The influence of hydraulic system parameters, temperature and grape juice concentration on the time required to drain from the intermediate tank
Authors:
Vladimir A. Naumov
Abstract:
The author developed a hydraulic model of the unsteady discharge of grape juice (GJ) from an intermediate tank under the force of gravity. Hydraulic losses in the pipe were calculated using known formulas modified for a power-law fluid. The Cauchy problem was reduced to dimensionless form. The author established three similarity criteria: an analogue of the Strouhal number St, the fluid flow index m, and the ratio b, of the vertical pipeline section length to the initial GJ layer depth in the tank. The solution to the problem was found numerically in MathCad. Under the conditions considered St << 1. Therefore, a quasi-steady-state approach was used: the flow velocity in the pipe was calculated based on the current liquid column height. A numerical study allowed us to establish the influence of similarity criteria and dimensional parameters on the total drain time (TDT). As b increased from 0.2 to 1.4, the dimensionless TDT decreased more than 11-fold. An increase in the flow index leads to a decrease in TDT for small b and an increase for b > 0.654. Among the dimensional parameters, the concentration of GJ and the pipeline diameter d have the greatest influence on TDT. As the concentration increases, the viscosity of the GJ increases significantly, leading to increased hydraulic losses, a decrease in flow rate and an increase in TDT. In turn, increasing d leads to a reduction in hydraulic losses and TDT. TDT can vary widely: from a few seconds to 20 minutes or more. The feasibility of an approximate TDT calculation without solving differential equations was tested. The error in the approximate TDT calculation is negative in all cases. If b ≥ 2, it is small; the approximate TDT calculation can be applied to all studied GJ samples. For small b, the approximate TDT calculation is applicable only to GJ with low concentrations. The results of the study can be used in the design of GJ production lines.
Keywords:
grape juice; concentration; temperature; interoperational transport; hydraulic model; similarity criteria; numerical study
For citation:
Naumov V.A. The influence of hydraulic system parameters, temperature and grape juice concentration on the time required to drain from the intermediate tank. Индустрия питания|Food Industry. 2026. Vol. 11, No. 3. Pp. 105–116. DOI: 10.29141/2500-1922- 2026-11-3-10. EDN: XFHISP.
