Analysis of the velocity field in a large rectangular channel with lateral shockwave
Tóm tắt
In this work the authors describe the main characteristics of the velocity field of hydraulic jumps in a very large channel where lateral shockwaves occur. Experiments were carried out at the Coastal Engineering Laboratory of the Water Engineering and Chemistry Department of the Technical University of Bari (Italy). Extensive flow velocity measurements were investigated in order to have a clearer understanding of both hydraulic jump development and lateral shockwave formation in a very large channel. Eight experiments were performed in a 4m wide rectangular channel; the experiments differed in the inlet Froude number F
0 and the jump type. Seven tests were carried out with undular jumps and one with a roller jump. The flow velocity and the flow free surface measurements were taken using a two-dimensional Acoustic Doppler Velocimeter (ADV) and an ultrasonic profiler, respectively. The experimental results can be summarized as follow: (i) the formation of well developed lateral shockwaves similar to those of oblique jumps were observed; (ii) the comparison of the experimental and theoretical data shows that the classic shockwave theory is sufficiently confirmed in the analyzed range of Reynolds number, taking into account the experimental errors and the difference between the theoretical and experimental assumptions; (iii) the transversal flow velocity profiles in the recirculating zone show a good agreement with the numerical simulations presented in literature in the case of a separated turbulent boundary layer over a flat plate. This conclusion enables us to confirm the hypothesis that the lateral shockwaves in the channel are the result of a boundary layer which, as observed, forms on the channel sidewalls.
Tài liệu tham khảo
Ben Meftah M, De Serio F, Mossa M, Pollio A (2006) Undular jump formation in very large channel. In: Proceedings of IDRA 2006, Italian conference of hydraulics and hydraulic construction, Roma, 10–15 September
Carling PA (1995). Flow-separation berms downstream of a hydraulic jump in a bedrock channel. Geomorphology 11: 245–253
Chanson H and Montes JS (1995). Characteristics of undular hydraulic jumps: experimental apparatus and flow patters. J Hydraul Eng 121(2): 129–144
Chow VT (1959). Open channel hydraulics. McGraw-Hill Book Company, New York
Ippen AT (1951). Mechanics of supercritical flow. Transactions ASCE 116: 268–295
Ippen AT and Harleman DRF (1956). Verification of theory for oblique standing waves. Transactions ASCE 121: 268–297
Leutheusser HJ and Alemu S (1979). Flow separation under hydraulic jump. J Hydraul Res 17(3): 193–206
Montes JS and Chanson H (1998). Characteristics of undular hydraulic jumps: experiments and analysis. J Hydraul Eng 124(2): 192–205
Na Y and Moin P (1998). Direct numerical simulation of a separated turbulent boundary layer. J Fluid Mech 374: 379–405
Ohtsu I, Yasuda Y and Gotoh H (1997). Discussion of Characteristics of undular hydraulic jumps: experimental apparatus and flow patterns by Chanson H and Montes JS (Paper 7859). J Hydraul Eng 123(2): 161–164
Ohtsu I, Yasuda Y and Gotoh H (2001). Hydraulic condition for undular-jump formations. J Hydraul Res 39(2): 203–209
Ohtsu I, Yasuda Y and Gotoh H (2003). Flow conditions of undular hydraulic jumps in horizontal rectangular channels. J Hydraul Eng 129(12): 948–955
Perry AE and Fairlie BD (1975). A study of turbulent boundary-layer separation and reattachments. J Fluid Mech 69: 657–672
Reinauer R and Hager WH (1995). Non-breaking undular hydraulic jumps. J Hydraul Res 33(5): 1–16
Rouse H, Bhoota V and Hsu EY (1951). Design of channel expansion. Transactions ASCE 121: 347–363
Schlichting H (1979). Boundary layer theory, 7th edn. McGraw-Hill, New York
Shiloh K, Shivaprasad BG and Simpson RL (1981). The structure of a separating turbulent layer. Part 3. Transverse velocity measurements. J Fluid Mech 113: 75–90
Simpson RL, Strickland JH and Barr PW (1977). Features of a separating turbulent boundary layer in the vicinity of a separation. J Fluid Mech 79: 553–594
Simpson RL, Chew YT and Shivaprasad BG (1981). The structure of a separating turbulent boundary layer. Part 1. Mean flow and Reynolds stresses. J Fluid Mech 113: 23–51
Simpson RL, Chew YT and Shivaprasad BG (1981). The structure of a separating turbulent boundary layer. Part 2. Higher-order turbulence results. J Fluid Mech 113: 53–73