scholarly journals Decomposition of the forces on a body moving in an incompressible fluid

2019 ◽  
Vol 881 ◽  
pp. 1097-1122
Author(s):  
W. R. Graham
Keyword(s):  
Velocity Field ◽  
Pressure Field ◽  
Rotational Velocity ◽  
Inviscid Flow ◽  
Added Mass ◽  
The Body ◽  
Mass Force ◽  
Natural Approach ◽  
Fluid Forces ◽  
Point Pressure

In analysing fluid forces on a moving body, a natural approach is to seek a component due to viscosity and an ‘inviscid’ remainder. It is also attractive to decompose the velocity field into irrotational and rotational parts, and apportion the force resultants accordingly. The ‘irrotational’ resultants can then be identified as classical ‘added mass’, but the remaining, ‘rotational’, resultants appear not to be consistent with the physical interpretation of the rotational velocity field (as that arising from the fluid vorticity with the body stationary). The alternative presented here splits the inviscid resultants into components that are unquestionably due to independent aspects of the problem: ‘convective’ and ‘accelerative’. The former are associated with the pressure field that would arise in an inviscid flow with (instantaneously) the same velocities as the real one, and with the body’s velocity parameters – angular and translational – unchanging. The latter correspond to the pressure generated when the body accelerates from rest in quiescent fluid with its given rates of change of angular and translational velocity. They are reminiscent of the added-mass force resultants, but are simpler, and closer to the standard rigid-body inertia formulae, than the developed expressions for added-mass force and moment. Finally, the force resultants due to viscosity also include a contribution from pressure. Its presence is necessary in order to satisfy the equations governing the pressure field, and it has previously been recognised in the context of ‘excess’ stagnation-point pressure. However, its existence does not yet seem to be widely appreciated.

The force exerted on a body in inviscid unsteady non-uniform rotational flow

1988 ◽  
Vol 197 ◽  
pp. 241-257 ◽  
Author(s):  
T. R. Auton ◽  
J. C. R. Hunt ◽  
M. Prud'Homme
Keyword(s):  
Velocity Field ◽  
Turbulent Flows ◽  
General Expression ◽  
Lift Force ◽  
Rotational Velocity ◽  
Added Mass ◽  
Rate Of Change ◽  
The Body ◽  
Three Dimensions ◽  
Inviscid Fluid

A general expression is derived for the fluid force on a body of simple shape moving with a velocity v through inviscid fluid in which there is an unsteady non-uniform rotational velocity field u0(x,t) in two or three dimensions. It is assumed that the radius is small compared with the scale over which the strain rate changes, though for the sphere it is also assumed that the changes in the ambient velocity field over the scale of the sphere are small compared with the velocity of the body relative to the flow. Given these approximations it is shown that the effects of the rate of change of the vorticity of the ambient flow is of second order and can be neglected. However the rate of change of the irrotational straining motion is included in the analysis. It is shown that the inertial forces derived by many authors for irrotational flow can be simply added to a generalization of the lift force derived by Auton (1987) in a companion paper. It is shown how this lift force is made up of a rotational and an inertial or added-mass component. For three-dimensional bluff bodies the latter is generally larger (by a factor of three for a sphere), and can be simply calculated from the added-mass coefficient. For illustration, the general expression is used to derive formulae for (i) the motion of a spherical bubble in a steady non-uniform flow to contrast with the motion in an unsteady flow, and (ii) the motion of rigid volumes of neutral density across an inviscid shear flow. These results show how added-mass (and lift) forces lead to different motions for a sphere and a cylinder. The general expression is useful in two-phase flow calculations, and for indicating the forces and motions of ‘lumps of fluid’ in turbulent flows.

A Double Birkhoff Wake Oscillator for the Modeling of Vortex-Induced Vibration

2011 ◽  
Author(s):  
R. H. M. Ogink
Keyword(s):  
Free Vibration ◽  
Added Mass ◽  
Mass Force ◽  
Near Wake ◽  
Vibration Measurements ◽  
Vortex Induced Vibration ◽  
Fluid Forces ◽  
Wake Oscillator ◽  
Model Equations ◽  
Far Wake

A double Birkhoff wake oscillator for the modeling of vortex-induced vibration is presented in which the oscillating variables are assumed to be associated with the boundary layer/near wake and the far wake. The fluid forces are assumed to consist of a potential added mass force and a force due to vortex shedding. In the limit of vanishing incoming flow velocity, the model equations reduce to a form similar to the Morison equation. The results of the double wake oscillator have been compared with forced vibration measurements and free vibration measurements over a range of mass and damping ratios. The model is capable of describing the most important trends in both the forced and free vibration experiments. Specifically, the double wake oscillator is able to model both the upper and lower branch of free vibration.

On the unsteady inviscid force on cylinders and spheres in subcritical compressible flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2161-2175 ◽  
Author(s):  
M Parmar ◽  
A Haselbacher ◽  
S Balachandar
Keyword(s):  
Mach Number ◽  
Compressible Flow ◽  
Propagation Speed ◽  
Added Mass ◽  
The Body ◽  
Mass Force ◽  
Unsteady Force ◽  
Mass Coefficient ◽  
Added Mass Coefficient ◽  
Cylinders And Spheres

The unsteady inviscid force on cylinders and spheres in subcritical compressible flow is investigated. In the limit of incompressible flow, the unsteady inviscid force on a cylinder or sphere is the so-called added-mass force that is proportional to the product of the mass displaced by the body and the instantaneous acceleration. In compressible flow, the finite acoustic propagation speed means that the unsteady inviscid force arising from an instantaneously applied constant acceleration develops gradually and reaches steady values only for non-dimensional times c ∞ t / R ≳10, where c ∞ is the freestream speed of sound and R is the radius of the cylinder or sphere. In this limit, an effective added-mass coefficient may be defined. The main conclusion of our study is that the freestream Mach number has a pronounced effect on both the peak value of the unsteady force and the effective added-mass coefficient. At a freestream Mach number of 0.5, the effective added-mass coefficient is about twice as large as the incompressible value for the sphere. Coupled with an impulsive acceleration, the unsteady inviscid force in compressible flow can be more than four times larger than that predicted from incompressible theory. Furthermore, the effect of the ratio of specific heats on the unsteady force becomes more pronounced as the Mach number increases.

scholarly journals Time-Periodic Wave Loading on a Submerged Circular Cylinder in a Current

1986 ◽  
Vol 30 (03) ◽  
pp. 153-158
Author(s):  
John Grue
Keyword(s):  
Circular Cylinder ◽  
Fluid Layer ◽  
Periodic Wave ◽  
Added Mass ◽  
The Body ◽  
Source Distribution ◽  
Mass Force ◽  
Damping Force ◽  
Time Periodic ◽  
A Current

The time-periodic pressure loading, added mass, damping, and exciting forces on a horizontal submerged circular cylinder in a current are examined. The fluid layer is infinitely deep and the motion is two-dimensional. The boundary-value problem is solved by applying a source distribution along the contour of the body. The forces become finite for τ = Uσlg approaching 1/4 (where U is the speed of the current, σ the frequency, and g the acceleration due to gravity). The added-mass force becomes negative for τ close to 1//4. The damping force is very small for τ > 1/4. The exciting loading on the cylinder is larger for incoming waves traveling against the current than for incoming waves traveling with the current.

Hydrodynamics of swimming in the water boatman, Cenocorixa bifida

1986 ◽  
Vol 64 (8) ◽  
pp. 1606-1613 ◽  
Author(s):  
R. W. Blake
Keyword(s):  
High Speed ◽  
Forward Direction ◽  
Added Mass ◽  
Mean Value ◽  
The Body ◽  
Power Stroke ◽  
Mass Force ◽  
Mean Power ◽  
Recovery Stroke ◽  
The Mean

Locomotion of a small water boatman (Cenocorixa bifida, Corixidae) was investigated employing high-speed cinematography and hydromechanical modelling based on a blade-element approach. The animal is propelled by the synchronous rowing action of its hind legs. The propulsive cycle consists of a power stroke and a recovery stroke phase. Force, impulse, power, and hydromechanical efficiency were calculated for a representative power stroke during which the mean body velocity was about 8 cms−1. A distinction is made between quasi-steady resistive and unsteady inertial (added mass) forces. The mean and maximum resistive thrust forces were calculated to be about 2.4 × 10−5 and 5.7 × 10−5 N per limb, respectively. By equating the total impulse of the power stroke for both legs (2.4 × 10−6 N s) with that of the drag force acting on the body over the same period, a drag coefficient of approximately 1.07 is inferred for the body. This value is comparable to those obtained for certain insects that operate at similar Reynolds numbers to C. bifida. The unsteady added mass force that acts in the forward direction is positive (propulsive) over most of the stroke with a mean value of about 1.17 × 10−5 N per limb, corresponding to an impulse of approximately 5.9 × 10−7Ns. The total propulsive mean force and impulse acting in the forward direction amount to about 3.6 × 10−5N and 1.8 × 10−6N s per limb, respectively, so the impulse of the forwardly directed added mass force amounts to about half that of the resistive thrust force. The total work and mean power associated with generating the resistive thrust were calculated to be about 6.7 × 10−7 J and 1.33 × 10−5 W per limb, respectively. Dividing the mean body drag power (1.4 × 10−5 W) by the total mean resistive power from both legs gave a hydromechanical efficiency of 0.52. When the mean inertial power associated with moving the body (2.3 × 10−6 W) and the added mass power required to accelerate and decelerate the legs (1.95 × 10−5 W per limb) are taken into account, the power stroke propulsive efficiency falls to 0.42. Taking the energy required to power the recovery stroke into account gives an overall propulsive cycle efficiency of about 0.40. This value is about twice that calculated in a previous study for drag-based pectoral fin rowing in the angelfish and reasons for this are suggested.

Design and fabrication of anisotropic textile brace for exerting corrective forces on spinal curvature

2021 ◽  
pp. 152808372110326
Author(s):  
Queenie Fok ◽  
Joanne Yip ◽  
Kit-lun Yick ◽  
Sun-pui Ng
Keyword(s):  
Medical Condition ◽  
Three Dimensional ◽  
Case Series ◽  
The Body ◽  
Spinal Curvature ◽  
Radiographic Examination ◽  
Interface Pressure ◽  
Pressure System ◽  
Case Series Study ◽  
Point Pressure

This study focuses on the fabrication of an anisotropic textile brace that exerts corrective forces based on the three-point pressure system to treat scoliosis, which is a medical condition that involves deformity of the spine. The design and material properties of the proposed anisotropic textile brace are discussed in detail here. A case series study with 5 scoliosis patients has been conducted to investigate the immediate in-brace effect and biomechanics of the proposed brace. Radiographic examination, three-dimensional scanning of the body and interface pressure measurements have been used to evaluate the immediate effect of the proposed brace on reducing the spinal curvature and asymmetry of the body contours and its biomechanics. The results show that the proposed brace on average reduces the spinal curvature by 11.7° and also increases the symmetry of the posterior trunk by 14.1% to 43.2%. The interface pressure at the corrective pad ranges from 6.0 to 24.4 kPa. The measured interface pressure shows that a sufficient amount of pressure has been exerted and a three-point pressure distribution is realized to reduce the spinal curvature. The obtained results indicate the effectiveness of this new approach which uses elastic textile material and a hinged artificial backbone to correct spinal deformity.

An Investigation to Added Mass Force on the Wing of Insect Inspired from a Rigid Sphere Model

2012 ◽  
Vol 476-478 ◽  
pp. 2485-2488
Author(s):  
Mei Jun Hu ◽  
Xing Yao Yan ◽  
Jin Yao Yan
Keyword(s):  
Insect Flight ◽  
Aerodynamic Force ◽  
Mass Effect ◽  
Added Mass ◽  
Rigid Sphere ◽  
Force Model ◽  
Mass Force ◽  
Real Time Control ◽  
Wing Model ◽  
Force Peak

There is a force peak at the beginning of each stroke during the insect flight, this force peak contributes a lot to the total aerodynamic force. To build a man made insect inspired man-made micro aero vehicle, this force need to be considered in the aero force model, and this model should as simple as possible in order to be used in feedback real-time control. Here we presented a simplified model to take the medium added mass effect of the wing into account. Simulated results show a high force peak at the beginning of each stroke and are quite similar to the measured forces on the physical wing model which were carried out by Dickinson et.al.

Theoretical and Numerical Calculation on the Added Mass of Ahmed Body

2017 ◽  
Vol 865 ◽  
pp. 247-252
Author(s):  
Gui Tao Du
Keyword(s):  
Numerical Calculation ◽  
Theoretical Calculation ◽  
Calculation Method ◽  
Aerodynamic Drag ◽  
Added Mass ◽  
The Body ◽  
Power Performance ◽  
Car Body ◽  
The Impact ◽  
Ahmed Body

Because of the added mass, the aerodynamic drag of the automobile will increase obviously when accelerating in the still air. In this paper, it firstly gave the definition of the added mass, and presented that there was little research on the calculation of the added mass of automobile. Then through the analysis of the theoretical calculation method for the added mass, it pointed out that, for the added mass of the car-body with a complex shape, there was much difficulty in the theoretical calculation. Alternatively, a numerical calculation method for the added mass of car-body was derived. The simulation model adopted the Ahmed body and the corresponding verification experiment was completed in the Tongji Automotive Wind Tunnel center. The results indicate that the added mass is a constant which is only dependent on the body-shape. For the model investigated, the added mass is 0.0052kg that is approximately equal to the air displaced by the car-body. As the body accelerates to 4m/s2, the aerodynamic drag is increased by 1.89% because of added mass. Therefore, it needs to pay more attention to the impact that the added mass has on the dynamic performance of vehicle when proceeding the aerodynamic designs (especially for the high power performance vehicles). Meanwhile, it still makes a correction to the conventional aerodynamic drag formula. This paper also demonstrates that, with the analysis of the flow-field of car-body, the added mass essentially stems from the additionally work done by the car-body to increase the kinetic energy of external fluid as it speeds up.

Vortex street impinging upon an elliptical leading edge

1990 ◽  
Vol 211 ◽  
pp. 211-242 ◽  
Author(s):  
Ismet Gursul ◽  
Donald Rockwell
Keyword(s):  
Velocity Field ◽  
Flow Visualization ◽  
Pressure Field ◽  
Leading Edge ◽  
Vortex Street ◽  
Transverse Displacement ◽  
Vorticity Field ◽  
Measured Velocity ◽  
Vortical Structures ◽  
Pressure Fields

The interaction of a Kármán vortex street with an elliptical edge is investigated experimentally. Basic types of interaction, as a function of scale and transverse displacement of the incident vortex street, are revealed using flow visualization. Unsteady pressure fields induced by these interactions are measured by a phase-averaging technique and correlated with the visualized flow patterns for basic classes of interactions.For a generic vortex–edge interaction, measurements of the phase-averaged velocity field allow construction of streamlines and vorticity contours showing the details of the interaction, including distortion of the vortical structures near the edge. The pressure field is calculated from the measured velocity field and interpreted in relation to the vortical structures.Simulation of flow visualization using the measured velocity field demonstrates possible misinterpretations related to the underlying vorticity field.

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