The calculations of Computational fluid dynamics

The following are some of the calculations whichan aerodynamist may be concerned with; itshould be remembered that these calculations areoften carried out on about 10 000 000 (ten mil-lion) individual grid squares, or cells, on the carbody, a slight change of design will need a newset of calculations. Even using the latest computersoftware, the slightest change may take severaldays; without CFD it would take months, and thelevel of accuracy would be much less. If youchoose to use any of these formulae, remember touse SI units, metres, newtons and seconds whereappropriate.Dynamic pressure, which is also a kinetic energyof unit volume in terms of cubic metres, comesfrom the Bernoulli equations. Bernoulli was a sci-entist whose fluid flow theories were first used inthe design of ships’ hulls.Dynamic pressure 1/2  air density  vehicle velocity squared 1/2 V2As you can see, the speed (velocity) of the vehicleis important for these calculations. Of coursevelocity is a vector quantity, it is related to thedirection of the wind. Wind is very rarely astraight-on head wind, so calculations can be donefor any of the 360 degree possible wind directions for each of the ten million grid squares. Yes, that is3.6 billion calculations for each speed and ofcourse the air density varies with altitude; at sealevel the value is 1.226 kilogrammes per cubicmetre.Reynolds Number is a ratio which gives a goodguide to the air flow pattern and is an importantconsideration of what is called scale effect.Reynolds Number air density  air velocity length of flow/air ViscosityRe  lDrag is the aerodynamic resistance of the vehicle,its resistance to pass through air. Drag in newtonsforce is found by the formula:Drag  1/2 air density  velocity squared frontal area  coefficient of drag 1/2V2ACDYou will see that part of the formula is familiar,and part of it is the same as dynamic pressure,therefore:Drag  dynamic pressure  frontal area coefficient of drag The coefficient of drag is a number which indicatesthe resistance of the car to pass through the air,typical values are between 0.25 and 0.35.Lift is the force generated by an aerofoil sectionnormal to the direction of fluid flow. In otherwords it is the upward lifting force which is gener-ated when passing horizontally through air. Forroad vehicles wings are used to hold a vehicle onto the road, this can be called downthrust or nega-tive lift.Lift  dynamic pressure  wing area coefficient of liftWhen working with road vehicles the frontal area isoften used for the wing area figure. On aircraft, thewing plan area is more appropriate. With advancedaerodynamic work the plan area is related to areference area. For most road vehicles the frontalarea and the plan area are proportional; also thecoefficient of lift and the coefficient of drag are alsoproportional.Lift 1/2V2ACL