ME 425: Aerodynamics

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Claribel Thornton
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ME 5: Aeodynamics D ABM Toufique Hasan Pofesso

Flow ove a stationay cylinde iscous sepaation (Not

Expeimental obsevation C p = ug potentialflow

1 ME 5: Aeodynamics D ABM Toufique Hasan Pofesso Depatment of Mechanical Engineeing, BUET Lectue- 8 Apil 7 teachebuetacbd/toufiquehasan/ toufiquehasan@mebuetacbd ME5: Aeodynamics (Jan 7) Flow ove a stationay cylinde iscous sepaation (Not pedicted by potential flow appoach) Flow Expeimental obsevation C p = ug potentialflow appoach c p pessue gadient, dc p 8 cos d L T, ME, BUET ME5: Aeodynamics (Jan 7)

2 otex flow Conside a flow whee all the steamlines ae concentic cicles about a given point as shown in figue Moeove, let the velocity along any given cicula steamline be constant, but let it vay fom one steamline to anothe invesely with distance fom the common cente Such a flow is called a (fee) votexflow θ p (, θ) ; Constant C To evaluate the constant, C, take the ciculation aound a given steamline of adius : C ds () C ( ) C Puely tangential flow (In contast to souce/k flow) Clockwise votex ; Clockwise votex, ciculation is (+ve) Thus the tangential velocity component of fee (iotational/potential) votex is: ; stength of the votex The dimension of ciculation is (length) /(time) L T, ME, BUET ME5: Aeodynamics (Jan 7) 3 otex flow The steam function is detemined as follows: Integating theaboveequationsgives : ln θ p (, θ) Clockwise votex ; The potential function is detemined in simila manne: Integating the aboveequationsgives : L T, ME, BUET ME5: Aeodynamics (Jan 7)

3 otex flow Is the otex flow iotational??? Ciculation aound closed cuve C C ds d C C C C d ; ve (anticlockwise votex) C d otex flow is iotational eveywhee except at the point = (oigin), whee velocity is infinite Theefoe, the oigin is a gula point in the flow field L T, ME, BUET Ciculation aound closed cuve C ds d C C C C ME5: Aeodynamics (Jan 7) C C C d d 5 d d d otex flow The steamlines in a paticula D flow field ae all concentic cicles as shown in figue The velocity is given by v θ = ω whee ω is the angula velocity of the otating mass of fluid Detemine the ciculation aound the path ABCD Ciculation aound closed cuve ABCD: ABCD ds AB BC CD DA ABCD ABCD ( b) b ( a) a ; diection of CD and velocityaein eveseode ABCD ( b a ) Such type of otation is called solid-body otation which is not iotational and cannot be defined ug a potential function This flow is known as foced votex Example- The swiling motion of the wate as it dains fom a bathtub is simila to that of a fee votex, wheeas the motion of a liquid in a tank that is otated about its axis with angula velocity coesponds to a foced votex L T, ME, BUET ME5: Aeodynamics (Jan 7) 6 3

4 otex flow L T, ME, BUET ME5: Aeodynamics (Jan 7) 7 otex flow Tonado A tonado can be appoximated by a fee votex of whee is the adius of the coe c At, velocity becomes infinite(gula point) if appoximated as fee votex athe, the coe of stength Γ fo, the full flow field is the tonado can be appoximated as foced votex Thus, a complete tonado can be modelled as combined votex flow c L T, ME, BUET ME5: Aeodynamics (Jan 7) 8

5 otex system L T, ME, BUET ME5: Aeodynamics (Jan 7) 9 Flow ove a otating cylinde p (, θ) Conside the addition of a non-lifting flow ove a stationay cylinde with a fee (potential) votex (clockwise otating), the combined steam function fo this type of flow is: stationay cylinde in unifom flow ln votex ; whee adiusof cicula cylinde stength of doublet L T, ME, BUET ME5: Aeodynamics (Jan 7) 5

6 6 Flow ove a otating cylinde The velocity field can be obtained as: cos New tem due to votex p (, θ) To locate the nation points in the flow field: cos ME5: Aeodynamics (Jan 7) and θ ae to be solved simultaneously to get the nation points At = ieon the cylinde suface, becomes zeo L T, ME, BUET Flow ove a otating cylinde Use = in the expession of θ to detemine the angula position of nation point (s) in the flow field: p (, θ) Thus the locations of nation point (s) is (ae): ME5: Aeodynamics (Jan 7) Thus the locations of nation point (s) is (ae):, ), ( L T, ME, BUET

Flow ove a otating cylinde The angula position of nation point depends on the elative magnitude of and, namelyon Clockwise otation x nation points () & () ; ; ; nation point (3) On vetical axis

7 Flow ove a otating cylinde The angula position of nation point depends on the elative magnitude of and, namelyon Clockwise otation x nation points () & () ; ; ; nation point (3) On vetical axis Physical nation point () at > : outside the body and on the vetical axis otation is too high L T, ME, BUET ME5: Aeodynamics (Jan 7) 3 Flow ove a otating cylinde In case of anti-clockwise otation of the cicula cylinde nation points (stationay) nation points ; otation is too high nation point On vetical axis ; ; Physical nation point at > : outside the body and on the vetical axis L T, ME, BUET ME5: Aeodynamics (Jan 7) 7

Applied Aerodynamics

Applied Aerodynamics Applied Aeodynamics Def: Mach Numbe (M), M a atio of flow velocity to the speed of sound Compessibility Effects Def: eynolds Numbe (e), e ρ c µ atio of inetial foces to viscous foces iscous Effects If