Design of choking cascade turns

Defence Science Journal, 1983

Modelling aspects of isentropic compressible gas flow using hydraulic analogy are discussed. Subsonic and supersonic flows through a typical nozzle are simulated as free surface incompressible water flow in a n equivalent 2-D model on a water table. The results are first compared for the well known classical analogy in order to estimate experimental errors. Correction factors for pressure and temperature, to account for non-ideal compressible gas flow are presented and the results obtained on the water table are modified and compared with gas dynamic solution. Within the experimental errors, it is shown that the hydraulic analogy can be used as a n effective tool for the study of two dimensional isentropic flows of gases.- .

In the first part of the article, an essential aspect of the limits of applicability of the hydraulic analogy is shown. The assumption is that there is no acceleration along the vertical axis when the fluid flows in an open channel. The effect of vertical acceleration is estimated. The authors suggest that when using the method of towing models in a fixed layer of "shallow water" in experiments in a hydraulic channel, new unique possibilities arise for modelling aerodynamic processes, including those that are difficult or even unreproducible by known means of physical modelling. Analog technical devices are described and examples of visualized pictures of complex shock wave structures are shown.

2007

The hydraulic analogy existing between the propagation of wavelets at the free surface flow of a liquid and the propagation of acoustic waves in a compressible gas is used to study aerodynamics problems with phenomena at flow around solids at supersonic velocities and aeroacoustic phenomena in supersonic divergent jets. In particular, water level fluctuations, which are proportional to pressure fluctuations in the gas, are measured with an optical fiber and special measuring apparatus. Investigations are carried out on a convergent-divergent (de Laval) nozzle. This phenomenon is linked to the existence of shock-cells in supersonic jets, which are formed in the output of the nozzle. These experimental results will be compared with the results from numerical solution and will be obtained from our own program and from the commercial program CFD Fluent.

Journal of Hydraulic Research, 2015

2017

Quite often, researchers model a flow as dynamically incompressible without realizing it. This version of the governing equations has been employed to model exhaust aftertreatment devices since the initial work of Vardi and Biller in 1968 (Vardi & Biller, 1968). The small channels in these devices, along with a relatively low flow rate of exhaust gases coming from the engine, promote laminar flow with a speed of approximately one to ten meters per second. This speed is well below the compressible threshold of around 100 m/s or a Mach number of 0.3. As a result, the chemical species equations can be decoupled from the energy equation promoting a computationally faster and easier to program numerical model. While this assumption is indeed valid in this example, only a few researchers have directly stated that the gas is being modeled as dynamically incompressible (Byrne & Norbury, 1993; Depcik et al., 2010). In fact, when this concept is mentioned, reviews of the main author’s submitt...

Journal of Propulsion and Power, 2006

The characteristics of propellant mixing near the injector have a profound effect on liquid rocket engine performance. Injector element geometry and propellant momentum are the only parameters available to control such mixing. A multiphase flow combustion model utilizing propellant real-fluid properties was developed to predict the mixing and thermal environment created by element configurations. The multiphase model was incorporated into a mature computational fluid dynamics code that can be used to simulate the flowfield near the injector and to analyze the combustion chamber and nozzle wall heating. The validity of the present model and code was investigated by comparing predictions to test data for two liquid oxygen/gaseous hydrogen unielement shear coaxial injector and two cryogenic nitrogen jet injection experiments. These simulations and those of several other investigators were critically compared at the 2nd International Workshop on Rocket Combustion Modeling. Based on these comparisons, it appears that the present model is a good, computationally efficient approximation of liquid rocket injector flows for both subcritical and supercritical spray combustion. Nomenclature a = speed of sound of a multicomponent mixture B ij = coefficients of the thermal property polynomial for a given species Cp = constant-pressure specific heat D = diameter of the center tube in an injector element D p = inverse of the matrix of the coefficients of the convective terms in the finite-difference form of the momentum equations H = real-fluid enthalpy of a given species H 0 = ideal-gas enthalpy of a given species O=F = oxidizer-fuel ratio in mass p = static pressure p 0 = pressure correction p n = pressure at the previous time step p n1 = pressure at the current time step p c = critical pressure of a given species p r = reduced pressure of a given species R = gas constant r = radial distance T = temperature T c = critical temperature of a given species T r = reduced temperature t = time V = velocity at the immediate time step V 0 = velocity correction X = axial distance Z c = compressibility of a given species at the critical point p = partial derivative of density with respect to pressure at constant temperature = specific heat of a multicomponent mixture = density of a given species or mean density of a mixture n = density at the previous time step = density at the immediate time step 0 = density correction c = density of a given species at the critical point r = reduced density of a given species

We are to define a fluid and how it differs between a solid and a gas.

Fluid Dynamics, 1979

2012