Method for estimating optimal efficiency point parameters and performance curve in axial-flow PAT power generation mode

Abstract

Provided is a method for estimating optimal efficiency point parameters in an axial-flow PAT power generation mode, including: I1, calculating an axial velocity of an optimal efficiency point; I2, calculating a flow rate of the optimal efficiency point; I3, calculating a theoretical hydraulic head; I4, calculating a frictional hydraulic head loss and a local hydraulic head loss of each segment; I5, calculating an output power of the optimal efficiency point; I6, calculating a hydraulic head of the optimal efficiency point in a power generation mode; and I7, calculating an optimal efficiency. Further provided is a method for estimating a performance curve in an axial-flow PAT power generation mode based on the above method for estimating an optimal efficiency point parameter, including: II1, calculating a normalized flow-hydraulic head curve; II2, calculating a normalized hydraulic head-output power curve; and II3, calculating a hydraulic head-efficiency curve.

Claims

1. A method for estimating optimal efficiency point parameters in an axial-flow pump as turbine power generation mode, wherein the method comprises: I0, obtaining parameters of an axial-flow pump as turbine unit; the parameters comprising a flow rate of the optimal efficiency point in a pumping mode, a radius of an airfoil position, a rotational velocity of an impeller, a diameter of an impeller, a diameter of a hub, an impeller airfoil setting angle, a guide blade setting angle, a circumferential velocity, and a circumferential component of the absolute velocity; I1, calculating an axial velocity ν.sub.ml,t of an optimal efficiency point in a power generation mode by utilizing the following formula: $v_{m1,t}=\frac{1}{\cot {\beta }_{e,g}+\cot \left(2{\beta }_e-\arctan \left(\frac{Q_{\mathrm{pb}}}{\frac{\pi }{4}\left(D^2-d_h^2\right)}\frac{60}{2\pi \mathrm{nR}}\right)\right)}\frac{2\pi n}{60}R,$ wherein Q.sub.pb is the flow rate of the optimal efficiency point in a pumping mode, R is the radius of an airfoil position, n is the rotational velocity of an impeller, D is the diameter of an impeller, d.sub.h is the diameter of a hub, β.sub.e is the impeller airfoil setting angle, and β.sub.e,g is the guide blade setting angle; I2, calculating a flow rate Q.sub.tb of the optimal efficiency point in the power generation mode based on the axial velocity of the optimal efficiency point and a flow area: $Q_{\mathrm{tb}}=\frac{\pi }{4}\left(D^2-d_h^2\right)v_{m1,t},$ I3, calculating a theoretical hydraulic head H.sub.t,th of an axial-flow pump as turbine: $H_{t,\mathrm{th}}=\frac{u_{1,t}{v}_{u1,t}}{g},$ wherein u.sub.l,t is the circumferential velocity, ν.sub.ul,t is the circumferential component of the absolute velocity, and g is a gravitational acceleration; I4, segmenting a whole flow channel of the axial-flow pump as turbine according to geometrical characteristics, and respectively calculating a frictional hydraulic head loss and a local hydraulic head loss of each segment according to formulas listed in Table 1: TABLE-US-00002 TABLE 1 Formulas for calculating a frictional hydraulic head loss and a local hydraulic head loss of each segment Flow passage component Frictional hydraulic head loss Local hydraulic head loss Elbow pipe $h_{f,e}={\lambda }_{f,e}\frac{{\theta }_e\pi }{360}.Math.\frac{r_e}{r_{0,e}}.Math.\frac{v_e^2}{2g}$ $h_{d,e}=\left[0.131+1.847{\left(\frac{r_{0,e}}{r_e}\right)}^{3.5}\right]\left(\frac{{\theta }_e}{90}\right)\frac{v_e^2}{2g}$ Reductive pipe $h_{f,s}={\lambda }_{f,s}\frac{1}{8\sin \left({\theta }_s/2\right)}.Math.\left[1-{\left(\frac{A_{s2}}{A_{s1}}\right)}^2\right].Math.\frac{v_{s2}^2}{2g}$ $h_{d,s}={\xi }_s\frac{v_{s2}^2}{2g}$ Guide blade zone $h_{f,g}=Z_g{\lambda }_g\frac{l_{b,g}}{D_{\mathrm{hyd},g}}\frac{{\stackrel{\_}{w}}_g^2}{2g}$ $\hspace{1em}\begin{array}{c}{h}_{\mathrm{shock},g}=0.7\frac{w_{i,g}^2}{2g}\\ h_{\mathrm{wake},g}={\left(1-{\xi }_g\right)}^2\frac{{\stackrel{\_}{w}}_g^2}{2g}\end{array}$ Impeller zone $h_f=Z\lambda \frac{l_b}{D_{\mathrm{hyd}}}\frac{{\stackrel{\_}{w}}^2}{2g}$ $\hspace{1em}\begin{array}{c}{h}_{\mathrm{shock}}=0.7\frac{w_i^2}{2g}\\ h_{\mathrm{wake}}={\left(1-\xi \right)}^2\frac{{\stackrel{\_}{w}}^2}{2g}\end{array}$ Diffuser $h_{f,d}={\lambda }_{f,d}\frac{1}{8\sin \left({\theta }_d/2\right)}.Math.\left[{\left(\frac{A_{d2}}{A_{d1}}\right)}^2-1\right].Math.\frac{v_{d2}^2}{2g}$ $h_{d,d}={k\left(\frac{A_{d2}}{A_{d1}}-1\right)}^2.Math.\frac{v_{d2}^2}{2g}$ wherein λ.sub.f,e is a hydraulic frictional resistance coefficient of the elbow pipe, θ.sub.e is a bend angle of the elbow pipe, r.sub.e is a radius of the elbow center line, r.sub.0,c is a radius of the elbow pipe, ν.sub.e is an average flow velocity of the elbow pipe, A.sub.f,s is a hydraulic frictional resistance coefficient, θ.sub.s is a convergence angle, A.sub.s1 and A.sub.s2 are respectively a flow area of an inlet of the reductive pipe and a flow area of an outlet of the reductive pipe, ν.sub.s1 and ν.sub.s2 are respectively an average flow velocity of the inlet of the reductive pipe and an average flow velocity of the outlet of the reductive pipe, ξ.sub.s is a local loss coefficient, h.sub.f is a frictional hydraulic head loss in an impeller flow channel, Z is the number of impeller blades, λ is a hydraulic frictional resistance coefficient, l.sub.b is a length of the impeller flow channel, D.sub.hyd is an equivalent hydraulic diameter of the impeller flow channel, w is an average relative velocity of the impeller flow channel: $\stackrel{\_}{w}=\sqrt{\frac{\left(w_{1^{\prime },p}^2+w_{2^{\prime },p}^2\right)}{2}},$ w.sub.1′,p is a relative velocity of a blade inlet, w.sub.2′,p is a relative velocity of a blade outlet, h.sub.shock is a fluid shock loss of the blade inlet, w.sub.i is a fluid shock velocity of the blade inlet, h.sub.wake is a wake loss of the blade outlet, ξ is an excretion coefficient of the impeller outlet, subscripts g in Z.sub.g, λ.sub.g, I.sub.b,g D.sub.hyd,g and w.sub.g represent the guide blade zone, the meaning of the other symbol is consistent with the symbols of the impeller zone, λ.sub.f,d is a hydraulic frictional resistance coefficient of the diffuser, O.sub.d is a diffusion angle of the diffuser, A.sub.d1 and A.sub.d2 are respectively a flow area of a diffuser inlet and a flow area of a diffuser outlet, ν.sub.d1 and ν.sub.d2 are respectively an average flow velocity of the diffuser inlet and an average flow velocity of the diffuser outlet, and k is a diffuser coefficient; I5, calculating an output power P.sub.tb of the optimal efficiency point in the power generation mode based on the theoretical hydraulic head and the flow rate of the optimal efficiency point in the power generation mode:
P.sub.tb=ρgQ.sub.tbH.sub.t,th, I6, calculating an actual hydraulic head H.sub.tb of the axial-flow pump as turbine at the optimal efficiency point in the power generation mode:
H.sub.tb=H.sub.t,th+Σh.sub.t,loss, wherein Σh.sub.t,loss is a sum of all hydraulic head losses; and I7, calculating an optimal efficiency η.sub.tb based on a ratio of the theoretical hydraulic head to a total hydraulic head: ${\eta }_{\mathrm{tb}}=\frac{H_{t,\mathrm{th}}}{H_{t,\mathrm{th}}+.Math.h_{t,\mathrm{loss}}}.$ I8, performing Pump as turbine unit selection based on the low rate at an optimal efficiency point in the power generation mode, the output power at the optimal efficiency point in the power generation mode, the actual hydraulic head of the axial-flow pump as turbine at the optimal efficiency point in the power generation mode and the optimal efficiency.

2. A method for estimating a performance curve in an axial-flow pump as turbine power generation mode, wherein the performance curve is estimated based on the above described estimation method of an optimal efficiency point parameter in an axial-flow pump as turbine power generation mode according to claim 1, and the estimation method comprises: II1, calculating a normalized flow-hydraulic head curve based on similarity hypothesis of an axial-flow pump as turbine normalized performance curve:
h.sub.t=2.55q.sub.t.sup.2−1.30q.sub.t−0.25, wherein h.sub.t is a normalized hydraulic head, and calculated according to $h_t=\frac{H_t}{H_{\mathrm{tb}}},$  H.sub.t is a hydraulic head, H.sub.tb is an optimal efficiency point hydraulic head, and q.sub.t is a normalized flow rate; and according to $q_t=\frac{Q_t}{Q_{\mathrm{tb}}},$  H.sub.t is a flow rate, and Q.sub.tb is an optimal efficiency point flow rate; I12, calculating a normalized hydraulic head-output power curve:
p.sub.t=1.27h.sub.t−0.27, wherein p.sub.t is a normalized output power, and according to $p_t=\frac{P_t}{P_{\mathrm{tb}}},$  P.sub.t is the output power, and P.sub.tb is an optimal efficiency point output power; and I13, calculating a hydraulic head-efficiency curve: ${\eta }_t=\frac{p_t}{q_t{h}_t}{\eta }_{\mathrm{tb}},$ wherein η.sub.tb is optimal efficiency.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a velocity triangle of an inlet and an outlet of an optimal efficiency point in a pumping mode, u represents a circumferential velocity, w represents a relative velocity, ν represents an absolute velocity, A represents an airfoil setting angle, a subscript 1 represents an inlet while a subscript 2 represents an outlet, and p represents an operating condition of the pumping mode;

(2) FIG. 2 is a velocity triangle of an inlet and an outlet of an optimal efficiency point in a power generation mode, u represents a circumferential velocity, w represents a relative velocity, ν represents an absolute velocity, A represents an airfoil setting angle, a subscript 1 represents an inlet while a subscript 2 represents an outlet, and t represents an operating condition of the pumping mode;

(3) FIG. 3 is a schematic structural diagram of a flow channel of an axial-flow PAT unit;

(4) FIG. 4 is a schematic diagram of a segment of an axial-flow PAT unit, where (A), (B) and (D) are side views, and (C) is an axial view; that is, an impeller zone is divided into several blade channels according to the number of blades (there are three blades in the figure, so there are three blade channels), parameter calculation of its hydraulic diameter is conducted according to a single blade channel, the final friction loss of the single blade channel is multiplied by the number of the blades so as to obtain a total friction loss of the impeller zone, and calculation method of a friction loss in the guide vane zone is similar;

(5) FIG. 5 is a schematic diagram showing decomposition of shock velocity of a blade inlet, that is, a relative velocity w of a fluid is orthogonally decomposed into two components in parallel with a wing chord and in a direction vertical to the wing chord, where a component wi in the direction vertical to the wing chord is the shock velocity;

(6) FIG. 6 is a three-dimensional model of an axial-flow PAT; and

(7) FIG. 7, FIG. 8 and FIG. 9 are comparison diagrams of a performance curve obtained by the estimation method provided by the present invention and original data, where FIG. 7 is a comparison diagram of a hydraulic head-flow curve, FIG. 8 is a comparison diagram of a hydraulic head-output power curve, and FIG. 9 is a comparison diagram of a hydraulic head-power curve.

DETAILED DESCRIPTION

(8) The following describes specific embodiments of a method for estimating an optimal efficiency point parameter and performance curve in an axial-flow PAT power generation mode according to the present invention in detail with reference to the accompanying drawings.

Embodiment 1

(9) As shown in FIG. 6, the rotational velocity of an impeller of an axial-flow PAT n is equal to 1450 r/min, the diameter of the impeller D is equal to 0.30 m, the diameter of the hub d.sub.h is equal to 0.108 m, an airfoil setting angle of the impeller A is equal to 23°, a setting angle of a guide blade β.sub.e.g is equal to 80°, and a radius R of 50% blade-height airfoil is equal to 0.105 m. Energy parameters of an optimal efficiency point in a pumping mode are: the hydraulic head is 3.33 m, the flow rate is 0.326 m.sup.3/s, the shaft power is 12.96 kW and the hydraulic efficiency is 82.09%. Energy parameters of an optimal efficiency point in a power generation mode are: the hydraulic head is 4.47 m, the flow rate is 0.457 m.sup.3/s, the output power is 16.04 kW and the hydraulic efficiency is 80.09%.

(10) Prediction results by using an optimal efficiency point estimation method provided by the present invention are: the flow rate is 0.471 m.sup.3/s (corresponding to the steps I1 and I2), the hydraulic head is 4.29 m (corresponding to the steps I3, I4 and I6), the output power is 15.49 kW (corresponding to the step I5), and the hydraulic efficiency is 78.11% (corresponding to the step I7). Prediction error of each parameter is as follows: the prediction error of the flow rate is 3.06%, the prediction error of the hydraulic head is 4.03%, the prediction error of the hydraulic efficiency is 1.98%, and the prediction error of the output power is 3.43%.

Embodiment 2

(11) The method provided by the present invention is used for predicting a performance curve of a certain axial-flow PAT (corresponding to the steps II1 to II3), and compares the obtained performance curve with the original data, as shown in FIG. 7, and it can be seen that the prediction results of the present invention is consistent with the trend of the original data and is in good agreement. Within the allowable operation range, the average error of the hydraulic head is 5.72%, the average error of the output power is 4.68% and the average error of the hydraulic efficiency is 2.42%.

(12) The above embodiments merely illustrate the technical solution of the present invention. The method for estimating an optimal efficiency point parameter and performance curve in an axial-flow PAT power generation mode associated with the present invention is not only limited to contents described in the above embodiments, but also is subject to a scope defined in the claims. Any modifications, supplementations or equivalent replacements made by a person skilled in the part based on the embodiments shall fall within the protection scope of the present invention.