[granzer]

I have read many posts dealing with the same subject but did not get a satisfactory answer. Is pressure gradient normal to the wall, zero?. Because if we consider an aerofoil then there is definitely a pressure gradient developing over the aerofoil wall. Also, I read that the pressure gradient within the boundary layer is zero and not outside the boundary layer. Is this correct?

[FMDenaro]

Originally Posted by granzer

I have read many dealing with the same subject but did not get a satisfactory answer. Is pressure gradient norma to the wall zero?. Because if we consider an aerofoil then there is definitely a pressure gradient developing over the aerofoil wall. Also, I read that the pressure gradient within the boundary layer is zero and not outside the boundary layer. Is this correct?

Not exactly, the NSE written at a wall will say you that dp/dn=ni*d^2u/dn^2. The BL approximation will drive you to consider dp/dn->0 for ni->0.
Thus, dp/dn =0 is a BL approximation accurate only at high Re numbers.

[agd]

Is it true in general? No. But for a large number of flows it is a reasonable approximation. For attached flows over surfaces that possess small curvature it is a good approximation if other effects are not present. For example, if the surface is accelerating in the wall-normal direction, then the pressure gradient in the normal direction will not be zero. The best way to answer this question is to apply the NS equations at the surface in question under whatever physics you are dealing with and see what happens to the terms in the equations. See the development of the flat plate boundary layer equations for a good example of this.

[granzer]

Originally Posted by agd

Is it true in general? No. But for a large number of flows it is a reasonable approximation. For attached flows over surfaces that possess small curvature it is a good approximation if other effects are not present. For example, if the surface is accelerating in the wall-normal direction, then the pressure gradient in the normal direction will not be zero. The best way to answer this question is to apply the NS equations at the surface in question under whatever physics you are dealing with and see what happens to the terms in the equations. See the development of the flat plate boundary layer equations for a good example of this.

sdasdas fa

[granzer]

Originally Posted by FMDenaro

Not exactly, the NSE written at a wall will say you that dp/dn=ni*d^2u/dn^2. The BL approximation will drive you to consider dp/dn->0 for ni->0.
Thus, dp/dn =0 is a BL approximation accurate only at high Re numbers.

Originally Posted by agd

Is it true in general? No. But for a large number of flows it is a reasonable approximation. For attached flows over surfaces that possess small curvature it is a good approximation if other effects are not present. For example, if the surface is accelerating in the wall-normal direction, then the pressure gradient in the normal direction will not be zero. The best way to answer this question is to apply the NS equations at the surface in question under whatever physics you are dealing with and see what happens to the terms in the equations. See the development of the flat plate boundary layer equations for a good example of this.

I have seen the derivations and how the pressure gradient tends to zero as the wall-normal tends to zero. What I cannot fathom is how is it possible over an aerofoil as there is an obvious pressure gradient? Are we assuming the first layer of air molecules that is over the wing wall (and exerting the pressure over the wall) and the wall should be at the same pressure(every action from molecules has equal and opposite reaction from wall) ?. Are we also assuming that the pressure varies as the distance from the wall increases? So this gets modeld as "pressure gradient is zero between the wall and the first cell center above the wall"?

[FMDenaro]

Originally Posted by granzer

I have seen the derivations and how the pressure gradient tends to zero as the wall-normal tends to zero. What I cannot fathom is how is it possible over an aerofoil as there is an obvious pressure gradient? Are we assuming the first layer of air molecules that is over the wing wall (and exerting the pressure over the wall) and the wall should be at the same pressure(every action from molecules has equal and opposite reaction from wall) ?. Are we also assuming that the pressure varies as the distance from the wall increases? So this gets modeld as "pressure gradient is zero between the wall and the first cell center above the wall"?

The BL theory for a flat plate should be extended with care to an airfoil. It should be considered in a local reference system in terms of the normal and tangential direction to the surface (see Schlichting). When the airfoil has curvature radius R>> delta you can assume the flat plate result dp/dy=0, provided the flow does not separate. Then, dp/dx in the theory is assumed to be a known term.
See also Sec.7 in Chap 10 of the Kundu textbook for the case of low R