Department of Energy Sciences, LTH C. Norberg, 12/02/2019 MMVF10 Fluid Mechanics LABORATION 1 Flow around Bodies OBJECTIVES (1) To understand how body shape influences the flow-related forces (2) To understand how scaling experiments can be used to determine the forces on a full- scale, real body (3) To understand the basic mechanisms of flow separation (4) To investigate pressure distributions around a circular cylinder and a wing profile SUMMARY The flow-related force vector acting on an immersed body can be divided into three named components, a drag (drag force), which acts in the flow direction, a lift (lift force) and a side force, all perpendicular to each other. The lift usually is in the direction so that it does a useful job, for instance upwards for an airplane in horizontal flight or downwards for inverted wings on race cars. In many cases the (time-mean) side force is zero, for instance when there is flow symmetry about the plane of lift and drag, as for an airplane flying in still air. Further, the components can be divided up with respect to their origin, wall surface pressure and wall friction. The pressure component of the drag, the pressure drag, is often referred to as the form drag since it is strongly dependent on the body form (shape). The remaining part is the friction drag, which is due to shearing viscous forces along the body surface. Flow similarity laws are crucial for model testing experiments. For instance, the Reynolds similarity law says that for incompressible flow about two geometrically similar bodies, without any effects of free surfaces, the flow itself is similar, if tested at the same Reynolds number. The lab session is based on three tests, in air flow. Test 1: Drag measurements Determine the drag for some different axisymmetric bodies and two circular cylinders. Test 2: Measurements of forces on an airfoil Determine lift and drag for an airfoil model at different angles of attack. Test 3: Pressure measurements Measure the distribution of static wall pressure around a circular cylinder in cross flow and an airfoil model, respectively. Also determine the form drag of the cylinder. PREREQUISITES Read this PM and Ch. 7.1, 7.5, and 7.6 in F. M. White, Fluid Mechanics 1 . REPORT Each student should account for all measurement data and results in the handed-out lab protocol, the report, which is to be finalized during the lab session. Time in lab: approx. 4 hours 1 Further references are to 8th edition in SI Units (2016).
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MMVF10 LABORATION 1 Flow around Fluid Mechanics Bodies
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Department of Energy Sciences, LTH
C. Norberg, 12/02/2019
MMVF10
Fluid Mechanics
LABORATION 1 Flow around
Bodies
OBJECTIVES
(1) To understand how body shape influences the flow-related forces
(2) To understand how scaling experiments can be used to determine the forces on a full-
scale, real body
(3) To understand the basic mechanisms of flow separation
(4) To investigate pressure distributions around a circular cylinder and a wing profile
SUMMARY
The flow-related force vector acting on an immersed body can be divided into three named
components, a drag (drag force), which acts in the flow direction, a lift (lift force) and a side
force, all perpendicular to each other. The lift usually is in the direction so that it does a useful
job, for instance upwards for an airplane in horizontal flight or downwards for inverted wings
on race cars. In many cases the (time-mean) side force is zero, for instance when there is flow
symmetry about the plane of lift and drag, as for an airplane flying in still air. Further, the
components can be divided up with respect to their origin, wall surface pressure and wall
friction. The pressure component of the drag, the pressure drag, is often referred to as the form
drag since it is strongly dependent on the body form (shape). The remaining part is the friction
drag, which is due to shearing viscous forces along the body surface. Flow similarity laws are
crucial for model testing experiments. For instance, the Reynolds similarity law says that for
incompressible flow about two geometrically similar bodies, without any effects of free
surfaces, the flow itself is similar, if tested at the same Reynolds number.
The lab session is based on three tests, in air flow.
Test 1: Drag measurements
Determine the drag for some different axisymmetric bodies and two circular cylinders.
Test 2: Measurements of forces on an airfoil
Determine lift and drag for an airfoil model at different angles of attack.
Test 3: Pressure measurements
Measure the distribution of static wall pressure around a circular cylinder in cross flow and an
airfoil model, respectively. Also determine the form drag of the cylinder.
PREREQUISITES
Read this PM and Ch. 7.1, 7.5, and 7.6 in F. M. White, Fluid Mechanics1.
REPORT
Each student should account for all measurement data and results in the handed-out lab
protocol, the report, which is to be finalized during the lab session.
Time in lab: approx. 4 hours
1 Further references are to 8th edition in SI Units (2016).
2
Forces on an immersed body
A solid body that is exposed to flow of a viscous fluid is also affected by a flow-induced
force. This force is the resultant of the normal and shear forces that acts locally on the body
surface. The normal surface force is completely dominated by pressure action, the shear forces
are due to viscous stresses only, and are normally referred to as friction forces. Consider a
wing-like body of large width in relation to its chord, see Fig. 1. The flow around this body
can be considered to be essentially two-dimensional.
Figure 1: Forces on an immersed body, two-dimensional flow.
The force vector F is divided into two components, the drag D, which acts in the flow
direction, and the lift L, which acts normal to the flow. The drag itself is divided into pressure
or form drag and friction drag. Form drag is due to the pressure forces acting on the surface
(static pressure p); the friction drag is due the surface viscous shearing (frictional) forces (wall
shear stress τ). The absolute value of F is normally expressed using a dimensionless
coefficient C, defined as
AV
CF2
2 (1)
V - oncoming, free stream velocity
A - characteristic area
- density of fluid
For geometrically similar bodies and for incompressible flows without influences of free
surface effects we have the Reynolds similarity law:
Flows around geometrically similar bodies are similar for equal Reynolds numbers
The Reynolds number, Re, is dimensionless and is defined as