Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Write a title that briefly explains what it is about. Between 20 and 90 characters
Typology: Cheat Sheet
1 / 300
This page cannot be seen from the preview
Don't miss anything!
by
Supervised by Assoc. Prof. Richard M. Kelso Dr. Peter V. Lanspeary
School of Mechanical Engineering, Faculty of Engineering, Computer and Mathematical Sciences, The University of Adelaide, South Australia 5005, Australia
A thesis submitted in fulfillment of the requirements for the degree Doctor of Philosophy in Mechanical Engineering on the 20th of December 2010
This page is intentionally blank.
List of Figures
2.15 Example of filtered and unfiltered strain gauge measurement (normal to the foil chord) of a flapping foil............................. 58 2.16 Hydrogen bubble imaging locations....................... 61
3.1 Steady-state lift coefficients vs α obtained a) numerically for a NACA 0025 foil at Re = 8 × 105 (Sheldahl and Klimas, 1981), and b) experimentally for a NACA 0026 foil at Re ≈ 6 , 500, performed at the University of Adelaide. c) is the linear curve fit of data from b)........................ 67 3.2 Steady-state drag coefficients vs α obtained a) numerically for a NACA 0025 foil at Re = 1 × 10 4 (Sheldahl and Klimas, 1981), b) experimentally, for a NACA 0015 foil at Re = 3. 6 × 105 (Sheldahl and Klimas, 1981), c) compu- tationally, for a flat plate at Re ≈ 1 , 800 (Wu and Sun, 2004), and d) experi- mentally for a NACA 0026 foil at Re ≈ 6 , 500, performed at the University of Adelaide. e) is the order-3 polynomial fit of data from a)............ 70 3.3 “Virtual mass” of fluid entrained by the foil................... 73 3.4 Vorticity shed into the wake of an unsteady foil due to the change in bound circulation.................................... 77 3.5 The vorticity shed at the trailing edge of the foil, due to the Kutta condition.. 79 3.6 Definition of wake width, A (^) c........................... 81 3.7 Relationship between αmax and Sth........................ 83 3.8 Predicted foil kinematic parameters as a function of Sth based on the Q-S model (continued on following page).......................... 84 3.8 Predicted foil kinematic parameters as a function of Sth based on the Q-S model (continued).................................... 85 3.9 Wake dynamics predicted by the Q-S model, for sets 1, 4, 7 and 10...... 89 3.10 Wake dynamics predicted by the Q-S model for sets 2, 5, 8 and 11....... 90
4.1 Thrust and side force coefficients, Ct and Cs, for set 1 : h c^0 = 0 .75, θ 0 = 0 o^... 96 4.2 Thrust and side force coefficients, Ct and Cs, for set 2 : h c^0 = 0 .5, θ 0 = 0 o^.... 97 4.3 Thrust and side force coefficients, Ct and Cs, for set 3 : h c^0 = 0 .25, θ 0 = 0 o^... 98 4.4 Productivity, η and Froude efficiency, ηF for set 2 : h c^0 = 0 .5, θ 0 = 0 o^..... 99 4.5 Thrust and side force coefficients, Ct and Cs, for set 4 : h c^0 = 0 .75, θ 0 = 15 o^.. 101
Page viii
List of Figures
4.6 Thrust and side force coefficients, Ct and Cs, for set 5 : h c^0 = 0 .5, θ 0 = 15 o^... 102 4.7 Thrust and side force coefficients, Ct and Cs, for set 6 : h c^0 = 0 .25, θ 0 = 15 o^.. 103 4.8 Productivity, η and Froude efficiency, ηF for set 4 : h c^0 = 0 .75, θ 0 = 15 o^.... 104 4.9 Thrust and side force coefficients, Ct and Cs, for set 7 : h c^0 = 0 .75, θ 0 = 30 o^.. 106 4.10 Thrust and side force coefficients, Ct and Cs, for set 8 : h c^0 = 0 .5, θ 0 = 30 o^... 107 4.11 Thrust and side force coefficients, Ct and Cs, for set 9 : h c^0 = 0 .25, θ 0 = 30 o^.. 108 4.12 Productivity, η and Froude efficiency, ηF for set 7 : h c^0 = 0 .75, θ 0 = 30 o^.... 109 4.13 Thrust and side force coefficients, Ct and Cs, for set 10 : h c^0 = 0 .75, θ 0 = 45 o^.. 110 4.14 Thrust and side force coefficients, Ct and Cs, for set 11 : h c^0 = 0 .5, θ 0 = 45 o^.. 111 4.15 Thrust and side force coefficients, Ct and Cs, for set 12 : h c^0 = 0 .25, θ 0 = 45 o^. 112 4.16 Productivity, η and Froude efficiency, ηF for set 11 : h c^0 = 0 .5, θ 0 = 45 o^.... 113 4.17 Comparison of current experimental results with results from Anderson et al. (1998), for θ 0 = 15 ◦^................................ 114 4.18 Comparison of current experimental results with results from Anderson et al. (1998), for θ 0 = 30 ◦^................................ 114 4.19 Time-averaged thrust coefficient based on an average of the PIV and strain gauge measurements, Ct,ave vs Sth for all flow cases. For a definition of set numbers, please refer to Table 2.1 or Table 4.1................. 116
5.1 Dye flow visualisation for St < St 0 , h c^0 = 0 .5, θ 0 = 45 o, St = 0 .14, St 0 ,exp = 0 .5, Re = 3 , 500.................................... 122 5.2 Dye flow visualisation for St ≈ St 0........................ 123 5.3 Dye flow visualisation for St > St 0........................ 124 5.3 Dye flow visualisation for St > St 0 (continued)................. 125 5.4 Definition of top dead centre (TDC) and bottom dead centre (BDC)...... 126 5.5 Hydrogen bubble image sequence, spanwise view, for group III, set 8 : h c^0 = 0 .5, θ 0 = 30 o, St = 0 .13, St 0 ,exp = 0 .26, Re = 2 , 800................. 127 5.6 Hydrogen bubble image sequence, spanwise view, for group III, set 8 : h c^0 = 0 .5, θ 0 = 30 o, St = 0 .29, St 0 ,exp = 0 .26, Re = 2 , 500 (continued on following page) 129 5.6 Hydrogen bubble image sequence, spanwise view, for group III, set 8 : h c^0 = 0 .5, θ 0 = 30 o, St = 0 .29, St 0 ,exp = 0 .26, Re = 2 , 500 (continued)........... 130
Page ix
List of Figures
5.19 Vorticity contours for group III, set 8 : h c^0 = 0 .5, θ 0 = 30 o, St = 0 .59, St 0 ,exp = 0 .26, Re = 5 , 000................................. 148 5.20 Vorticity contours for group I, set 2 : h c^0 = 0 .5, θ 0 = 0 o, St = 0 .14, St 0 = 0 .2, Re = 8 , 750.................................... 150 5.21 Vorticity contours for group I, set 2 : h c^0 = 0 .5, θ 0 = 0 o, St = 0 .18, St 0 = 0 .2, Re = 7 , 000.................................... 150 5.22 Vorticity contours for group I, set 2 : h c^0 = 0 .5, θ 0 = 0 o, St = 0 .24, St 0 = 0 .2, Re = 5 , 000.................................... 151 5.23 Vorticity contours for group I, set 2 : h c^0 = 0 .5, θ 0 = 0 o, St = 0 .36, , St 0 = 0 .2, Re = 3 , 500.................................... 151 5.24 Vorticity contours for group I, set 2 : h c^0 = 0 .5, θ 0 = 0 o, St = 0 .48, St 0 = 0 .2, Re = 5 , 000.................................... 152 5.25 The interaction of leading edge and trailing edge vorticity. Foil parameters : h c (^0) = 0 .5, θ 0 = 0 o (^) and St = 0 .36, St 0 = 0 .2, Re = 3 , 500 (continued on following page)....................................... 153 5.25 The interaction of leading edge and trailing edge vorticity (continued). Foil parameters : h c^0 = 0 .5, θ 0 = 0 o^ and St = 0 .36, St 0 = 0 .2, Re = 3 , 500...... 154 5.26 Schematic of wake patterns behind the unsteady hydrofoil........... 156 5.27 Proposed vortex skeleton of the 3D unsteady foil wake............. 157 5.28 Observed vortex patterns in the wake of an unsteady hydrofoil. For a brief description of these wake patterns, please refer to Table 5.1........... 162
6.1 Formation of optimal vortical structures..................... 165 6.2 Schematic of possible simulated wake patterns with Nvortices = 2 (continued on following page).................................. 168 6.2 Schematic of possible simulated wake patterns with Nvortices = 2 (continued). 169 6.3 Example of vorticity fields produced in the Q-S-II simulations. Vorticity con- tours have units (^1) s................................. 171 6.4 Results of Q-S-II wake simulations, part 1 (continued on following page)... 173 6.4 Results of Q-S-II wake simulations, part 1 (continued)............. 174 6.5 Results of Q-S-II wake simulations, part 2 (continued on following page)... 175
Page xi
List of Figures
6.5 Results of Q-S-II wake simulations, part 2 (continued)............. 176 6.6 Evaluation of circulation of shed vortical structures behind the foil. Flow is from left to right. Foil kinematic parameters: h c^0 = 0 .25, θ 0 = 15 o, and St = 0. 44 (continued on following page).......................... 177 6.6 Evaluation of circulation of shed vortical structures behind the foil. Flow is from left to right. Foil kinematic parameters: h c^0 = 0 .25, θ 0 = 15 o, and St = 0. 44 (continued).................................... 178 6.7 Wake dynamics for set 2 : h c^0 = 0 .5, θ 0 = 0 o^ (Group I)............. 180 6.8 Wake dynamics for set 5 : h c^0 = 0 .5, θ 0 = 15 o^ (Group II)............ 181 6.9 Wake dynamics for set 8 : h c^0 = 0 .5, θ 0 = 30 o(Group III)............ 182 6.10 Wake dynamics for set 11 : h c^0 = 0 .5, θ 0 = 45 o(Group IV)........... 183 6.11 Summary of wake measurements for all flow cases. Set numbers refer to foil kinematic parameters defined in Table 2.1 (continued on following page)... 185 6.11 Summary of wake measurements for all flow cases. Set numbers refer to foil kinematic parameters defined in Table 2.1 (continued).............. 186 6.12 Relationship between the foil time-averaged thrust coefficient, Ct and the non- dimensional first moment of circulation, M˜Γ. Set numbers refer to foil kinematic parameters defined in Table 2.1......................... 188
7.1 Summary of experimentally measured time-averaged foil thrust coefficients, Ct,ave vs the heave-based Strouhal number, St (^) h. Set numbers refer to foil kine- matic parameters defined in table 7.2...................... 195 7.2 Schematic representation of possible wake profiles behind an unsteady foil.. 198 7.3 Summary of experimentally measured time-averaged foil thrust coefficients, Ct,ave vs the non-dimensional moment of circulation, M˜Γ. Set numbers refer to foil kinematic parameters defined in table 7.2................. 199
B.1 Control volume around a hydrofoil....................... 232 B.2 A hydrofoil in a control volume V (t)....................... 237 B.3 Time averaged velocity fields relative to the foil at various St, for selected test cases where h c^0 = 0 .5 and θ 0 = 30 o. Flow is from left to right. Note that the vectors in the shadow of the foil are disabled.................. 242
Page xii
1.1 Examples of mathematical models applied to carangiform propulsion..... 6 1.2 Summary of observed Strouhal numbers of swimming and flying creatures.. 18
2.1 Summary of foil kinematics, organised into individual sets and groups..... 36
3.1 Summary of values of ktheory obtained from literature and current experiments. 68 3.2 Results for St 0 based on the quasi-steady model................. 87 3.3 Foil wake width A˜ (^) c and moment of circulation M˜Γ when Sth = St (^) h, 0 ,qs..... 91
4.1 Summary of experimentally measured values of St 0............... 117
5.1 Summary of observed wake patterns behind the unsteady foil. For a schematic representation of these wake patterns, refer to Figure 5.28............ 159
7.1 Summary of observed wake patterns behind the unsteady foil. For a schematic representation of these wake patterns, refer to figure 7.2............. 197 7.2 Summary of foil kinematic parameters...................... 200 7.3 Summary of significant experimental observations as a function of St. For defi- nitions of wake pattern abbreviations (LK-H, P+Xs, etc), refer to 7.1)..... 201 7.4 Summary of significant experimental observations as a function of foil kine- matic parameters................................. 202
A.1 Summary of foil kinematic parameters...................... 218 A.2 Experimental results for set 1........................... 219 A.3 Experimental results for set 2........................... 220 A.4 Experimental results for set 3........................... 221
Page xiv
List of Symbols c (^) pro jected Projected chord of the foil
CL Time-averaged lift coefficient of the unsteady foil
Cs Time-averaged side force coefficient of the unsteady foil
Ct Time-averaged thrust coefficient of the unsteady foil. Subscripts “piv” and “sg” refer to the value of Ct measured from particle image velocimetry and strain gauges respectively. Subscript “ave” refers to the average value of Ct,piv and Ct,sg D Diameter of jet orifice d (^) e Effective seeding particle image size d (^) p Diameter of seeding particles ds Diffraction limited image size of seeding particle f Frequency of foil oscillation, in Hz F Total force vector acting on the foil FC(t) Instantaneous chordwise component of the force developed by the unsteady foil D^ f f-number of the camera lens FD(t) Instantaneous drag developed by the unsteady foil FD f (t) Instantaneous drag developed by the unsteady foil due to pressure drag and skin friction FDi(t) Instantaneous drag developed by the unsteady foil due to induced drag FL(t) Instantaneous lift force developed by the unsteady foil FN (t) Instantaneous force developed normal to the unsteady foil chord FN(t) Formation number, defined as FN(t) = UD^ j·t FS(t) Instantaneous side force developed by the unsteady foil FSD(t) Side force component of FD(t)
Page xvii
List of Symbols FSL(t) Side force component of FL(t) FSV (t) Side force due to “virtual” or “added” mass of entrained fluid f (^) shedding Frequency of the “free” vortex shedding behind the undriven foil FT (t) Instantaneous thrust force developed by the unsteady foil FT (t) Time-averaged thrust force developed by the unsteady foil FT D(t) Thrust component of FD(t) FT L(t) Thrust component of FL(t) h(t) Unsteady foil instantaneous heave hcen,n Location of centroid (along y axis) of negative vorticity. Subscripts “shed,bound” and “kutta” refer to the centroids of vorticity shed due to the change in bound circulation around the foil, and the no-slip boundary condition at the foil trailing edge, respectively hcen,p Location of centroid (along y axis) of positive vorticity. Subscripts “shed,bound” and “kutta” refer to the centroids of vorticity shed due to the change in bound circulation around the foil, and the no-slip boundary condition at the foil trailing edge, respectively h 0 Unsteady foil heave amplitude ˆi Unit vector in the x-direction
I Unit tensor
jˆ Unit vector in the y-direction k Reduced frequency, k = πU^ f c∞ ≡ πSt (^) c ˆk Unit vector in the z-direction k (^) i Correction factor for induced drag ktheory Constant relating CL to sin α Kscheme Random noise transmission coefficient of the vorticity estimation scheme kΓ,sim Constant relating Ct to M˜Γ, as determined using simulations
Page xviii
