8.7-Model-Prototype Performance.pdf

ModelPrototype Performance

http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...

8.7 ModelPrototype Performance

Geometric (scale model) and dynamic (same πgroups) similitude mean that the dependent πgroups are the

same for both the model and the prototype. For this reason, measurements made with the model can be applied

directly to the prototype. Such correspondence is illustrated in this section.

Example 8.6 shows how the pressure difference measured in a model test can be used to find the pressure

difference between the corresponding two points on the prototype.

EXAMPLE 8.6 APPLICATIO OF PRESSURE

COEFFICIET

A 1/10 scale model of a blimp is tested in a wind tunnel under dynamically similar conditions. The

speed of the blimp through still air is 10 m/s. A 17.8 kPa pressure difference is measured between

two points on the model. What will be the pressure difference between the two corresponding points

on the prototype? The temperature and pressure in the wind tunnel is the same as the prototype.

PROBLEM DEFINITION

Situation: A 1/10 scale of a blimp is tested in a wind tunnel under dynamically similar conditions. A

pressure difference of 17.8 kPa is measured on model.

Find: Corresponding pressure difference (Pa) on prototype.

Properties: Pressure and temperature are the same for wind tunnel test and prototype, so ν m = ν p .

PLAN

Reynolds number is the only significant πgroup. Thus Eq. 8.4 reduces to

For dynamic similitude, Re m = Re p . Then with geometric similitude, C pm = C pp .

1. Calculate the model/prototype velocity ratio.

2. Calculate pressure difference on prototype.

SOLUTION

1. Reynoldsnumber similitude

1 of 3

1/15/2009 12:49 AM

ModelPrototype Performance

http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...

2. Pressure coefficient correspondence

Pressure difference on prototype

Example 8.7 illustrates calculating the fluid dynamic force on a prototype blimp from wind tunnel data using

similitude.

EXAMPLE 8.7 DRAG FORCE FROM WID TUEL

TESTIG

A 1/10 scale of a blimp is tested in a wind tunnel under dynamically similar conditions. If the drag

force on the model blimp is measured to be 1530 N, what corresponding force could be expected on

the prototype? The air pressure and temperature are the same for both model and prototype.

PROBLEM DEFINITION

Situation: A 1/10 scale model of blimp is tested in a wind tunnel, and a drag force of 1530 N is

measured.

Find: The drag force (in newtons) on the prototype.

Properties: Pressure and temperature are the same, ν m = ν p .

PLAN

Reynolds number is the only significant πgroup, so Eq. 8.4 reduces to C F = f (Re). For dynamic

similtude, Re m = Re p . Thus with geometric similitude C F,m = C F,p .

1. Find velocity ratio by equating Reynolds numbers.

2. Find the force ratio from force coefficient.

SOLUTION

1. Reynoldsnumber similitude

2 of 3

1/15/2009 12:49 AM

ModelPrototype Performance

http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...

2. Force coefficient correspondence

Therefore

REVIEW

The result that the model force is the same as the prototype force is interesting. When Reynolds

number similitude is used, and the fluid properties are the same fluid for model and prototype, the

forces on the model will always be the same as the forces on the prototype.

3 of 3

1/15/2009 12:49 AM

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: