Experiments and Simulations on the Factors Governing Fast Transient Responses in Cavity Discharge

Abstract

Experimental investigations and datasets in the open literature remain scarce for the fast transient response of air systems induced by sudden internal structural failures, hindering rigorous experimental validation of the governing trends associated with multiple influencing factors. To address this gap, we establish a fast transient air-system test platform and develop a step boundary simulation device based on mechanical energy storage, enabling rapid and repeatable boundary transients. The experiments demonstrate that the minimum boundary-change time is less than 6 ms, satisfying the simulation requirement for boundary transients associated with typical sudden structural failures (≤10 ms). Guided by a dimensionless analysis, we conduct fast transient cavity-venting experiments under varying outlet areas, cavity geometric parameters, and initial pressure ratios, thereby obtaining the transient response data of the cavity pressure. In parallel, we simulate the test process using a three-dimensional numerical approach validated against the experiments; by combining experimental and numerical results, we systematically analyze the effects of key factors on the fast transient response during cavity venting and elucidate the underlying mechanisms. This paper provides experimentally validated data and a reliable experimental methodology for studying fast transient response processes in air systems, and it supports the passive safety design of aero-engines.

1. Introduction

The aero-engine Secondary Air System (SAS) is a critical subsystem that ensures safe engine operation [1]. Operating over long durations in an extreme environment characterized by the coupled effects of high temperature, high pressure, and high rotational speed, its internal structures face a substantial risk of sudden failure. Such failures typically occur on a millisecond timescale and are accompanied by abrupt changes in flow-path geometry and boundary conditions, thereby inducing a fast transient response in the SAS. During these events, sudden structural failures can lead to a partial loss of air-system functions, resulting in rapid variations in pressure and mass flow and disrupting normal engine operation; in severe cases, hazardous consequences may arise. Taking shaft fracture as a representative sudden failure scenario, Ref. [2] reports that a turbine shaft may fracture within approximately 10 ms; once the load is lost, the turbine can rapidly accelerate to its burst speed, generating high-energy fragments and posing a risk of casing penetration. In accordance with airworthiness requirements such as FAR-33 [3], passive safety design must be implemented to mitigate the accident risk induced by such failures. Therefore, investigating the mechanisms and predictive methods of the fast transient SAS response triggered by sudden structural failures is of significant engineering importance for passive safety design.

As an internal-flow system, the SAS features boundary conditions that are intrinsically coupled to the mainstream flow path and the overall system state; studies of fast transient behavior therefore typically must account for multi-boundary coupling at the engine level [4]. Owing to the complex flow-path topology, millisecond-scale rapid transients, and strong coupling among multiple engine boundaries, full-engine destructive testing is prohibitively expensive and rarely provides access to internal flow-field details under extreme conditions [5]. Although three-dimensional CFD can deliver high fidelity, it demands substantial computational resources and remains impractical for long-duration, full-engine-scale dynamic simulations [6]. Consequently, engineering analyses commonly rely on reduced-order, system-level approaches: the SAS is represented using a network method and is solved in a coupled manner with a mainstream-path model based on the component method, enabling the rapid simulation of SAS transient processes in a full-engine environment [7]. Within this network-modeling framework, the element partitioning strategy and the fidelity of individual element models directly govern the accuracy of fast transient SAS-response predictions. Existing studies have proposed various partitioning schemes, for example representing the system as cavities and ducts [8], or further refining the elements to include holes, slots, and labyrinth seals [9,10].

In the above partitioning strategies, cavities and ducts are typically the core elements that govern system transient characteristics: cavities represent volumetric effects, whereas ducts capture inertial and wave-propagation effects. Compared with duct elements, existing reduced-order cavity models often rely on stronger simplifying assumptions, including neglecting the influence of the cavity outlet area, ignoring momentum effects within the cavity, and assuming a spatially uniform distribution of cavity properties [8,9,10]. Considering the connections among these assumptions, they can be summarized as follows: when the cavity outlet area is much smaller than the cavity surface area, i.e., when ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\ll 1$, the inflowing or outflowing mass flow exerts only a minor influence on the gas properties within the cavity; consequently, the cavity state at each instant can be treated as uniform, and the cavity can be approximated as a lumped-parameter control volume whose pressure response is governed primarily by mass and energy conservation. To validate such models, studies in the open literature often cite Dutton’s classical cavity charging/discharging experiments as benchmark data [11]; however, in those experiments, the order of magnitude of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ is approximately 0.001, which fully satisfies the underlying modeling assumptions.

In practical SAS configurations, however, the outlet geometry of many critical cavities, including compressor and turbine disk cavities, cannot be neglected. The open literature includes studies that target cavities with such non-negligible geometries and use three-dimensional simulations to model the fast transient venting response under abrupt boundary changes, with particular attention to the mechanisms associated with multiple factors, including the cavity inlet and outlet areas and cavity shape [12]. Nevertheless, corresponding experimental datasets remain largely unavailable, leaving the reported trends insufficiently supported by direct measurements.

For fast transient SAS responses triggered by sudden structural failures, the central experimental challenge is to reproduce, in a controlled manner, the boundary-geometry change induced by the failure. According to the data reported in Ref. [2], this boundary change is completed within 10 ms. A survey of the state of the art indicates that fast transient experiments commonly rely on two approaches to emulate step boundary-geometry changes: diaphragm-rupture methods and fast-valve methods. In the diaphragm-rupture method, a membrane separates the high- and low-pressure regions prior to the test, and a rapid rupture provides the required abrupt change in boundary conditions [13]. Although the rupture can be sufficiently fast, the process is inherently difficult to control; residual fragments may interfere with the flow, thereby compromising repeatability. Fast valves, in contrast, create boundary changes via the rapid opening and closing of a valve [14]. While this approach offers improved repeatability, the actuation speed is limited by practical constraints, and millisecond-scale boundary-geometry changes remain difficult to achieve in large-diameter flow paths.

To overcome these limitations, we design and construct a fast transient air-system experimental platform to reproduce cavity venting under abrupt boundary changes. The platform incorporates a repeatable step boundary simulation device to generate rapid boundary opening. Guided by key parameters identified through a dimensionless analysis, we perform fast transient cavity-venting experiments across a range of cavity outlet areas, cavity shapes, and initial pressure ratios. The experiments provide transient measurements of cavity pressure under abrupt boundary changes, revealing how the outlet area, cavity geometry, and initial pressure ratio govern the response. In addition, we simulate the corresponding test conditions using a three-dimensional numerical approach validated against the measurements, providing complementary verification of the influencing factors and their underlying mechanisms. Collectively, this paper establishes a reliable experimental methodology and delivers experimental data to support further studies of fast transient air-system responses.

2. Theoretical Analysis for the Experimental Platform

In aero-engine air systems, cavities with relatively large outlet areas are mainly compressor and turbine disk cavities, as schematically shown in Figure 1. These cavities are axisymmetric; therefore, this paper describes the in-cavity flow using a cylindrical coordinate system $\left(r,\theta ,z\right)$. $\rho$, $p$, and $T$ denote the density, pressure, and temperature, respectively; $t$ denotes the time; $\mu$, $C_P$, and $\lambda$ denote the dynamic viscosity, specific heat at constant pressure, and thermal conductivity; and $v_r$, $v_{\theta }$, and $v_z$ are the velocity components in the $r$, $\theta$, and $z$ directions.

To establish similarity criteria for the fast-transient response under step-change boundary conditions, the governing equations are nondimensionalized. The characteristic quantities are chosen as follows:

(1)

Characteristic lengths: cavity length $L$, cavity diameter $D$, outlet diameter $d$;

(2)

Characteristic velocity: the maximum flow velocity $v_t$;

(3)

Characteristic time: $t_t=\raisebox{1ex}{$L$}\!\left/ \!\raisebox{-1ex}{$v_t$}\right.$;

(4)

Characteristic pressure and temperature: initial pressure $p_0$ and initial temperature $T_0$;

(5)

Other flow-property parameters: initial-state ${\rho }_0$, $c_{p,0}$, and ${\lambda }_0$.

The dimensionless forms of the variables are defined in Equation (1). The key dimensionless groups include the following:

$$\begin{array}{l}\overline{r}={\displaystyle \frac{r}{D}}, \overline{z}={\displaystyle \frac{z}{L}}, \overline{v_r}={\displaystyle \frac{v_r}{v_t}}, \overline{v_{\theta }}={\displaystyle \frac{v_{\theta }}{v_t}}, \overline{v_z}={\displaystyle \frac{v_z}{v_t}}, \overline{\rho }={\displaystyle \frac{\rho }{{\rho }_0}}, \\ \overline{c_p}={\displaystyle \frac{c_p}{c_{p,0}}}, \overline{\lambda }={\displaystyle \frac{\lambda }{{\lambda }_0}}, \overline{p}={\displaystyle \frac{p}{p_0}}, \overline{T}={\displaystyle \frac{T}{T_0}}, \overline{t}={\displaystyle \frac{t}{t_t}}\end{array}$$

(1)

Reynolds number: $Re={\rho }_0{v}_{t}d/\mu$

Mach number: $Ma=v_t/\sqrt{\kappa RT}$

Prandtl number: $Pr=c_{p,0}\mu /{\lambda }_0$

Geometric parameters: ${\displaystyle \frac{d}{D}},{\displaystyle \frac{L}{D}}$

The nondimensionalized governing equations can be written as shown below:

• Continuity equation:

$${\displaystyle \frac{\partial \overline{\rho }}{\partial \overline{t}}}+{\displaystyle \frac{L}{D}}{\displaystyle \frac{\partial \left(\overline{r}\overline{\rho }\overline{v_r}\right)}{\overline{r}\partial \overline{r}}}+{\displaystyle \frac{L}{D}}{\displaystyle \frac{\partial \left(\overline{\rho }\overline{v_{\theta }}\right)}{\overline{r}\partial \overline{\theta }}}+{\displaystyle \frac{\partial \left(\overline{\rho }\overline{v_z}\right)}{\partial \overline{z}}}=0;$$

(2)

2.

Momentum equations:

$$\begin{array}{l}\frac{\partial \overline{\rho }\overline{v_r}}{\partial \overline{t}}+\frac{L}{D}\frac{\partial \left(\overline{r}\overline{\rho }{\overline{v_r}}^2\right)}{\overline{r}\partial \overline{r}}+\frac{L}{D}\frac{\partial \left(\overline{\rho }\overline{v_{\theta }}\overline{v_r}\right)}{\overline{r}\partial \overline{\theta }}+\frac{\partial \left(\overline{\rho }\overline{v_z}\overline{v_r}\right)}{\partial \overline{z}}=-\frac{1}{\kappa }\frac{L}{D}\frac{1}{M{a}^2}\frac{\partial \overline{p}}{\partial \overline{r}}\\ +\frac{2}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left(\overline{\mu }\overline{r}\frac{\partial \overline{v_r}}{\partial \overline{r}}\right)+\frac{1}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left(\overline{\mu }\frac{\partial \overline{v_r}}{\overline{r}\partial \theta }+\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\partial \overline{r}}-\overline{\mu }\frac{\overline{v_{\theta }}}{\overline{r}}\right)\\ +\frac{1}{Re}\frac{d}{D}\frac{\partial }{\partial \overline{z}}\left(\frac{L}{D}\overline{\mu }\frac{\partial \overline{v_r}}{\partial \overline{z}}+\overline{\mu }\frac{\partial \overline{v_z}}{\partial \overline{r}}\right)-\frac{2}{Re}\frac{d}{D}\frac{L}{D}\left(\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\overline{r}\partial \theta }+\overline{\mu }\frac{\overline{v_r}}{\overline{r}}\right)\\ +\frac{L}{D}\overline{{\rho }_0}\frac{{\overline{v_{\theta }}}^2}{\overline{r}}-\frac{2}{3}\frac{1}{Re}\frac{d}{D}\frac{\partial }{\partial \overline{r}}\left(\frac{L}{D}\overline{\mu }\frac{\partial \overline{r}\overline{v_r}}{\overline{r}\partial \overline{r}}+\frac{L}{D}\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\overline{r}\partial \theta }+\overline{\mu }\frac{\partial \overline{v_z}}{\partial \overline{z}}\right)\end{array}$$

(3)

$$\begin{array}{l}\frac{\partial \overline{\rho }\overline{v_{\theta }}}{\partial \overline{t}}+\frac{L}{D}\frac{\partial \left(\overline{r}\overline{\rho }\overline{v_r}\overline{v_{\theta }}\right)}{\overline{r}\partial \overline{r}}+\frac{L}{D}\frac{\partial \left(\overline{\rho }{\overline{v_{\theta }}}^2\right)}{\overline{r}\partial \overline{\theta }}+\frac{\partial \left(\overline{\rho }\overline{v_z}\overline{v_{\theta }}\right)}{\partial \overline{z}}=-\frac{1}{\kappa }\frac{L}{D}\frac{1}{M{a}^2}\frac{\partial \overline{p}}{\overline{r}\partial \theta }\\ +\frac{1}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left[\overline{\mu }\overline{r}\left(\frac{\partial \overline{v_{\theta }}}{\partial \overline{r}}+\frac{\partial \overline{v_r}}{\overline{r}\partial \theta }-\frac{\overline{v_{\theta }}}{\overline{r}}\right)\right]+\frac{2}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left(\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\overline{r}\partial \theta }+\overline{\mu }\frac{\overline{v_r}}{\overline{r}}\right)\\ +\frac{1}{Re}\frac{d}{D}\frac{\partial }{\partial \overline{z}}\left(\frac{L}{D}\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\partial \overline{z}}+\overline{\mu }\frac{\partial \overline{v_z}}{\overline{r}\partial \theta }\right)-\frac{1}{Re}\frac{d}{D}\frac{L}{D}\left(\overline{\mu }\frac{\partial \overline{v_r}}{\overline{r}\partial \theta }+\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\partial \overline{r}}-\overline{\mu }\frac{\overline{v_{\theta }}}{\overline{r}}\right)\\ +\frac{L}{D}\overline{{\rho }_0}\frac{\overline{v_{\theta }}\overline{v_r}}{\overline{r}}-\frac{2}{3}\frac{1}{Re}\frac{d}{D}\frac{\partial }{\overline{r}\partial \theta }\left(\frac{L}{D}\overline{\mu }\frac{\partial \overline{r}\overline{v_r}}{\overline{r}\partial \overline{r}}+\frac{L}{D}\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\overline{r}\partial \theta }+\overline{\mu }\frac{\partial \overline{v_z}}{\partial \overline{z}}\right)\end{array}$$

(4)

$$\begin{array}{l}\frac{\partial \overline{\rho }\overline{v_z}}{\partial \overline{t}}+\frac{L}{D}\frac{\partial \left(\overline{r}\overline{\rho }\overline{v_r}\overline{v_z}\right)}{\overline{r}\partial \overline{r}}+\frac{L}{D}\frac{\partial \left(\overline{\rho }\overline{v_{\theta }}\overline{v_z}\right)}{\overline{r}\partial \overline{\theta }}+\frac{\partial \left(\overline{\rho }{\overline{v_z}}^2\right)}{\partial \overline{z}}=-\frac{1}{\kappa }\frac{L}{D}\frac{1}{M{a}^2}\frac{\partial \overline{p}}{\partial \overline{z}}\\ +\frac{1}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left[\overline{\mu }\overline{r}\left(\frac{\partial \overline{v_r}}{\partial \overline{z}}+\frac{\partial \overline{v_z}}{\partial \overline{r}}\right)\right]+\frac{2}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left(\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\partial \overline{z}}+\overline{\mu }\frac{\partial \overline{v_z}}{\overline{r}\partial \theta }\right)\\ +\frac{2}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\partial \overline{z}}\left(\overline{\mu }\frac{\partial \overline{v_z}}{\partial \overline{z}}\right)-\frac{2}{3}\frac{1}{Re}\frac{d}{D}\frac{\partial }{\partial \overline{z}}\left(\frac{L}{D}\overline{\mu }\frac{\partial \overline{r}\overline{v_r}}{\overline{r}\partial \overline{r}}+\frac{L}{D}\overline{\mu }\frac{\partial \overline{v_{\theta }}}{\overline{r}\partial \theta }+\overline{\mu }\frac{\partial \overline{v_z}}{\partial \overline{z}}\right)\end{array};$$

(5)

3.

Energy equation:

$$\begin{array}{l}\frac{\partial \overline{\rho }\overline{C_P}\overline{T}}{\partial \overline{t}}+\frac{L}{D}\frac{\partial \left(\overline{\rho }\overline{r}\overline{v_r}\overline{C_P}\overline{T}\right)}{\overline{r}\partial \overline{r}}+\frac{L}{D}\frac{\partial \left(\overline{\rho }\overline{v_{\theta }}\overline{C_P}\overline{T}\right)}{\overline{r}\partial \overline{\theta }}+\frac{\partial \left(\overline{\rho }\overline{v_z}\overline{C_P}\overline{T}\right)}{\partial \overline{z}}=\\ \frac{1}{Re}\frac{1}{Pr}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left(\overline{r}\overline{\lambda }\frac{\partial \overline{T}}{\partial \overline{r}}\right)+\frac{1}{Re}\frac{1}{Pr}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \theta }\left(\overline{\lambda }\frac{\partial \overline{T}}{\overline{r}\partial \theta }\right)\\ +\frac{1}{Re}\frac{1}{Pr}\frac{L}{D}\frac{\partial }{\partial \overline{z}}\left(\overline{\lambda }\frac{\partial \overline{T}}{\partial \overline{z}}\right)+\frac{1}{\kappa }\frac{L}{D}\frac{1}{M{a}^2}\frac{\partial \overline{P}}{\partial \overline{z}}\\ +\frac{1}{Re}\frac{d}{D}\frac{L}{D}\frac{\partial }{\overline{r}\partial \overline{r}}\left[\overline{\mu }\overline{r}\left(\frac{\partial \overline{v_r}}{\partial \overline{z}}+\frac{\partial \overline{v_z}}{\partial \overline{r}}\right)\right]+\kappa \frac{R}{C_{Pt}}M{a}^2\frac{1}{Re}\frac{L}{D}\overline{\varphi }+\frac{R}{C_{Pt}}\frac{D\overline{p}}{D\overline{t};}\end{array}$$

(6)

4.

Ideal-gas equation of state:

$$\overline{p}={\displaystyle \frac{1}{\kappa }}{\displaystyle \frac{1}{M{a}^2}}\overline{\rho }\overline{T}.$$

(7)

According to standard gas-dynamics relations, the mass-flow rate can be expressed using the flow function $q\left(\lambda \right)$ and the aerodynamic function $\pi \left(\lambda \right)$, as shown in Equations (8)–(10), where $\lambda$ is the dimensionless velocity coefficient. Accordingly, the Reynolds number at the outlet can be rewritten as shown in Equation (11).

$$q\left(\lambda \right)={\left({\displaystyle \frac{\kappa +1}{2}}\right)}^{{\displaystyle \frac{1}{\kappa -1}}}\lambda {\left(1-{\displaystyle \frac{\kappa -1}{\kappa +1}}{\lambda }^2\right)}^{{\displaystyle \frac{1}{\kappa -1}}}$$

(8)

$$\pi \left(\lambda \right)={\displaystyle \frac{p}{p^{\ast }}}={\left(1-{\displaystyle \frac{\kappa -1}{\kappa +1}}{\lambda }^2\right)}^{{\displaystyle \frac{\kappa }{\kappa -1}}}$$

(9)

$$\stackrel{·}{m}=K{\displaystyle \frac{p^{\ast }}{\sqrt{T^{\ast }}}}{A}_{t}q\left(\lambda \right)$$

(10)

$$Re={\displaystyle \frac{d}{\mu }}K{\left({\displaystyle \frac{\kappa +1}{2}}\right)}^{{\displaystyle \frac{1}{\kappa -1}}}{\left({\displaystyle \frac{\kappa +1}{\kappa -1}}\right)}^{{\displaystyle \frac{1}{2}}}{\displaystyle \frac{p^{\ast }}{\sqrt{T^{\ast }}}}\left[1-{\left({\displaystyle \frac{p}{p^{\ast }}}\right)}^{{\displaystyle \frac{\kappa -1}{\kappa }}}\right]{\left({\displaystyle \frac{p}{p^{\ast }}}\right)}^{{\displaystyle \frac{1}{\kappa }}}$$

(11)

The velocity can be expressed in terms of $\lambda$, as shown in Equation (12); by substituting $\pi \left(\lambda \right)$, one obtains Equation (13). Using the relations between total and static quantities as expressed in Equation (14), the Mach number can be rewritten as shown in Equation (15).

$$v=v_{cr}\lambda$$

(12)

$$v=\sqrt{{\displaystyle \frac{2\kappa R{T}^{\ast }}{\kappa +1}}}\sqrt{1-{\left({\displaystyle \frac{p}{p^{\ast }}}\right)}^{{\displaystyle \frac{\kappa -1}{\kappa }}}}$$

(13)

$${\displaystyle \frac{T}{T^{\ast }}}={\left({\displaystyle \frac{p}{p^{\ast }}}\right)}^{{\displaystyle \frac{\kappa -1}{\kappa }}}$$

(14)

$$Ma={\displaystyle \frac{v}{\sqrt{\kappa RT}}}=\sqrt{{\displaystyle \frac{2}{\kappa -1}}}\sqrt{{\left({\displaystyle \frac{p}{p^{\ast }}}\right)}^{-{\displaystyle \frac{\kappa -1}{\kappa }}}-1}$$

(15)

For the tube exit section, the initial duct pressure $p_0$ is treated as the total pressure $p^{\ast }$, and the ambient pressure $p_t$ is treated as the static pressure $p$. Thus, $Ma$ is governed by the boundary dimensionless pressure ratio $p_0/p_t$, while $Re$ is governed by $p_0/p_t$ and $p_t/\sqrt{T_t}$.

To complete the similarity framework, the boundary and initial conditions are also nondimensionalized. In the present process, the boundary change is a step change, and heat transfer is neglected. Therefore, a step-change pressure boundary condition is applied, and no thermal boundary condition is prescribed. The primary initial conditions and the corresponding dimensionless forms are given in Equation (16), and the step-change pressure boundary condition is given in Equation (17).

$$\left\{\begin{array}{l}t=0\\ \overline{t}=0\end{array}\right.:\left\{\begin{array}{l}u\left(r,\theta ,z,t\right)=0\\ \overline{u}\left(r,\theta ,z,t\right)=0\end{array}\right.,\left\{\begin{array}{l}p\left(r,\theta ,z,t\right)=p_0\\ \overline{p}\left(r,\theta ,z,t\right)=p_0/p_t\end{array}\right.,\left\{\begin{array}{l}T\left(r,\theta ,z,t\right)=T_0\\ \overline{T}\left(r,\theta ,z,t\right)=T_0/T_t\end{array}\right.$$

(16)

$$\left\{\begin{array}{l}\left\{\begin{array}{l}p\left(t\right)=p_0,t=0^{-}\\ p\left(t\right)=p_t,t=0^{+}\end{array}\right.\\ \left\{\begin{array}{l}\overline{p}\left(t\right)=p_0/p_t,t=0^{-}\\ \overline{p}\left(t\right)=1,t=0^{+}\end{array}\right.\end{array}\right.$$

(17)

The dimensionalization introduces the pressure ratio $p_0/p_t$ and the temperature ratio $T_0/T_t$. The pressure ratio is already reflected in $Ma$. In this paper, the initial in-cavity temperature equals the ambient temperature, so $T_0/T_t$ is a constant. The derivation ensures kinematic and dynamic similarity; combined with the geometric ratios $L/D$ and $d/D$, geometric similarity is also satisfied. Because heat transfer is neglected in this experimental campaign, the influence of $Pr$ can be ignored.

From the analysis above, the dependent variables $\phi$ of the dimensionless governing equations for the fast-transient response under step-change boundary conditions depend on dimensionless independent variables $\overline{t}$, $\overline{r}$, $\overline{\theta }$, $\overline{z}$ and the dimensionless groups $p_0/p_t$, $L/D$, and $d/D$, as expressed in Equation (18). Under the similarity of the initial pressure ratio, cavities with different geometries become comparable.

$$\phi =f\left(\overline{t},\overline{r},\overline{\theta },\overline{z},{\displaystyle \frac{p_0}{p_t}},{\displaystyle \frac{L}{D}},{\displaystyle \frac{d}{D}}\right)$$

(18)

${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ has a fixed functional relationship with $L/D$ and $d/D$ for the present cavity geometry, as expressed in Equation (19). Therefore, when $L/D$ is fixed, ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ is an independent dimensionless group equivalent to $d/D$, enabling unified characterization and a comparative analysis of different test specimens.

$${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}={\left({\displaystyle \frac{\pi }{4}}\right)}^{{\displaystyle \frac{1}{3}}}\cdot {\displaystyle \frac{{\left(d/D\right)}^2}{{\left(l/D\right)}^{2/3}}}$$

(19)

Based on the dimensionless analysis, experiments are designed to investigate how ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$, $L/D$, and $p_0/p_t$ affect the fast-transient discharge process, extract governing trends, and interpret the underlying mechanisms.

3. Design and Validation of the Fast-Transient Air-System Experimental Platform

3.1. Overall Platform Design

Based on the theoretical analysis presented above, the experimental platform must enable fast transient response tests over a range of cavity geometrical parameters and initial pressure ratios, and it must also be capable of operating under supercritical pressure-ratio conditions. Moreover, Ref. [2] indicates that sudden internal structural failures in the SAS develop within 10 ms. Accordingly, the key specifications of the sensors must be sufficient to resolve both the boundary change and the ensuing fast transient response of the cavity. On this basis, the primary system-level design requirements of the test platform are defined, as summarized in

Table 1. Main design indicators for the experimental platform.

Design Indicators	Scope
Specimen	Cavity
Maximum Initial Pressure (Gauge Pressure)/kPa	150
Boundary Change Time/ms	≤10
Pressure Sensor Response/kHz	≥50
Detection Parameters: Flow Path Pressure, Flow Path Temperature

.

Guided by the research objectives and these design requirements, we develop a preliminary fast transient air-system experimental platform. Figure 2 presents the system schematic and a photograph of the test rig. The platform comprises five main subsystems: a gas-supply system, a test section, a step boundary simulation device, auxiliary tooling for boundary setting, and a data-acquisition system. The gas-supply system is used to establish the prescribed initial conditions; the test section enables the rapid reconfiguration of test–article combinations with different geometrical parameters; the step boundary simulation device provides repeatable and rapid boundary conditions that meet the fast transient test requirements; the auxiliary boundary-setting tooling supports safe reset and re-arming of the device; and the data-acquisition system records and outputs the measurements required for the study.

Following a preliminary survey, we find that commercially available standard equipments can meet the requirements of both the gas-supply system and the data-acquisition system. Therefore, this paper focuses on the design and verification of the test articles, the step boundary simulation device, and the auxiliary tooling for boundary setting in order to confirm that all key specifications satisfy the overall performance targets of the experimental platform.

3.2. Step Boundary Simulation Device and Auxiliary Fixture

The primary function of the step boundary simulation device is to rapidly reconfigure the flow-path boundary, thereby providing an approximately step-like boundary condition for the experiments. A survey of the open literature indicates that no existing experimental methodology or off-the-shelf hardware can satisfy the requirements of this paper. We therefore design a dedicated step boundary simulation device, as shown in Figure 3. The device is based on mechanical energy storage: the elastic potential energy of a spring is converted into the kinetic energy of a plug that seals the flow passage, accelerating the plug to eject and thus producing an abrupt change in the flow-path boundary. The working process is shown in Figure 4. Because a relatively large initial spring force is required, auxiliary tooling for boundary setting is developed to improve operational safety and to reduce reset effort. Specifically, a hydraulic jack is used to compress the energy-storage spring, and a sensor records the initial spring force in each test, providing a quantitative basis for test repeatability and consistency analyses.

To ensure that the expelled plug does not continue to obstruct the outlet flow, its ejection stroke must exceed a minimum threshold. Fitzgerald [15] showed that the influence of the plug position on the outlet flow is markedly reduced when the ejection distance $L_e$ satisfies $L_e/D>1.5$ where $D$ is the flow-path diameter. In the present rig, the maximum outlet diameter of the test article is 50 mm; therefore, the required plug travel is greater than 75 mm. To prevent impact-induced vibration from contaminating the measurements, a cushioning pad is installed between the plug and the base. Accounting for the pad thickness, the total ejection travel is approximately 80 mm, which exceeds the 75 mm criterion; consequently, the post-ejection effect of the plug on the flow path can be neglected.

To further reduce the ejection time, we decrease the mass of the moving assembly and increase the initial spring force while maintaining structural integrity. A titanium alloy is therefore selected for the plug to minimize weight. Measurements indicate that the total mass of the moving assembly—including the plug, the retaining nut, and the washer used to secure the spring—is approximately 550 g. The device employs a custom spring with a maximum force rating of 10 kN. The relationship between spring deflection and spring force is described by Equation (20) with a maximum deflection of 60 mm. Because the contact area between the plug and its sleeve is small and lubricated with oil, the friction force is negligible compared with the spring force. Under these assumptions, the plug motion is analyzed for different initial spring forces to evaluate the time required to reach a 75 mm stroke; the displacement–time relationship is shown in Figure 5. The results indicate that under idealized conditions, the time to reach 75 mm falls below 10 ms when the initial spring force exceeds 3 kN.

$$F_s=225.208x$$

(20)

$F_s$ denotes the spring force, and $x$ denotes the spring deflection.

3.3. Feasibility Verification of the Step-Change Boundary Emulation Device

As a critical component of the experimental platform, the step boundary simulation device must be validated against its design specifications, including the plug travel distance and the plug speed. The travel distance is fixed by the design and assembly, whereas the speed is verified experimentally using high-speed imaging. Here, a 50 kFPS high-speed camera is employed to capture the plug motion. Representative image sequences obtained under different initial spring forces are shown in

Table 2. Plug movement time under different initial force conditions.

Parameter	Value
Initial force/kN	600	700	800	900	1000
Movement time/ms	9.32	6	5.8	5.76	5.8

and Figure 6. The results indicate that when the initial spring force reaches 6 kN, the time required for the plug to travel 75 mm is less than 10 ms. Further increasing the initial force beyond 7 kN yields only marginal reductions in the boundary-change duration, suggesting an upper limit of the device capability of approximately 6 ms. Although some discrepancy exists between the experimental measurements and the theoretical predictions, the design targets are met, confirming the feasibility of the proposed step boundary simulation device.

3.4. Uncertainty Analysis

The experimental uncertainties can be grouped as follows.

• Machining error

Machining tolerances may be present. The specified machining tolerances for the specimen length and diameter are ±0.05 mm, leading to an estimated cavity-volume uncertainty of approximately 0.25%.

2.

Assembly error

Assembly error may arise from tolerance stack-up at mating surfaces. Based on the machining requirements, the axial fit tolerance is ±0.05 mm, yielding a maximum cavity-volume uncertainty of approximately 0.16%. The radial fit is a clearance fit with a tolerance of ±0.1 mm, contributing a cavity-volume uncertainty of approximately 0.016‰, which is negligible. The dominant assembly-related volume uncertainty is therefore from the axial fit; because each cavity has at least two mating interfaces, the overall assembly uncertainty is about 0.32%. Combined with machining uncertainty, the maximum cavity-volume uncertainty for a single cavity is 0.57%. Under the ideal-gas relation, this volume uncertainty propagates to pressure uncertainty at a comparable level; hence, the induced pressure uncertainty is also approximately 0.57%.

3.

Instrumentation error

The instrumentation error primarily reflects sensor accuracy. The main measurement instruments are pressure sensors and thermocouples. Thermocouples are used mainly to confirm the initial-condition stability and do not affect the reported results. Pressure sensors contribute directly to measurement uncertainty. Calibration using a standard pressure calibrator yields the results shown in Figure 7, where the maximum relative deviation between the standard pressure and the sensor reading is below 0.1%. Overall, the total experimental uncertainty is within 1%.

4. Experimental Results and Discussion

4.1. Effect of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

Guided by the theoretical analysis, we focus on three dimensionless criteria, which are denoted as ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$, $L/D$, and $p_0/p_t$. Specifically, experiments are designed to interrogate how the third dimensionless criterion influences the fast transient venting process of the cavity while the other two criteria are held fixed. The parameters entering the dimensionless criteria are illustrated in Figure 8, and the selected values of the three dimensionless criteria together with their corresponding experimental conditions are summarized in

Table 3. Corresponding values of the dimensionless parameters.

Different $L/D$
$\mathrm{cavity} \mathrm{diameter} L$/mm	80			90				100
$\mathrm{cavity} \mathrm{length} D$/mm	187.5			148.1				120
$L/D$	2.34			1.65				1.2
Different $p_0/p_t$
$\mathrm{initial} \mathrm{pressure} p_0$/kPa	110	130		150		170		190		250
$\mathrm{ambient} \mathrm{pressure} p_t$/kPa	100
$p_0/p_t$	1.1	1.3		1.5		1.7		1.9		2.5
Different ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$
$\mathrm{outlet} \mathrm{diameter} l$/mm	10		20		30		40		50
${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	0.008		0.033		0.074		0.131		0.204

and Table 4. In Table 3, $A$ denotes the cavity outlet area, and $V$ denotes the cavity volume.

Given the limited types and quantities of data available from the experimental measurement points, only qualitative and quantitative assessments of the governing trends can be conducted. To further elucidate the underlying mechanisms, it is necessary to integrate an experimentally validated three-dimensional simulation framework and perform numerical investigations under identical operating conditions for in-depth analysis.

Accordingly, the validated three-dimensional numerical approach reported in Ref. [12] was adopted. Three-dimensional simulation models corresponding to the experiments were established on the basis of the different geometric parameters and initial pressures listed in Table 3 and the simulations were then performed, as shown in Figure 9. All simulations were conducted in ANSYS CFX 2021 with the working fluid treated as an ideal gas. Because the response associated with the fast transient process occurs over an extremely short timescale, wall heat transfer was neglected, and all walls were specified as adiabatic no-slip boundaries. Owing to the small diameter of the interaction interface between the fluid domains, the flow near the cavity port during the simulation resembles a circular jet. According to the study by Kmecova [16], the SST turbulence model provides high accuracy in the simulation of circular jets. Therefore, the SST turbulence model was given priority, and mesh independence and time-step sensitivity analyses were first carried out before the final turbulence model was confirmed. The entire computational domain was discretized using hexahedral meshes. The cavity fluid domain and the atmospheric fluid domain were each treated using the O-Block partitioning technique, enabling the construction of structured hexahedral meshes over curved surfaces. To capture the flow details in critical regions more accurately, local mesh refinement was applied near the walls and near the interface between the two fluid domains. The height of the first boundary layer was set to 0.001 mm, with a normal growth rate of 1.2, and a smooth transition was maintained between refined and unrefined regions. The initial time step was provisionally set to 1 × 10⁻⁵ s, which is consistent with the sampling frequency of the experimental data.

To reproduce the boundary variation observed in the experiments, the displacement of the plug was represented in the three-dimensional model by prescribing the time-dependent position of the plug region. The plug positions at different times were extracted from high-speed camera images, and the corresponding time-varying positional relationship of the plug region was implemented in the three-dimensional model, as shown in Figure 10. After simulation, the average y+ remained below 1, satisfying the requirement of the SST model. Throughout the calculations, convergence was considered to be achieved when the residuals were generally reduced to the order of 1 × 10⁻⁶.

An appropriate mesh resolution was determined through mesh independence verification. Under the condition that y+ satisfied the requirement of the SST turbulence model, the mesh was progressively refined, and simulations were performed using 0.24 million, 0.31 million, 0.42 million, 0.70 million, and 1.27 million cells. Static-pressure monitoring points were arranged in the model according to the pressure measurement locations in the experiments. By comparing the temporal evolution of static pressure at these monitoring points, a suitable mesh resolution was selected. The comparison is presented in Figure 11. The results indicate that when the mesh number increased from 0.31 million to 1.27 million, the maximum deviation in the simulation results was 1.1%, demonstrating that further mesh refinement had only a minor influence on the predicted results. Therefore, 0.31 million cells were selected for the subsequent simulations. The corresponding mesh distribution is also shown in Figure 11.

A time-step independence analysis was then carried out using 0.24 million cells. Simulations were performed with time steps of 1 × 10⁻⁴ s, 5 × 10⁻⁵ s, 2 ×10⁻⁵ s, 1 × 10⁻⁵ s, and 5 × 10⁻⁶ s, respectively. The pressure histories at the same static-pressure monitoring points were again compared, as shown in Figure 12. When the time step decreased from 1 × 10⁻⁴ s to 5 ×10⁻⁶ s, the maximum deviation in the simulation results was 0.7%, indicating that the influence of time-step reduction on the results was limited. Therefore, 1 × 10⁻⁵ s, consistent with the experiments, was selected as the time step for the subsequent study.

Because severe mesh volume variations occur during the displacement of the plug region, other turbulence models were unable to achieve convergence under the same time step and mesh-number conditions during turbulence-model selection. Therefore, the SST model was ultimately adopted for the subsequent study. On the basis of the independence analyses and comparison with the experimental data, the final numerical strategy was established as 0.34 million cells, a time step of 1 × 10⁻⁵ s, and the SST turbulence model, and this strategy was then used for the subsequent numerical investigation.

4.2. Effect of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

To examine the influence of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$, we compare experiments and simulations across multiple operating conditions listed in Table 4, while the other two dimensionless criteria are fixed at $p_0/p_t=1.5$ and $L/D=1.2$. The effects of $p_0/p_t$ and $L/D$ are discussed subsequently. In Table 3, the outlet-orifice length is selected as the minimum value that satisfies experimental safety and assembly requirements, as shown in Figure 13.

Table 4. Test-specimen parameters for investigating the effect of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$.

Parameter	Value
$L/D$	1.2
Outlet–hole length/mm	15
$p_0/p_t$	1.5
Outlet diameter $l$/mm	10	20	30	40	50
${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	0.008	0.033	0.074	0.131	0.204

Table 4. Test-specimen parameters for investigating the effect of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$.

Parameter	Value
$L/D$	1.2
Outlet–hole length/mm	15
$p_0/p_t$	1.5
Outlet diameter $l$/mm	10	20	30	40	50
${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	0.008	0.033	0.074	0.131	0.204

The locations of the pressure measurement points are shown in Figure 13. To facilitate a consistent comparison of the static-pressure response histories under different values of the dimensionless criterion ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$, the static pressure at measurement point $p_i$ is cast into a dimensionless form according to Equation (21), where $p_0$ denotes the initial cavity pressure and $p_t$ denotes the ambient pressure. A direct comparison between the experimental measurements and the three-dimensional simulation results is presented in Figure 14. In this figure, $t_p=0.006 \mathrm{s}$ represents the time required for the plug to complete its prescribed motion.

$$\overline{p_i}={\displaystyle \frac{p_i-p_t}{p_0-p_t}}$$

(21)

Both the experiments and the simulations show that at a fixed value of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=0.008$, the pressure signal $\overline{p_i}$ decreases in an approximately monotonic manner and eventually approaches a steady state. As ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ increases, the pressure drop within the cavity accelerates, and pronounced pressure oscillations emerge. With further increases in ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$, the oscillation amplitude increases while the oscillation period decreases, as quantified in

Table 5. Effect of ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ variation on the oscillatory parameters of test pressure.

Parameter	Value
${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	0.008	0.033	0.074	0.131	0.204
$\mathrm{Minimum} \mathrm{experimental} \mathrm{relative} \mathrm{pressure} {\left(\overline{p_i}\right)}_{\min }$	-	−0.045	−0.055	−0.073	−0.205
Experimental oscillation period/s	-	0.0046	0.0042	0.0038	0.0037
$\mathrm{Minimum} 3\mathrm{D} \mathrm{simulation} \mathrm{relative} \mathrm{pressure} {\left(\overline{p_i}\right)}_{\min }$	-	−0.006	−0.007	−0.012	−0.100
3D simulation oscillation period/s	-	0.0055	0.0040	0.0035	0.0030
$\mathrm{Difference} \mathrm{in} \mathrm{minimum} \mathrm{relative} \mathrm{pressure} \Delta \overline{p_i}$		0.039	0.048	0.061	0.105

.

However, a comparison between the three-dimensional simulations and the experimental results under identical operating conditions shows that the simulated pressure-oscillation amplitudes are consistently smaller than those measured experimentally, and the discrepancy increases with increasing ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$. The variation in $\Delta \overline{p_i}$ with ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ is shown in Figure 15, where $\Delta \overline{p_i}$ exhibits an approximately linear dependence on ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$. This trend indicates that the deviation is likely dominated by a single factor. Under conditions where the influence of plug motion must be considered, the deviation is attributed to the plug motion.

For condition ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=0.204$, a three-dimensional model was selected, and monitoring points were arranged as illustrated to track the axial gas velocity at the cavity outlet and in the vicinity of the plug during the simulation. The corresponding results are presented in Figure 16. The axial velocity at Point 2 follows a trend broadly consistent with that at Point 1, but it exhibits a distinct temporal lag. Specifically, the onset of a pronounced change in axial velocity at Point 2 is delayed by 0.00175 s relative to Point 1. A preliminary interpretation is that after the plug begins to move, the gas near the plug remains initially stagnant. Only after the flow perturbation from the cavity outlet propagates to the region near the plug does the local gas undergo appreciable acceleration. This behavior indicates that in the three-dimensional simulation, representing plug motion solely through wall displacement cannot capture the entrainment imposed on the surrounding gas. In the experiment, by contrast, plug motion induces ambient gas movement, and the ambient flow in the discharge direction further enhances the cavity outflow to a certain extent. Consequently, although the pressure response in the experiment and simulation remains largely consistent in phase, the experimental response exhibits a greater amplitude. Therefore, the three-dimensional simulation results are most appropriately used for qualitative interpretation and as support for mechanistic analysis.

Building on the conclusions of Ref. [12] and the flow-driving mechanism, we analyze how increasing ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ affects the static pressure at the measurement point. When a pressure difference exists between the cavity and the ambient environment, the gas near the outlet accelerates outward under the pressure-gradient driving force. As the cavity pressure approaches the ambient level, the accelerated gas cannot be brought to rest instantaneously; instead, it continues to discharge due to inertia, causing a pressure “overshoot”; i.e., the cavity pressure temporarily drops below the ambient pressure and thereby initiates pressure oscillations. Increasing ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ enlarges the region of gas accelerated during the pressure-driven stage, increases the mass of gas that still carries momentum in the inertia-dominated stage, and thus increases both the inertially driven discharged mass and the oscillation amplitude. Meanwhile, a larger outlet area accelerates the overall flow and shortens the oscillation period.

4.3. Effect of $L/D$

On the basis of this analysis, we select the outlet-area condition ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=0.204$ and investigate the influence of the length-to-diameter ratio $L/D$ on the pressure response. The corresponding geometric parameters are listed in

Table 6. Test-specimen parameters for investigating the effect of $L/D$.

Parameter	Value
Cavity diameter/mm	80	90	100
Cavity length/mm	187.5	148.1	120
$L/D$	2.34	1.65	1.2
Outlet-hole length/mm	15
$p_0/p_t$	1.5
${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	0.204

. The associated experiments are conducted, and the corresponding three-dimensional models are established for simulation. The static-pressure data at the measurement point are processed in dimensionless form following Equation (21).

Figure 17 compares the static-pressure histories at the measurement point obtained from experiments and three-dimensional simulations under condition ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=0.204$. As $L/D$ increases, both the oscillation amplitude and the oscillation period increase. When $L/D$ is increased from 1.2 to 2.34, the minimum dimensionless pressure at the measurement point decreases from −0.205 to −0.264 (a reduction of 28.8%), while the oscillation period increases from 0.0034 s to 0.0039 s (an increase of 41.7%). A preliminary interpretation is as follows: with ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ held constant and inertial effects being relevant, increasing $L/D$ lengthens the axial propagation distance, thereby increasing the travel time of pressure disturbances and enlarging the oscillation period. Consistent with Ref. [12], a larger $L/D$ also intensifies inertial effects within the cavity, increasing the mass of gas discharged under inertia and thus amplifying the pressure oscillations. The three-dimensional simulations are further used to verify these explanations.

Figure 18 compares the evolution of the total amount of gas discharged from the cavity $m_{total}$ under different values of $L/D$. As $L/D$ increases, ${\left(m_{total}\right)}_{\max }$ rises during the venting process: when $L/D$ is increased from 1.2 to 2.34, ${\left(m_{total}\right)}_{\max }$ increases from 4.69 × 10⁻⁴ to 4.82 × 10⁻⁴. The increase in ${\left(m_{total}\right)}_{\max }$ directly lowers the minimum pressure attained within the cavity and amplifies the pressure-oscillation magnitude. In addition, the onset of ${\left(m_{total}\right)}_{\max }$ is delayed as $L/D$ increases.

Figure 19 delineates the venting and refilling stages of the cavity based on the time evolution of the outlet mass flow rate. To compare how the internal flow field develops under different values of $L/D$, several representative instants within the first venting stage are selected, and the corresponding velocity-field distributions inside the cavity are juxtaposed in Figure 20.

According to the analysis presented in Figure 20, during the charge and discharge processes of the cavity, an increase in $L/D$ enlarges the region occupied by flowing gas within the cavity at the corresponding moments of the discharge process. As a result, the influence of inertial forces inside the cavity is strengthened, leading to an increase in the gas mass discharged from the cavity under inertial-force-driven motion during discharge, thereby causing ${\left(m_{total}\right)}_{\max }$ to increase. A comparison of the gas mass discharged from the cavity during the discharge process under different $L/D$ conditions is provided in

Table 7. Total mass of gas discharged from the cavity under different $L/D$ conditions.

Parameter	Value
$L/D$	1.2	1.65	2.34
${\left(m_{total}\right)}_{\max }$	4.69 × 10−4	4.72 × 10−4	4.82 × 10−4
${\left(m_{total}\right)}_{steady}$	4.33 × 10−4
$\Delta m_{total}$	3.6 × 10−5	3.9 × 10−5	4.9 × 10−5

. Here, C denotes the gas mass at the steady state, and $\Delta m_{total}$ represents the difference between ${\left(m_{total}\right)}_{\max }$ and ${\left(m_{total}\right)}_{steady}$—namely, the gas mass discharged from the cavity under inertial-force-driven motion in the absence of a pressure difference. The data in the table show that as $L/D$ increases from 1.2 to 2.34, $\Delta m_{total}$ increases from 3.6 × 10⁻⁵ kg to 4.9 × 10⁻⁵ kg, corresponding to an increase of 36.1%. This analysis demonstrates that an increase in $L/D$ enhances the influence of inertial forces within the cavity, thereby increasing the gas mass discharged from the cavity under inertia-driven motion and ultimately amplifying both the amplitude and period of pressure oscillation, which is in agreement with the preceding analysis.

4.4. Effect of $p_0/p_t$

Building on the trends identified above for the effect of increasing ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ on the fast transient venting response of the cavity, we select—among the existing test geometries—the configuration ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=0.204$ that exhibits the strongest inertial influence within the cavity, and then we investigate how the initial pressure ratio $p_0/p_t$ governs the fast transient response during cavity venting. Because air is used as the working gas in the present experiments, the critical pressure ratio is 1.89, and the tested conditions therefore include supercritical pressure ratios. The experimental matrix is summarized in

Table 8. Test-specimen parameters for investigating the effect of $p_0/p_t$.

Parameter	Value
$L/D$	1.2
Outlet-hole length/mm	15
$p_0/p_t$	1.1	1.3	1.5	1.7	1.9	2.5
${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	0.204

. Corresponding three-dimensional models are also constructed based on the parameters in Table 8 to perform the simulations.

The static pressure at the measurement point is rendered dimensionless using Equation (22), where $p_t$ is taken as the ambient pressure for each individual test.

$$\overline{p_i}={\displaystyle \frac{p_i-p_t}{p_0-p_t}}$$

(22)

Figure 21 compares the evolution of $\overline{p_i}$ at the pressure-measurement location between the experiments and the simulations under different values of $p_0/p_t$. As $p_0/p_t$ increases, both datasets exhibit broadly consistent, yet distinctly nonlinear, variations in the pressure-oscillation amplitude. Within regime $p_0/p_t<1.5$, the oscillation amplitude increases with $p_0/p_t$; within regime $1.5\le p_0/p_t<1.9$, it instead decreases as $p_0/p_t$ increases; and in regime $1.9\le p_0/p_t$, a modest increasing trend re-emerges with further increases in $p_0/p_t$. Overall, the influence of $p_0/p_t$ on the oscillation amplitude and period is not monotonic, suggesting a coupled, multi-factor interplay involving $p_0/p_t$ and the plug-motion history. We therefore leverage the three-dimensional simulations for further mechanistic interrogation.

The temporal variation in the cavity outlet mass flow rate is used to distinguish between the venting and refilling stages, as illustrated in Figure 22. Because our focus is the oscillation amplitude during the first pressure-drop event, we define the duration of the first venting stage as $\Delta t_{discharge}$. Representative instants within this venting stage are then selected to compare the plug position and the corresponding evolution of the flow field, as depicted in Figure 23.

To interpret the nonlinear dependence of the pressure-oscillation amplitude and period on $p_0/p_t$, we account explicitly for the plug-motion history. In general, increasing $p_0/p_t$ simultaneously raises the peak discharge velocity and prolongs the pressure-drop process. In stage $1.1\le p_0/p_t<1.5$, the pressure drop is short; gas acceleration within the orifice and the discharged mass remain limited, and a sufficiently strong localized high-pressure region does not develop near the cavity inlet and outlet to suppress outflow. In this regime, the dominant control on discharge is the distance between the plug and the cavity inlet and outlet. Accordingly, as $p_0/p_t$ increases, the pressure-drop duration increases and the plug moves farther from the cavity, weakening the suppression of outflow; the oscillation amplitude increases, whereas the period decreases. In stage $1.5\le p_0/p_t<1.9$, increasing $p_0/p_t$ further extends the pressure-drop duration, and the high-velocity discharge together with the external jet establishes a localized high-pressure region between the cavity inlet and outlet and the plug. Because the plug is already relatively distant from the cavity inlet and outlet, this localized high-pressure region becomes the primary factor governing the discharge. As $p_0/p_t$ increases, the localized high-pressure region intensifies, leading to a reduced oscillation amplitude and an increased period. When $p_0/p_t$ reaches stage $1.9\le p_0/p_t$, the localized high-pressure region diminishes with increasing $p_0/p_t$, lowering its ability to suppress discharge; consequently, the oscillation amplitude increases again and the period decreases.

Further analysis was conducted using the total outlet mass flow rate under different $p_0/p_t$ conditions. Specifically, the steady total outlet mass flow rate ${\left(m_{total}\right)}_{steady}$ and the maximum total outlet mass flow rate ${\left(m_{total}\right)}_{\max }$ were compared, and their difference was defined as $\Delta m_{total}$, which represents the gas mass discharged from the cavity under inertial-force-driven motion in the absence of a pressure difference. The comparison is summarized in

Table 9. Total mass of gas discharged from the cavity under different $p_0/p_t$ conditions.

Parameter	Value
$p_0/p_t$	1.1	1.3	1.5	1.7	1.9	2.5
${\left(m_{total}\right)}_{\max }$	1.14 × 10−4	2.63 × 10−4	4.69 × 10−4	6.29 × 10−4	8.03 × 10−4	1.37 × 10−4
${\left(m_{total}\right)}_{steady}$	8.29 × 10−5	2.25 × 10−4	4.33 × 10−4	6.03 × 10−4	7.87 × 10−4	1.35 × 10−3
$\Delta m_{total}$	3.13 × 10−5	3.84 × 10−5	3.66 × 10−5	2.59 × 10−5	1.57 × 10−5	1.60 × 10−5

. The data indicate that as $p_0/p_t$ increases from 1.3 to 1.9, $\Delta m_{total}$ decreases from 3.84 × 10⁻⁵ kg to 1.57 × 10⁻⁵ kg, corresponding to a reduction of 59.11%. With increasing $p_0/p_t$, the gas mass discharged from the cavity under inertial-force-driven motion decreases. This finding confirms that a suppressive effect on the outflow exists in this stage, consistent with the preceding analysis, and further verifies the presence of a local high-pressure region that inhibits the outflow.

5. Conclusions

(1)

To investigate the fast transient response of air-system components induced by sudden structural failures in aero-engine air systems, we designed and commissioned a dedicated fast transient air-system test facility, providing an experimental basis for mechanistic studies and model validation. A mechanical stored-energy device was further proposed and implemented to generate a step boundary. High-speed imaging indicates that with an initial spring force of 6 kN, the plug completes an effective separation of 75 mm in <10 ms; the upper-limit capability of the imposed boundary-change timescale is 6 ms. This performance meets the requirement for millisecond-level step boundary emulation associated with abrupt structural events while maintaining good repeatability.

(2)

Increasing ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ markedly strengthens inertial effects during venting. As ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$ increases from 0.008 to 0.204, the pressure oscillations evolve from weak to pronounced and progressively intensify; the minimum dimensionless pressure reaches approximately −0.205. Mechanistically, a larger outlet enhances the venting mass flow rate and expands the volume of gas being accelerated, thereby increasing the inertia-driven discharged mass and leading to more prominent pressure overshoot and oscillations.

(3)

Increasing $L/D$ provides a modest enhancement of inertial effects within the cavity. Under condition ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=0.204$, as $L/D$ increases, a larger fraction of the gas inside the cavity becomes mobile; the inertia-driven discharged mass increases accordingly, resulting in larger oscillation amplitude and a longer period. The increase in period is primarily attributed to the longer axial propagation distance, which extends the disturbance travel time.

(4)

The isolated effect of increasing $p_0/p_t$ on inertial behavior is limited. Under condition ${A/V}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}=0.204$, variations in $p_0/p_t$ are coupled with the plug-motion history: the plug-to-cavity-outlet distance and the localized high-pressure region near the outlet alternately dominate the discharge in different stages, yielding a non-monotonic dependence of the oscillation amplitude on $p_0/p_t$.

(5)

This paper integrates experiments with three-dimensional simulations to elucidate the dominant factors governing the fast transient response of a cavity while explicitly accounting for fluid inertial forces within the cavity. The results establish a reliable experimental validation approach and provide foundational datasets for investigating cavity fast transient dynamics. In addition, the findings offer a quantitative basis for improving existing low-dimensional cavity models by incorporating the effects of fluid inertia, thereby enabling more accurate predictions of load evolution during fast transient responses triggered by abrupt structural failures in air systems.