodynamic coefficients of subsea manifolds are significant parameters in predicting dynamic responses during deep-water installation. To calculate these coefficients, a series of model tests of the drag coefficients of a typical subsea manifold with eight slots were carried out at Zhejiang University. A numerical simulation was performed using the computational fluid dynamics (CFD) method, and the Navier–Stokes equations were solved to obtain the drag and added mass coefficients. On the prediction of drag coefficient, a similar tendency was found for both the numerical and experimental results, proving the accuracy and reliability of the proposed CFD method. The effects of variables such as the Keulegan-Carpenter (KC) number and frequency of forced oscillation on the added mass coefficients were analysed. The added mass coefficients increase nearly linearly as the KC number increases, but the oscillation frequency has little influence on the added mass coefficients.

A BEM-isogeometric method for the ship wave-resistance problem

Vortex-Induced Motion (VIM) is an important cause of fatigue damage of a Truss Spar. Response frequency is one of the critical components in estimating VIM. Response frequency is related to the natural frequency of the structure, and it is also impacted by the effect of the added mass. In this study, Reynolds numbers of the experiment varied from 8E04 to 2E05. The experiment results indicate that the added mass coefficient decreases with the increasing reduced velocity and the oscillation frequency of the low mass ratio cylinder locks in the natural frequency instead of still water natural frequency. The estimated added mass coefficient from one oscillation cycle to the next varied considerably. The oscillation frequency from one oscillation cycle to the next is associated with the natural frequency which is estimated by the time-variable added mass coefficient.

Flow around circular and noncircular cylinders by a low-order panel method

A closed form for low-order panel methods

A zonal method based on the iterative coupling between an in viscid panel method and a Navier-Stokes (NS) method has been developed to analyze the complex flowfield associated with the V/STOL flow environment in order to improve the prediction of aerodynamic characteristics. The low-order panel method, VSAERO, developed by Analytical Methods, Inc. is used to solve for the entire flow region, which includes the V/STOL configuration and jet boundary model. In two separate investigations presented here, ARC3D, a well-known compressible thin layer NS code developed at NASA Ames Research Center, and APPL, a parabolized NS code developed at Amtec Engineering, are used to solve for the details of the jet region subject to the boundary condition provided by VSAERO. Overlapping boundaries are used for the purpose of coupling. Comparisons with the available experimental data for a jet-in-crossflow and a V/STOL configuration with lift-jet in a subsonic freestream show qualitative agreement with experiment and improved correlations over those by inviscid computations alone.

When bottom mounted structures of large displacement are immersed in the sea, earthquake induced hydrodynamic loads may become important design factors. Specifically, as the earth oscillates, a bottom mounted structure is forced to describe time dependent motion in an otherwise still fluid. As a result, hydrodynamic loads in addition to the inertial loads of the structure itself are induced. In this paper, a theoretical approach to the calculation of these hydrodynamic loads is outlined and numerical results are presented for several submerged configurations. Practical geometries considered include a submerged oil storage tank configuration and a conical configuration as has been proposed for offshore drilling rig designs for deployment in the Arctic. Also, computations were carried out for a sphere and vertical circular cylinder and various comparisons with classical results are made. Numerical results for these submerged structures are presented in the form of a dimensionless hydrodynamic load parameter or added mass coefficient. Results corresponding to a number of different water depths are presented to show the rather sizable effect of the relative water depth on the hydrodynamic force. It is shown that for typical earthquake frequencies, the effect of the free water surface is to reduce the hydrodynamic loads in comparison to the corresponding infinite depth values. Experimental results obtained by vibration testing are presented for a submerged sphere and a vertical circular cylinder. These results show excellent agreement with the theoretical results. Introduction Principal attention in earthquake engineering has been given to the generation of tsunami waves, the shoreline run-up and damage caused by these waves, as well as the damage to dry land structures caused by strong ground motion. With the increased deployment of large submerged structures, an additional facet of this important problem has come to light. Namely, if a large bottom mounted structure submerged in the ocean is excited by oscillatory ground motion, hydrodynamic loads in addition to its own inertia forces come into play. As the structure is caused to move through the water, hydrodynamic forces which are dependent upon the size and shape of the structure as well as the water depth and frequency of oscillation arise. On account of the large density of water, these forces are often quite large and have considerable influence on the structural design. When an object is accelerated through a fluid there are, in general, two types of forces that are recognized, one being a drag component and a second, the inertial component. The nature of the flow produced by the time dependent motion of the immersed rigid object and the relative contribution of these two components of force is generally considered to be strongly dependent on the amplitude of the relative fluid motion in comparison to the characteristic lineal dimension of the object. For example, Keulegan and Carpenter [1] found that, for harmonic motion of the fluid past a fixed circular cylinder, major flow separation did not occur and the forces were well represented by potential flow values provided the amplitude of the motion was less than about a half diameter.

As the interest in arctic shipping and arctic exploration of oil and gas is increasing in recent years, the number of ice class vessels is increasing rapidly. Also the choices for propulsion devices are getting wider and these include podded propulsion systems. This study is a framework for the numerical prediction of the ice interaction loads acting on a podded propeller blade. The results of this study will help us to understand the propeller-ice interaction problem more comprehensively. Several studies for propeller-ice interaction have been carried out in the past few decades. Propeller-ice interaction, however, is a complicated process with a high level of uncertainties due to ice properties, ship operating conditions, and environmental conditions. Full-scale measurements involve high costs. In order to overcome these difficulties, model tests were carried out with model ice in an ice tank. The model tests provide well-controlled ice properties and interaction conditions to reduce the uncertainties. The tests were carried out in the ice tank with scaled down model ice at the National Research Council of Canada’s Institute for Ocean Technology. The ice loads acting on the propeller blade were measured with a six-component force and moment load cell fitted to the shaft and one of the propeller blades. Based on the experimental results, a numerical prediction model was developed to estimate the ice loads on the propeller blade. The numerical prediction is composed of three parts: the hydrodynamic calculations including separable and inseparable hydrodynamic loads, and the ice milling loads calculation. The separable and inseparable hydrodynamic loads can be obtained from clear water and blocked flow respectively. The hydrodynamic calculations were done by a low order panel method. The subroutines for calculating the ice milling loads are implemented into the panel method. The numerical prediction model for ice milling loads is described and the results are compared with those of experiments.

A new CFD method for determination of translational added mass coefficients of an underwater vehicle

Hydrodynamic force investigation of a rigid cylinder under the coupling CF and IL motion

Pumping efficiency and rotordynamic stability are paramount to subsea multiphase pump operation since, during the life of a well, the process fluid transitions from a pure liquid to a mixture of gas in the liquid to just gas. Circumferentially grooved seals commonly serve as balance pistons in pumps while also restricting secondary flow. Prior experimental results obtained with a grooved seal operating with a mixture of air and mineral oil show the seal rotordynamic force coefficients vary significantly with the gas volume fraction (GVF). This paper, complementing an exhaustive experimental program, presents a computational fluid dynamics (CFD) analysis to predict the leakage and dynamic force coefficients of a circumferentially grooved seal supplied with air in an oil mixture with a GVF varying from 0 to 0.7. The test seal has 14 grooves, an overall axial length of 43.6 mm, and radial clearance of 0.211 mm. The 127 mm diameter rotor spins at constant angular speed (Ω = 3500 rpm). The mixture enters the seal at a supply pressure (Pin) of 2.9 bar(a), and the seal exit pressure (Pout) is 1 bar(a). The CFD two-phase flow simulations utilize the Euler–Euler multiphase model to predict the mass flowrate and the pressure field as a function of the operating conditions. Using a multi-frequency shaft orbit motion method, the CFD simulations deliver the variations of reaction force on the rotor with respect to the excitation frequency. For a pure liquid condition (GVF = 0), both the CFD and experimental results produce constant stiffness, damping, and added mass coefficients. The experimental and CFD results demonstrate the seal rotordynamic force coefficients are quite sensitive to the GVF. When introducing a small amount of air into the oil (GVF = 0.1), the direct damping coefficient increases by approximately 10%. For operation with a mixture with inlet GVF > 0.1, the cross-coupled stiffness coefficients develop strong frequency-dependent characteristics. In contrast, the direct damping coefficient has a negligible variation with excitation frequency. The CFD predictions, as well as the experimental results, evidence that air injection in a liquid stream can significantly change the seal rotordynamic characteristics, and thus can affect the rotordynamic stability of a pump. An accurate CFD analysis provides engineers to design reliable grooved seals operating under two-phase flow conditions.

The heat transfer rate and the hydrodynamic forces experienced by a single vapor bubble of variable radius moving in a superheated or subcooled liquid are studied by means of numerical simulation. For that purpose the full Navier–Stokes equations and the temperature equation are solved in a frame of reference where the bubble surface is steady. The time evolution of the bubble radius is determined by solving the energy balance at the bubble surface. The numerical method is first validated by comparing present predictions with previous asymptotic or numerical results in the case where no relative motion between the liquid and the bubble exists. Then the situation where a constant relative velocity exists is considered. Effects of the mean flow on the heat transfer rate and on the bubble radius evolution are first discussed. Two different stages are generally observed in the computations. First, the radial motion induced by the displacement of the bubble surface dominates and the bubble evolution is essentially identical to the one observed in a liquid at rest. Then the ratio between the radial velocity and the translatory velocity decreases and the heat transfer rate becomes governed by streamwise advection effects. In this second stage a substantial increase of the growth or collapse rate of the bubble is observed, compared to the case of a liquid at rest. For a growing bubble it is shown that the complete process is successively described by the analytical solutions given by Scriven [Chem. Eng. Sci. 10, 1 (1959)] and Rückenstein [Chem. Eng. Sci. 10, 22 (1959)]. The situation is much less simple for a collapsing bubble and the reasons of this increased complexity are discussed. It is found that, when the heat transfer mechanism is dominated by streamwise advection, the bubble evolution and the collapse time predicted by the simulations agree well with the experimental results obtained by Chen and Mayinger [Int. J. Multiphase Flow 18, 877 (1992)]. Based on the present results, a general correlation giving the collapse time as a function of the characteristic parameters of the problem is proposed. The second contribution of the present work concerns the hydrodynamic force experienced by the bubble. Using a general decomposition procedure, the added mass effect and the viscous contribution are separately identified. It is first shown that the added mass coefficient is strictly constant and equal to one half, whatever the Reynolds number and the relative magnitude of the radial velocity. The viscous drag is then systematically compared with the quasisteady viscous drag corresponding to the instantaneous value of the Reynolds number. In situations of boiling, effects due to unsteadiness are found to exist during the first stages of the motion if the initial Reynolds number is not very large. In contrast, for a collapsing bubble, such effects remain significant all along the process because the relative importance of viscous phenomena increases in time. In both cases it is shown that the time variations of the bubble radius may affect deeply the viscous drag force. For example, when the radial velocity is high enough, the viscous drag force is found to be identical to the one corresponding to a potential flow, even if the instantaneous Reynolds number is low. These effects are discussed with the help of two asymptotic expressions of this force derived recently by Magnaudet and Legendre [Phys. Fluids 10, 550 (1998)] for a bubble with a time-dependent radius.

Hydrodynamic force coefficients are important parameters in design and assessment of marine risers. The hydrodynamic coefficients are widely used for assessing marine riser responses due to floater motion excitation and vortex-induced vibrations (VIV). Traditionally, the hydrodynamic coefficients have been obtained from physical model tests on short rigid riser sections. Recently, the offshore industry has started to use computational fluid dynamics (CFD) analysis for predicting the hydrodynamic coefficients due to the recent advancement of CFD software and high-performance computing capabilities, but a reliable CFD modeling practice is requested for CFD analysis to be a more widely accepted prediction tool in the industry. A joint industry effort has been made for developing and verifying the reliable CFD modeling practice through a working group of the Reproducible Offshore CFD JIP. In the working group, a CFD modeling practice document was written based on existing practices already validated for model test data, and verified by blind validations with three CFD practitioners. The first year works are focused on the bare riser with circular cross-section, and the second year work will be extended to the other riser sections such as staggered buoyancy module and straked riser. This paper presents the working group’s first-year verification activities for a bare riser with circular cross-section. The verification works covers three test problems: 1) stationary simulation in steady current, 2) forced-oscillation in calm water, 3) forced-oscillation in steady current. In the stationary simulation, mean drag coefficient, standard deviation of lift coefficient, and Strouhal numbers are compared. In the forced-oscillation simulation in calm water, the fully-submerged riser section oscillates with a sinusoidal motion, and damping and added mass coefficients are compared. In the forced-oscillation simulation in current, the riser section oscillates in cross-flow direction to the steady current, and lift coefficient and added mass coefficient are compared. By following the modeling practice, the CFD predictions are consistent with each other and close to the model test data for a majority of test cases.

Efficient measurement of hydrodynamic coefficients for vibrating cylinders at supercritical Reynolds numbers